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1
CHAPTER 3
MEASUREMENT SYSTEMS
APPLICATION
Content
bull Position and displacement measurement
bull Acceleration measurement
bull Velocity measurement
bull Force measurement
2
Position and displacement
bull Sensing methods
bull Potentiometers
bull Linear Variable Differential Transformer
(LVDT)
bull Synchro systems
bull Resolvers
bull Optical encoder
bull Proximity sensor
bull Photoelectric sensors
bull Additional Accelerometer and Gyroscope
3
Position and displacement
Linear Rotary
Potentiometer Potentiometer
Capacitive Capacitive
Inductive Inductive
Linear Variable-Differential
Transformer (LVDT)
Rotary Variable-Differential
Transformer (RVDT)
Synchro systems
Resolvers
Optical encoder
Photoelectric sensors
Proximity sensor
Accelerometers Gyroscope
4
Already covered in
previous slides
Add in
Position and displacement
Synchro and Resolver
5
Position and displacement
Synchro
6
bull Synchro act as a ldquotransmitterrdquo and ldquoreceiverrdquo
bull ldquotransmitterrdquo to control the rotary position of ldquoreceiver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Synchro
7
bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not
rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo
rotor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Content
bull Position and displacement measurement
bull Acceleration measurement
bull Velocity measurement
bull Force measurement
2
Position and displacement
bull Sensing methods
bull Potentiometers
bull Linear Variable Differential Transformer
(LVDT)
bull Synchro systems
bull Resolvers
bull Optical encoder
bull Proximity sensor
bull Photoelectric sensors
bull Additional Accelerometer and Gyroscope
3
Position and displacement
Linear Rotary
Potentiometer Potentiometer
Capacitive Capacitive
Inductive Inductive
Linear Variable-Differential
Transformer (LVDT)
Rotary Variable-Differential
Transformer (RVDT)
Synchro systems
Resolvers
Optical encoder
Photoelectric sensors
Proximity sensor
Accelerometers Gyroscope
4
Already covered in
previous slides
Add in
Position and displacement
Synchro and Resolver
5
Position and displacement
Synchro
6
bull Synchro act as a ldquotransmitterrdquo and ldquoreceiverrdquo
bull ldquotransmitterrdquo to control the rotary position of ldquoreceiver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Synchro
7
bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not
rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo
rotor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
bull Sensing methods
bull Potentiometers
bull Linear Variable Differential Transformer
(LVDT)
bull Synchro systems
bull Resolvers
bull Optical encoder
bull Proximity sensor
bull Photoelectric sensors
bull Additional Accelerometer and Gyroscope
3
Position and displacement
Linear Rotary
Potentiometer Potentiometer
Capacitive Capacitive
Inductive Inductive
Linear Variable-Differential
Transformer (LVDT)
Rotary Variable-Differential
Transformer (RVDT)
Synchro systems
Resolvers
Optical encoder
Photoelectric sensors
Proximity sensor
Accelerometers Gyroscope
4
Already covered in
previous slides
Add in
Position and displacement
Synchro and Resolver
5
Position and displacement
Synchro
6
bull Synchro act as a ldquotransmitterrdquo and ldquoreceiverrdquo
bull ldquotransmitterrdquo to control the rotary position of ldquoreceiver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Synchro
7
bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not
rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo
rotor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
Linear Rotary
Potentiometer Potentiometer
Capacitive Capacitive
Inductive Inductive
Linear Variable-Differential
Transformer (LVDT)
Rotary Variable-Differential
Transformer (RVDT)
Synchro systems
Resolvers
Optical encoder
Photoelectric sensors
Proximity sensor
Accelerometers Gyroscope
4
Already covered in
previous slides
Add in
Position and displacement
Synchro and Resolver
5
Position and displacement
Synchro
6
bull Synchro act as a ldquotransmitterrdquo and ldquoreceiverrdquo
bull ldquotransmitterrdquo to control the rotary position of ldquoreceiver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Synchro
7
bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not
rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo
rotor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
Synchro and Resolver
5
Position and displacement
Synchro
6
bull Synchro act as a ldquotransmitterrdquo and ldquoreceiverrdquo
bull ldquotransmitterrdquo to control the rotary position of ldquoreceiver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Synchro
7
bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not
rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo
rotor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
Synchro
6
bull Synchro act as a ldquotransmitterrdquo and ldquoreceiverrdquo
bull ldquotransmitterrdquo to control the rotary position of ldquoreceiver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Synchro
7
bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not
rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo
rotor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
Synchro
7
bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not
rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo
