Aerospace applications of PKM

Prof. Rosario Sinatra

Dipartimento di Ingegneria Industriale e MeccanicaUniversità degli Studi di Catania

March 30, 2007

EURON07 WINTER SCHOOL PARALLEL ROBOTS: Theory and Applications 2nd International UMH Robotics Winter School Flamingo Oasis Hotel, Benidorm, SpainMarch 26 - 30, 2007

AEROSPACE MECHANISMSPOINTING SYSTEMS FOR SATELLITE ANTENNAS

CONTROL SYSTEM SCHEME FOR POINTING ERROR COMPENSATION

RESEARCH PROJECTS IN WITH PARTNERSHIP WITH

THE SATELLITE COMMUNICATIONS REQUIRES A VERY

ACCURATE POINTING SYSTEM, COMPOSED BY

DIFFERENT ELECTRO-MECHANICAL DEVICES

Sinatra Rosario

Pirrotta Simone

ANTENNA MECHANICAL and MECHANISM DESIGN SECTION, ING. ABERTO MESCHINI

AEROSPACE MECHANISMSPOINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA

PARABOLIC REFLECTOR

SUBREFLECTOR

FEED

OLD PONTING CONCEPT NEW PONTING CONCEPT

W24

AEROSPACE MECHANISMS

RADIATION DIAGRAM

ORBITAL RE-POINTING

RE-POINTING BY SUBREFLECTOR DYNAMIC POSITIONING

POINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA

AEROSPACE MECHANISMS

FIXED PLATFORM

MOBILE PLATFORM

LEGS

)(11 SiiiiPSP

OCQCOOOOOp KINEMATIC EQUATION

SPHERICAL JOINT

PRISMATIC JOINT

UNIVERSAL JOINT

POINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA

tJtJq

tJq

uQrpuQrp

][][q i

Tiii i

''

AEROSPACE MECHANISMS

0 500 1000 1500 2000 2500 3000 3500 4000-1

0

1

L1

Elongazioni dei giunti attuati

0 500 1000 1500 2000 2500 3000 3500 4000-5

0

5

L2

0 500 1000 1500 2000 2500 3000 3500 4000-1

0

1

L3

0 500 1000 1500 2000 2500 3000 3500 4000-2

0

2

L4

0 500 1000 1500 2000 2500 3000 3500 4000-1

0

1

L5

0 500 1000 1500 2000 2500 3000 3500 4000-0.5

0

0.5

L6

t (secondi)

0 500 1000 1500 2000 2500 3000 3500 4000-5

0

5x 10

-3

L1

Velocità dei giunti attuati

0 500 1000 1500 2000 2500 3000 3500 4000-0.02

0

0.02

L2

0 500 1000 1500 2000 2500 3000 3500 4000-0.01

0

0.01

L3

0 500 1000 1500 2000 2500 3000 3500 4000-0.01

0

0.01

L4

0 500 1000 1500 2000 2500 3000 3500 4000-5

0

5x 10

-3

L5

0 500 1000 1500 2000 2500 3000 3500 4000-2

0

2x 10

-3

L6

t (secondi)

0 500 1000 1500 2000 2500 3000 3500 4000-8

0

8x 10

-5

L1

Accelerazioni dei giunti attuati

0 500 1000 1500 2000 2500 3000 3500 4000-2

0

2x 10

-4

L2

0 500 1000 1500 2000 2500 3000 3500 4000-1

0

1x 10

-4

L3

0 500 1000 1500 2000 2500 3000 3500 4000-1

0

1x 10

-4

L4

0 500 1000 1500 2000 2500 3000 3500 4000-8

0

8x 10

-5

L5

0 500 1000 1500 2000 2500 3000 3500 4000-3

0

3x 10

-5

L6

t (secondi)

DISPLACEMENT VELOCITY ACCELERATION

0 500 1000 1500 2000 2500 3000 3500 4000-0.02

0

0.02

0.04

0.06

0.08

0.1

gra

di

t (secondi)

Disturbo totale in normal mode

-0.4

-0.3

-0.2

-0.1

0

0.1

-80.7-80.6

-80.5-80.4

-80.3-80.2

476.2

476.3

476.4

476.5

476.6

476.7

asse X (mm)

Traiettoria del centro del subriflettore

asse Y (mm)

asse

Z

(m

m)

ORBITAL DISTURBANCE

SIGNAL (STATION KEEPING)

