KINEMATICS OF MECHANISMS
• Dynamics: Kinematics & Kinetics
– Kinematics: Study of motion without regard to forces, gravity of motion.
– Kinetics: Study of forces on systems in motion
KINEMATICS OF MECHANISMS
MECHANISM
Mechanism – Part of a machine, which transmit motion and power from input point to output point
Example for Mechanism
KINEMATICS
RELEVANCE OF KINEMATIC STUDY
• Motion requirements
• Design requirements
MOTION STUDY
Study of position, displacement, velocity and acceleration of different elements of mechanism
Given input Desired output
Motion requirement
DESIGN REQUIREMENTS
Design: determination of shape and size
1. Requires knowledge of material
2. Requires knowledge of stress
3. Requires knowledge of load acting
(i) static load
(ii) dynamic/inertia load
DYNAMIC/INERTIA LOAD
Inertia load require acceleration
Examples of rigid links
PAIRING ELEMENTS
Pairing elements: the geometrical forms by which two members of a mechanism are joined together, so that the relative motion between these two is consistent. Such a pair of links is called Kinematic Pair.
PAIRING ELEMENTS
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PAIRING ELEMENTS
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DEGREES OF FREEDOM (DOF):
It is the number of independent coordinates required to describe the position of a body.
• Degree of Freedom (DOF)
– The directions an object can move in.
How about 3D Space?
In 2D plane
DEGREES OF FREEDOM (DOF):
• DOF (Contd.)– 2D Motion (3 DOF)
• 2 translation & 1 rotation (2 lengths & 1 angle)
– 3D Motion (6 DOF)• 3 translation & 3 rotation (3 lengths & 3
angles)
DEGREES OF FREEDOM (DOF):
• How joints affect DOF– Joints (or constraints) restrict specific
degrees of freedom between parts.– In doing this, they limit the directions the
parts are free to move with respect to each other.
DEGREES OF FREEDOM (DOF):
Revolute Joint1 DOF(2 DOF restricted)
Slider Joint1 DOF(2 DOF restricted)
Pin in slot2 DOF(1 DOF restricted)
TYPES OF KINEMATIC PAIRS
Based on nature of contact between elements (i) Lower Order Joint : The joint by which two
members are connected has surface contact.
(ii) Higher Order joint: The contact between the
pairing elements takes place at a point or along a line.
Based on relative motion between pairing elements
(a) Siding pair [DOF = 1]
(b) Turning pair (revolute pair) [DOF = 1]
Based on relative motion between pairing elements
(c) Cylindrical pair [DOF = 2]
(d) Rolling pair [DOF = 1]
Based on relative motion between pairing elements
(e) Spherical pair [DOF = 3]
Eg. Ball and socket joint
(f) Helical pair or screw pair [DOF = 1]
Based on the nature of mechanical constraint
(a) Closed pair
(b) Unclosed or force closed pair
CONSTRAINED MOTION
one element has got only one definite motion relative to the other
(a) Completely constrained motion
(b) Successfully constrained motion
(c) Incompletely constrained motion
KINEMATIC CHAIN
Group of links either joined together or arranged in a manner that permits them to move relative to one another.
LOCKED CHAIN OR STRUCTURE
Links connected in such a way that no relative motion is possible.
MECHANISM
A mechanism is a constrained kinematic chain. Motion of any one link in the kinematic chain will give a definite and predictable motion relative to each of the others. Usually one of the links of the kinematic chain is fixed in a mechanism
MECHANISM
Slider crank and four bar mechanisms
Working of slider crank mechanism
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Unconstrained kinematic chain
MACHINE
A machine is a mechanism or collection of mechanisms, which transmit force from the source of power to the resistance to be overcome.
Though all machines are mechanisms, all mechanisms are not machines
PLANAR MECHANISMS
When all the links of a mechanism have plane motion, it is called as a planar mechanism. All the links in a planar mechanism move in planes parallel to the reference plane.
Degrees of freedom/mobility of a mechanism
It is the number of inputs (number of independent coordinates) required to describe the configuration or position of all the links of the mechanism, with respect to the fixed link at any given instant.
DOF of a mechanism
– What is DOF of a mechanism:
The number of links that have independent motion.
– Formula:
F=3n-(2PL+Ph)
Where
n —— number of moving links
PL ——number of lower order joints
Ph —— number of higher order joints
Examples - DOF
F=3n-(2PL+Ph)
• Here, n = 3, PL= 4 & Ph = 0.
• F = 3(3)-2(4-0) = 1
• I.e., one input to any one link will result in definite motion of all the links.
Examples - DOF
F=3n-(2PL+Ph)
• Here, n = 4, PL= 5 & Ph = 0.
• F = 3(4)-2(5-0) = 2
I.e., two inputs to any two links are required to yield definite motions in all the links.
Examples - DOF
n=2
Pl=2
Ph=1
F=3n-(2Pl+Ph)
=6-(4+1)
=1
Conditions for a mechanism to have determined motion
1. DOF F ≥1
2. The DOF of the mechanism should be equal to the numbers of the driving links.
Example:
F=0 F=1 F=2