rotor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
8
Position and displacement
Resolver
bull two stator winding placed at 90deg to each other and a
single rotor winding driven by alternating current
bull polar to rectangular conversion
bull angle (rotor) co-ordinates sin and cosine (stator)
bull proportional voltages on the stator windings
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
9
Position and displacement
Resolver
bull The coordinates (X Y) are available on the resolver stator
coils
bull 119883 = 119881 cos ang119887119890119886119903119894119899119892
bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
10
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
11
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A TDX torque differential transmitter sums an electrical
angle input with a shaft angle
bull input producing an electrical angle output
bull A TDR torque differential receiver sums two electrical
angle inputs producing a shaft
bull angle output
bull A CT control transformer detects a null when the rotor
is positioned at a right angle to the stator angle input A
CT is typically a component of a servondash feedback
system
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
12
Position and displacement
Applying Synhros as Resolver
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
bull A Resolver outputs a quadrature sin and cosine(theta)
representation of the shaft angle
bull input instead of a three-phase output
bull The three-phase output of a TX is converted to a
resolver style output by a Scott-T transformer
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
Synchro and Resolver
13
Both act as rotary position sensor
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Stator winding fixed
at 120deg to each
other
Stator winding fixed
at 90deg to each
other
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
Synchro in linear displacement
14
bull Modify synchro to resolver to measure linear
displacement
bull Inductsyn product brand Also known as linear encoder
Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in
openbookprojectnetelectricCircuits
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
Optical encoder
15
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
16
Concepts related to encoders
bull What is an encoder
A rotary encoder is a sensor for
converting rotary motion or position to
a series of electronic pulses
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
17
Basic architectures of
encoders
bull Linear architecture
Linear encoders which consist of a long linear read
track (analogous to the code disk of a rotary
encoder) together with a compact read head
address these concerns We offer three grades of
linear encoders to suit a variety of application
requirements
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Introduction
bull Encoders and sensors allow control and feedback loops to be established
bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control
bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Encoders - Introduction
bull Incremental encoders emit pulses which
determine how far the device has rotated (if a
rotary encoder) or moved (if a linear encoder)
bull Incremental encoders may be rotary or linear
The first key specification is the number of
pulses per revolution (PPR) or pulses per inch
(or centimeter) PPR of 250 512 1000 1024 or
even up to 100000 pulses per revolution are
available
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Encoders - Introduction
bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine
bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12
bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions
bull Some linear encoders can measure movements as small as 10microm to 10nm
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
21
bull rotary motion
bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals
bull ef fec t ive and low cost feedback dev ices
bull In high-accuracy applications
bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)
Incremental Rotary Encoders
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
22
Absolute Rotary Encoders
bull Absolute encoders have a unique code that can be detected for each angular position
bull Absolute encoders are much more complex and
expensive than incremental encoders
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
23
Incremental encoders bull Pulses from LEDS are counted to provide rotary position
bull Two detectors are used to determine direction
(quadrature)
bull Index pulse used to denote start point
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
24
The applications
bull Positioning
bull a lead screw or rack-and-pinion converts rotary motion to linear
motion
bull an encoder converts the same motion into electronic pulses
The pulses typically are used as input signals for counters
PLCs or numerical-control equipment
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
25
The applications
bull Length measurement
bull Roll or sheet materials
bull cut-to-length machinery
bull An encoder + a measuring wheel or coupled to a roller
bull electronic pulses == units of length
bull very precise operation is possible
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
26
Encoders are wildly used in industry
bull machine tools
bull textile machinery
