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Mechanism
1. Mechanism
Theory at a glance (IES, GATE & PSU)
What is TOM
The subject theory of machine may be defined as that branch of engineering science
which deals with the study of relative motion both the various parts of m/c and forces
which act on them.
The theory of m/c may be sub divided into the following branches:
1. Kinemics: It deals with the relative motion between the various parts of the
machine
2. Dynamics: It deals with the force and their effects, while acting upon the m/c part in
motion.
Resistance Body: Resistant bodies are those which do not suffer appreciable
distortion or change in physical form by the force acting on them e.g., spring, belt.
Kinematic Link Element: A resistant body which is a part of an m/c and has motion
relative to the other connected parts is term as link.
A link may consist of one or more resistant bodies. Thus a link may consist of a number
of parts connected in such away that they form one unit and have no relative motion to
each other.
? A link should have the following two characteristics:
1. It should have relative motion, and
2. It must be a resistant body.
Functions of Linkages
The function of a link mechanism is to produce rotating, oscillating, or reciprocating motion
from the rotation of a crank or vice versa. Stated more specifically linkages may be used to
convert:
1. Continuous rotation into continuous rotation, with a constant or variable angular
velocity ratio.
2. Continuous rotation into oscillation or reciprocation (or the reverse), with a constant or
variable velocity ratio.
3. Oscillation into oscillation, or reciprocation into reciprocation, with a constant or
variable velocity ratio.
Linkages have many different functions, which can be classified according on the primary goal
of the mechanism:
Page 2
Mechanism
1. Mechanism
Theory at a glance (IES, GATE & PSU)
What is TOM
The subject theory of machine may be defined as that branch of engineering science
which deals with the study of relative motion both the various parts of m/c and forces
which act on them.
The theory of m/c may be sub divided into the following branches:
1. Kinemics: It deals with the relative motion between the various parts of the
machine
2. Dynamics: It deals with the force and their effects, while acting upon the m/c part in
motion.
Resistance Body: Resistant bodies are those which do not suffer appreciable
distortion or change in physical form by the force acting on them e.g., spring, belt.
Kinematic Link Element: A resistant body which is a part of an m/c and has motion
relative to the other connected parts is term as link.
A link may consist of one or more resistant bodies. Thus a link may consist of a number
of parts connected in such away that they form one unit and have no relative motion to
each other.
? A link should have the following two characteristics:
1. It should have relative motion, and
2. It must be a resistant body.
Functions of Linkages
The function of a link mechanism is to produce rotating, oscillating, or reciprocating motion
from the rotation of a crank or vice versa. Stated more specifically linkages may be used to
convert:
1. Continuous rotation into continuous rotation, with a constant or variable angular
velocity ratio.
2. Continuous rotation into oscillation or reciprocation (or the reverse), with a constant or
variable velocity ratio.
3. Oscillation into oscillation, or reciprocation into reciprocation, with a constant or
variable velocity ratio.
Linkages have many different functions, which can be classified according on the primary goal
of the mechanism:
? Function generation: the relative motion between the links connected to the frame,
? Path generation: the path of a tracer point, or
? Motion generation: the motion of the coupler link.
Types
1. Rigid Link: It is one which does not undergo any deformation while transmitting
motion–C.R, etc.
2. Flexible Link: Partly deformed while transmitting motion–spring, belts.
3. Fluid Link: It formed by having the motion which is transmitted through the fluid by
pressure. e. g, hydraulic press, hydraulic brakes.
Kinematic Pair
Two element or links which are connected together in such a way that their relative motion is
completely or successfully constrained form a kinematic pair. i.e. The term kinematic pairs
actually refer to kinematic constraints between rigid bodies.
The kinematic pairs are divided into lower pairs and higher pairs, depending on how the
two bodies are in contact.
? Lower Pair: When two elements have surface contact while in motion.
? Higher Pair: When two elements have point or line of contact while in motion.
Lower Pairs
A pair is said to be a lower pair when the connection between two elements is through the area
of contact. Its 6 types are:
? Revolute Pair
? Prismatic Pair
? Screw Pair
? Cylindrical Pair
? Spherical Pair
? Planar Pair.
Revolute Pair
A revolute allows only a relative rotation between
elements 1 and 2, which can be expressed by a single
coordinate angle '? ' .Thus a revolute pair has a
single degree of freedom.
Page 3
Mechanism
1. Mechanism
Theory at a glance (IES, GATE & PSU)
What is TOM
The subject theory of machine may be defined as that branch of engineering science
which deals with the study of relative motion both the various parts of m/c and forces
which act on them.
The theory of m/c may be sub divided into the following branches:
1. Kinemics: It deals with the relative motion between the various parts of the
machine
2. Dynamics: It deals with the force and their effects, while acting upon the m/c part in
motion.
