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