bull printing presses
bull wood working machines
bull handling technology
bull conveying and storage technology
bull robotics
The applications
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
27
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Anatomy of Rotary Optical
Absolute Encoder
trelectroniccom
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Encoders ndash Types (Rotary)
bull Absolute optical
ndash robots
bull Incremental Hollow shaft
bull Modular
bull Panel mount optical
ndash medical devices audio equipment
bull Magnetoresistive
ndash cranes dirty environments
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Application of Rotary
Encoders
bull Painting Robots (automotive)
bull CAT Scan machines
bull Precision machining equipment
bull Microscopes
bull Aerospace
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Applications Continued
Vtech
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Vendors
bull Omega
bull Renishaw
bull TRElectronic
bull RENCO
bull ServoTek
bull AMCI
bull DuraCoder
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
33
Vendors
bull Heidenhain
bull Renco
bull Renishaw
bull autonics
bull Stegmann
bull Pepperl+Fuchs
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Key Encoder Specs You must know the following information to specify an
encoder
bull Absolute or Incremental Encoder
bull Rotary or Linear Encoder
bull Resolution required
bull Uni-directional or Bi-directional motion
bull Operating voltage very commonly 5 volts also 12 and 24 volts available
bull Mechanical requirements ndash Shaft diameter and length
ndash Mounting holes and spacing
ndash Overall length and diameter
bull Environmental considerations ndash Dust moisture etc
ndash Shock Vibration etc
ndash Operating temperature
ndash RPM duty cycle
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
35
How to integrate
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
36
Application examples
Model 716 (Cube Encoder) made by ECP were
equipped on the lumber devices to produce up to
15 more lumber from each log
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
37
Application examples
The Company of Ground Force mounts EPC
encoder on the trucks used at mining operations to
measure the rotation of pump shafts and of augers
The pumps deliver wet ingredients while the
augers deliver the dry ingredients
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
38
Example
Given an incremental encoder of 50 pulsesrev
determine
a) The resolution
b) What is the rotational angle if 15 pulses are
recorded
c) 500 pulses are recorded in 4 seconds What is the
rotational speed (rpm)
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Example
An automatic cutting machine is designed to cut a
continuous plastic strip into blocks of specific length It is
fed continuously to a cutter via a pair of feeder discs whose
diameter is 200mm An incremental encoder of 100
pulsesrev is coupled to the disc Determine the number of
encoder output pulses if the block length is
(a) 30mm
(b) 1000mm 39
Feeder disc
Cut blocks
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
40
Example An numerical control (NC) worktable operates by
closed-loop positioning The system is shown below
The lead screw has a pitch of 6mm and is coupled to
the motor shaft with a gear ratio of 51 (five turns of
drive motor for each turn of the screw) The optical
encoder generates 48 pulsesrev of its output shaft
The table is programmed to move a distance of
250mm at a feed speed rate = 500mmmin
Determine
Continued next page
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
41
Example continued a) How many pulses should be received by the
control system to verify that the table has moved
exactly 250mm (Ans 2000 pulses)
b) The pulse rate of the encoder (Ans 66667Hz)
c) The drive motor speed that correspond to the
specified feed rate (Ans 416667 revmin)
MP Groove (2008) Automation Production Systems and
Computer-Integrated Manufacturing Ed 3 pg184
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Rotary Encoder Online ref
bull httpwwwomron-
apcommyapplication_solutionsmainasp
bull httpwwwiaomroncomproductscategorysensorsrota
ry-encodersincrementalindexhtml
bull httpabrockwellautomationcomMotion-Control
bull httpwwwfestocomcmsnl-be_be9733htm
bull Morehellip
42
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Mechatronics - Foundations and Applications
Position Measurement in Inertial Systems
Adopted from
Title Lecture Position Measurement in Inertial Systems
DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on
launch platform (complementary error characteristics) ndash PowerPoint PPT presentation
httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation
Accelerometer
Gyroscope
Position and displacement
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Position and displacement
1 Motivation applications
2 Basic principles of position measurement
3 Sensor technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Motivation
Johnnie A biped walking machine
Orientation
Stabilization
Navigation
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Motivation
Automotive Applications
Drive dynamics Analysis
Analysis of test route topology
Driver assistance systems
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Motivation
Aeronautics and Space Industry