Resistance Body: Resistant bodies are those which do not suffer appreciable
distortion or change in physical form by the force acting on them e.g., spring, belt.
Kinematic Link Element: A resistant body which is a part of an m/c and has motion
relative to the other connected parts is term as link.
A link may consist of one or more resistant bodies. Thus a link may consist of a number
of parts connected in such away that they form one unit and have no relative motion to
each other.
? A link should have the following two characteristics:
1. It should have relative motion, and
2. It must be a resistant body.
Functions of Linkages
The function of a link mechanism is to produce rotating, oscillating, or reciprocating motion
from the rotation of a crank or vice versa. Stated more specifically linkages may be used to
convert:
1. Continuous rotation into continuous rotation, with a constant or variable angular
velocity ratio.
2. Continuous rotation into oscillation or reciprocation (or the reverse), with a constant or
variable velocity ratio.
3. Oscillation into oscillation, or reciprocation into reciprocation, with a constant or
variable velocity ratio.
Linkages have many different functions, which can be classified according on the primary goal
of the mechanism:
? Function generation: the relative motion between the links connected to the frame,
? Path generation: the path of a tracer point, or
? Motion generation: the motion of the coupler link.
Types
1. Rigid Link: It is one which does not undergo any deformation while transmitting
motion–C.R, etc.
2. Flexible Link: Partly deformed while transmitting motion–spring, belts.
3. Fluid Link: It formed by having the motion which is transmitted through the fluid by
pressure. e. g, hydraulic press, hydraulic brakes.
Kinematic Pair
Two element or links which are connected together in such a way that their relative motion is
completely or successfully constrained form a kinematic pair. i.e. The term kinematic pairs
actually refer to kinematic constraints between rigid bodies.
The kinematic pairs are divided into lower pairs and higher pairs, depending on how the
two bodies are in contact.
? Lower Pair: When two elements have surface contact while in motion.
? Higher Pair: When two elements have point or line of contact while in motion.
Lower Pairs
A pair is said to be a lower pair when the connection between two elements is through the area
of contact. Its 6 types are:
? Revolute Pair
? Prismatic Pair
? Screw Pair
? Cylindrical Pair
? Spherical Pair
? Planar Pair.
Revolute Pair
A revolute allows only a relative rotation between
elements 1 and 2, which can be expressed by a single
coordinate angle '? ' .Thus a revolute pair has a
single degree of freedom.
Y
A
X
F=1
REVOLUTE (R)
?
Prismatic Pair
A prismatic pair allows only a relative translation
between elements 1 and 2, which can be expressed
by a single coordinate 'x'. Thus a prismatic pair has
a single degree of freedom.
Y
X
Screw Pair
A screw pair allows only a relative movement
between elements 1 and 2, which can be
expressed by a single coordinate angle '? ' or
=x‘. Thus a screw pair has a single degree of
freedom. Example-lead screw and nut of
lathe, screw jack.
Page 4
Mechanism
1. Mechanism
Theory at a glance (IES, GATE & PSU)
What is TOM
The subject theory of machine may be defined as that branch of engineering science
which deals with the study of relative motion both the various parts of m/c and forces
which act on them.
The theory of m/c may be sub divided into the following branches:
1. Kinemics: It deals with the relative motion between the various parts of the
machine
2. Dynamics: It deals with the force and their effects, while acting upon the m/c part in
motion.
Resistance Body: Resistant bodies are those which do not suffer appreciable
distortion or change in physical form by the force acting on them e.g., spring, belt.
Kinematic Link Element: A resistant body which is a part of an m/c and has motion
relative to the other connected parts is term as link.
A link may consist of one or more resistant bodies. Thus a link may consist of a number
of parts connected in such away that they form one unit and have no relative motion to
each other.
? A link should have the following two characteristics:
1. It should have relative motion, and
2. It must be a resistant body.
Functions of Linkages
The function of a link mechanism is to produce rotating, oscillating, or reciprocating motion
from the rotation of a crank or vice versa. Stated more specifically linkages may be used to
convert:
1. Continuous rotation into continuous rotation, with a constant or variable angular
velocity ratio.
2. Continuous rotation into oscillation or reciprocation (or the reverse), with a constant or
variable velocity ratio.
3. Oscillation into oscillation, or reciprocation into reciprocation, with a constant or
variable velocity ratio.
Linkages have many different functions, which can be classified according on the primary goal
of the mechanism:
? Function generation: the relative motion between the links connected to the frame,
? Path generation: the path of a tracer point, or
? Motion generation: the motion of the coupler link.
Types
1. Rigid Link: It is one which does not undergo any deformation while transmitting
motion–C.R, etc.