SUBREFLECTOR’S CENTRE 3D-PATH

KINEMATICS VARIABLES OF

THE ACTUATED PRISMATIC

JOINTS

POINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA

AEROSPACE MECHANISMS2 DOF POINTING SYSTEM

FIXED PLATFORM

MOBILE PLATFORM

LINEAR ACTUATOR

0

coscos2

sincossin

cossinsin2sinsincoscos2

sincossin2coscos22

0

coscos2

sincossin

cossinsin2sinsincoscos2

sincossin2coscos22

20

20

22100

10120

210202121

2

1122100222

20

20

22100

10120

210202121

2

1122100121

ABBA

AA

BB

BA

ABBA

AA

BB

BA

zzlzz

zz

zzbb

bzzss

zzlzz

zz

zzbb

bzzss

POINTING CONTROL RELATIONS

AEROSPACE MECHANISMS

MATLAB GUI FOR DIRECT AND INVERSE KINEMATICS

z = -1.6529E -5+ 0.135*x -0.135*y -3.8847E -6*x *x + 8.9256E -8*x *y + 4.0004E -6*y *y

MATLAB GRAPHICS OUTPUT

[deg]

3213.6101986.1

6367.2101091.8

103511.1

42

41

91

322

31

8

12

222

173

23

18

211

1

ssssss

ssssss

ss

[deg]

0384.1

8832.1102428.1

100636.1103511.1

42

41

8

12

222

173

23

17

22

21

521

1

2

ss

ssssss

ssss

POINTING SURFACE

1 = f(s1, s2)

2 DOF POINTING SYSTEM

AEROSPACE MECHANISMS

RESIDUALS MAP AND

DISTRIBUTION WITH RESPETC TO ANALYTIC

POINTING RELATIONS

2 DOF POINTING SYSTEM

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

-30 -20 -10 0 10 20 30

Elongazione s1 [mm]

( 1

s- 1

CA

D)

[deg

]s2=-25 [mm] s2=-20[mm] s2=-15 [mm]

s2=-10[mm] s2=-5 [mm] s2=0 [mm]

s2=5 [mm] s2=10[mm] s2=15 [mm]

s2=20[mm] s2=25 [mm]

COMPARISON WITH CAD “EUCLID”

KINEMATIC RESULTS

0

5

10

15

20

25

30

35

40

45

-0.000179 -0.000124 -0.000068 -0.000012 0.000044 0.000100Residuo su 1 [deg]

Fre

que

nza

perc

entu

ale

[%] Media Dev. st.

-4.3360E-06 8.9632E-05[deg] [deg]

AEROSPACE MECHANISMSULTRASONIC MOTOR

2 Supply Channels

ELECTRICAL

Equal amplitude VmaxA=VmaxB

Opposite phase (90°)

Flexural vibration

2 waves with time phase

of 90°

Rotational motion around

vertical axes

ROTORS

STATOR

Travelling wave

PIEZOELECTRICS

ROTORS

STATOR

AEROSPACE MECHANISMSULTRASONIC MOTOR

NORMAL AND TANGENTIAL FORCES

FROM ROTOR TO STATOR

PRELOAD FORCE

EXTERNAL TORQUE

NORMAL AND TANGENTIAL FORCES

FROM STATOR TO ROTOR

MULTIBODY SYSTEM

AEROSPACE MECHANISMSULTRASONIC MOTOR

EQUATIONS OF MOTION

),,,(),( ppFpFvΘpKpCpM fTfNstatstatstat ww

appffzfr FwFwCwM ),(int p

appfr wCI ),,,(int pp

appint

appint

TN

r

rn,4

n,n21n,n

f

f

r

z

rn2,4

4,n211n,nn,n

f

f

FF

FFv

M

10

00

0I

100

0

0M

0

w

w

p

p

I

C000

1000

00I

C0

0010

0

0CMKM

I0

w

w

p

p

Piezo elements' thickness - tp Stator thickness - ts

Inte

rfac

e th

ickn

ess

- ti

Too

th h

eigh

t - h

t

Piezo elements' inner radius - rpi

Piezo elements' outer radius - rpe

Stator's inner radius - rsi

Teeth inner radius - rti

Teeth outer radius - rte

Stator's outer radius - rse

AEROSPACE MECHANISMSULTRASONIC MOTOR

a)

b)