Autopilot systems
Helicopters
Airplane
Space Shuttle
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Motivation
Military Applications
ICBM CM
Drones (UAV)
Torpedoes
Jets
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Motivation
Maritime Systems
Helicopter Platforms
Naval Navigation
Submarines
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Motivation
Industrial robotic Systems
Maintenance
Production
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Measurement by inertia and integration
Acceleration
Velocity
Position
Newtonlsquos 2 Axiom
F = m x a
BASIC PRINCIPLE OF DYNAMICS
Measurement system
with 3 sensitive axes
3 Accelerometers
3 Gyroscope
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles Gimballed Platform Technology
3 accelerometers
3 gyroscopes
cardanic Platform
ISOLATED FROM ROTATIONAL MOTION
TORQUE MOTORS TO MAINTAINE DIRECTION
ROLL PITCH AND YAW DEDUCED FROM
RELATIVE GIMBAL POSITION
GEOMETRIC SYSTEM
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Strapdown Technology
Body fixed
3 Accelerometers
3 Gyroscopes
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Strapdown Technology
The measurement principle
SENSORS FASTENED DIRECTLY ON THE VEHICLE
BODY FIXED COORDINATE SYSTEM
ANALYTIC SYSTEM
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Reference Frames
i-frame
e-frame
n-frame
b-frame
Also normed WGS 84
15041 e
ie h
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Vehiclelsquos acceleration in inertial axes (1Newton)
Problem All quantities are obtained in vehiclersquos frame (local)
Euler Derivatives
Basic Principles
2
2( )i p i OP i i ie e e
d dv r f g A f g
dt dt
Interlude relative kinematics
Differentiation
2 2
2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe
d d d dv r A r r r r
dt dt dt dt
trans cor rot cent
Inertial system i
Moving system e
P = CoM
O
P
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Frame Mechanisation I i-Frame
Vehiclelsquos velocity (ground speed) and Coriolis Equation
abbreviated
Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
( ) ( )
ie
i e
d dr r r
dt dt
( )
e
e
dr v
dt
2
2
( ) ( )( )
e ie
i ii
d d dr v r
dt dt dt
2
2
( )( )
e ie e ie ie
ii
d dr v v r
dt dt
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Frame Mechanisation II i-Frame
Newtonrsquos 2nd axiom
abbreviated
Recombination i-frame axes Substitution
subscipt with respect to superscript denotes the axis set slash resolved in axis set
Basic Principles
2
2
( )
e ie e ie ie
i
dv f v r g
dt l ie ieg g r
2
2
( )
e ie e l
i
dv f v g
dt
i i i i i
e ie e lv f v g i b i i i
e ib ie e lv A f v g
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Strapdown Attitude Representation
Direction cosine matrix
Quaternions
Euler angles
No singularities perfect for internal
computations
singularities good physical appreciation
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Strapdown Attitude Representation Direction Cosine Matrix
11 12 13
21 22 23
31 32 33
nb
c c c
A c c c
c c c
1 313 cos n b
c n n
For Instance
Simple Derivative Axis projection
b
nb nb nbA A
0
0
0
z y
b
nb z x
y x
With skew symmetric matrix
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Strapdown Attitude Representation Quaternions
Idea Transformation is single rotation about one axis
cos 2
( )sin 2
( )sin 2
( )sin 2
x
y
z
a
bp
c
d
x y z
Components of angle Vector
defined with respect to reference frame
Magnitude of rotation
Operations analogous to 2 Parameter Complex number
p a ib jc kd
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Basic Principles
Strapdown Attitude Representation Euler Angles
Rotation about reference z axis through angle
Rotation about new y axis through angle
Rotation about new z axis through angle
cos cos cos sin sin sin cos sin sin cos sin cos
cos sin cos sin sin sin sin sin cos cos sin sin
sin sin cos cos cos
nbA
1 T
nb bn bnA A A 90 Singularity
Gimbal angle pick-off
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Accelerometers
Physical principles
Potentiometric
LVDT (linear voltage differential transformer)
Piezoelectric
F ma mg Newtonrsquos 2nd axiom
gravitational part Compensation
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Accelerometers
Potentiometric
+
-
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Accelerometers
LVDT (linear voltage differential transformer)
Uses Induction
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Accelerometers
Piezoelectric
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Accelerometers
Servo principle (Force Feedback)
Intern closed loop feedback
Better linearity
Null seeking instead of displacement measurement
1 - seismic mass
2 - position sensing device
3 - servo mechanism
4 - damper
5 - case
Many more different construction of a accelerometer For more detail refer to D H
Titterton J L Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes
Vibratory Gyroscopes
Optical Gyroscopes
Historical definition
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)
2 axis rotation
3 axis acceleration measurement
Problems High noise
Temperature drifts
Translational acceleration
vibration
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology
Sensor Technology
Gyroscopes Vibratory Gyroscopes
Many more different construction of a gyroscope For more detail refer to D H Titterton J L
Weston Strapdown Inertial Navigation Technology