Dv>0

V rot

V stat

x l-x l x r-x r x

z T res

T m ot +

T m ot + T m ot -

T res

V rot

V stat

Dv = 0Dv>0

Dv<0

x lx r-x l -x r x

z

)22(2

)(2)(220

motmott

ttmdrtapp

TTNr

drpdrphtNrl

r

r

)2(2)(220

motttmdrtapp TNrdrphtNr

l

)2(2)(220

mottw

mdrT NdrphtNl

TΦ

F

drptN twrN

l

0)(22 ΦF

)22(2

)(2

)(22

0

motmot

tw

tw

mdrT

N

drp

drphtN

l

r

r

TT

Φ

Φ

F

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25-0.5

0

0.5

1

1.5

2

2.5

3x 10

5

Pressure [N/m2]

Contact angle l [rad]

Hertz

Linear stiffness

Visco-elastic contact

Hertz second formulation

r

Eapp

r

tEapp

tt

ll

AtN

CF

AtN

rCF

rr

x33

2 28,0

2

2

6,1

TORQUE CALCULATION

AREA-FORCE RELATIONSHIP

AEROSPACE MECHANISMSULTRASONIC MOTOR

LOAD PULLEY

ULTRASONIC MOTOR

TACHOMETER

WEIGHT

Torque-speed curve (F app =39.8N, V max =300V, N =7, d =0.23, h =0.08)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Angular speed [rad/s]

Tor

que

[Nm

]

Experimental

Symulated

Torque-speed curves (Vmax =300 V, d =0.07, h =0.05)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Speed [rad/s]

To

rqu

e

[Nm

]

Prec=1 NPrec=5 NPrec=10 NPrec=15 NPrec=20 NPrec=25 NPrec=30 NPrec=38 NPrec=45 NPrec=60 NPrec=80 NPrec=100 NPrec=130 N

AEROSPACE MECHANISMSULTRASONIC MOTOR

Torque-speed curves (Prec =10 N, d =0.07, h =0.05)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Speed [rad/s]

To

rqu

e [

Nm

]

Vmax=100 V

Vmax=150 V

Vmax=200 V

Vmax=250 V

Vmax=300 V

Vmax=350V

Torque-speed curves (Prec =40 N, d =0.07, h =0.05)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5

Speed [rad/s]

To

rqu

e [

Nm

]

Vmax=100 V

Vmax=150 V

Vmax=200 V

Vmax=250 V

Vmax=300 V

Vmax=350V

Torque-speed curves (Prec =15 N, Vmax =300 V, h =0.05)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Speed [rad/s]

To

rqu

e [

Nm

]

11111

TORQUE-SPEED CURVES PARAMETRIZED WITH RESPECT TO:

1-MAXIMUM VOLTAGE AMPLITUDE (CASE a and b)

2-FRICTION COEFFICIENT

A. Meschini, R. Sinatra and S. Pirrotta, 2002. A Parallel Mechanism for a Gregorian offset Satellitare Antenna with double reflector, Proceedings of the WORKSHOP on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, October 3–4, Quebec City, Quebec.

A. Cammarata and R. Sinatra, 2005, Dynamics of a two-dof parallel pointing mechanism, Fifth ASME International Conference on Multibody Systems, Nonlinear Dynamics and Control , Sept. 24-28, 2005, Long Beach, California, USA. R. Di Gregorio, A. Cammarata and R. Sinatra, 2005, On The Dynamic Isotropy Of 2-Dof Mechanisms, Fifth ASME International Conference on Multibody Systems, Nonlinear Dynamics and Control , Sept. 24-28, 2005, Long Beach, California, USA.

R. Sinatra, D. Scalora and A. Meschini, 2004, Direct Kinematics of a Parallel Pointing Mechanism Configuration, Proceedings of the WSEAS Conferences, August 17-19, 2004, Corfu, Greece.

S. Pirrotta, R. Sinatra, A. Meschini, 2006. Evaluation of the Effect of Preaload Force on Resonance Frequencies for a Traveling Wave Ultrasonic Motor, IEEE Transactions on ultrasonics, ferroelectrics, and frequency control, Vol. 53, n.4, pp. 746-753.

S. Pirrotta, R. Sinatra and A. Meschini, 2007. A novel simulation model for ring type ultrasonic motor, Meccanica International Journal, Vol. 42, n.2, pp. 127-139.

References