2. Flexible Link: Partly deformed while transmitting motion–spring, belts.
3. Fluid Link: It formed by having the motion which is transmitted through the fluid by
pressure. e. g, hydraulic press, hydraulic brakes.
Kinematic Pair
Two element or links which are connected together in such a way that their relative motion is
completely or successfully constrained form a kinematic pair. i.e. The term kinematic pairs
actually refer to kinematic constraints between rigid bodies.
The kinematic pairs are divided into lower pairs and higher pairs, depending on how the
two bodies are in contact.
? Lower Pair: When two elements have surface contact while in motion.
? Higher Pair: When two elements have point or line of contact while in motion.
Lower Pairs
A pair is said to be a lower pair when the connection between two elements is through the area
of contact. Its 6 types are:
? Revolute Pair
? Prismatic Pair
? Screw Pair
? Cylindrical Pair
? Spherical Pair
? Planar Pair.
Revolute Pair
A revolute allows only a relative rotation between
elements 1 and 2, which can be expressed by a single
coordinate angle '? ' .Thus a revolute pair has a
single degree of freedom.
Y
A
X
F=1
REVOLUTE (R)
?
Prismatic Pair
A prismatic pair allows only a relative translation
between elements 1 and 2, which can be expressed
by a single coordinate 'x'. Thus a prismatic pair has
a single degree of freedom.
Y
X
Screw Pair
A screw pair allows only a relative movement
between elements 1 and 2, which can be
expressed by a single coordinate angle '? ' or
=x‘. Thus a screw pair has a single degree of
freedom. Example-lead screw and nut of
lathe, screw jack.
Cylindrical Pair
A cylindrical pair allows both
rotation and translation between
elements 1 and 2, which can be
expressed as two independent
coordinate angle '? ' and =x‘. Thus a
cylindrical pair has two degrees of
freedom.
S
CYLINDRICAL (C)
f=2
?
Spherical Pair
A spherical pair allows three degrees of freedom since
the complete description of relative movement between
the connected elements needs three independent
coordinates. Two of the coordinates ' ? ' and ' ? ' are
required to specify the position of the axis OA and the
third coordinate '? ' describes the rotation about the
axis OA. e.g. – Mirror attachment of motor
cycle.
SPHERICAL (G)
f=3
X
Z
?
?
?
Page 5
Mechanism
1. Mechanism
Theory at a glance (IES, GATE & PSU)
What is TOM
The subject theory of machine may be defined as that branch of engineering science
which deals with the study of relative motion both the various parts of m/c and forces
which act on them.
The theory of m/c may be sub divided into the following branches:
1. Kinemics: It deals with the relative motion between the various parts of the
machine
2. Dynamics: It deals with the force and their effects, while acting upon the m/c part in
motion.
Resistance Body: Resistant bodies are those which do not suffer appreciable
distortion or change in physical form by the force acting on them e.g., spring, belt.
Kinematic Link Element: A resistant body which is a part of an m/c and has motion
relative to the other connected parts is term as link.
A link may consist of one or more resistant bodies. Thus a link may consist of a number
of parts connected in such away that they form one unit and have no relative motion to
each other.
? A link should have the following two characteristics:
1. It should have relative motion, and
2. It must be a resistant body.
Functions of Linkages
The function of a link mechanism is to produce rotating, oscillating, or reciprocating motion
from the rotation of a crank or vice versa. Stated more specifically linkages may be used to
convert:
1. Continuous rotation into continuous rotation, with a constant or variable angular
velocity ratio.
2. Continuous rotation into oscillation or reciprocation (or the reverse), with a constant or
variable velocity ratio.
3. Oscillation into oscillation, or reciprocation into reciprocation, with a constant or
variable velocity ratio.
Linkages have many different functions, which can be classified according on the primary goal
of the mechanism:
? Function generation: the relative motion between the links connected to the frame,
? Path generation: the path of a tracer point, or
? Motion generation: the motion of the coupler link.
Types
1. Rigid Link: It is one which does not undergo any deformation while transmitting
motion–C.R, etc.
2. Flexible Link: Partly deformed while transmitting motion–spring, belts.
3. Fluid Link: It formed by having the motion which is transmitted through the fluid by
pressure. e. g, hydraulic press, hydraulic brakes.
Kinematic Pair
Two element or links which are connected together in such a way that their relative motion is
completely or successfully constrained form a kinematic pair. i.e. The term kinematic pairs
actually refer to kinematic constraints between rigid bodies.
The kinematic pairs are divided into lower pairs and higher pairs, depending on how the
two bodies are in contact.
? Lower Pair: When two elements have surface contact while in motion.
? Higher Pair: When two elements have point or line of contact while in motion.
Lower Pairs
A pair is said to be a lower pair when the connection between two elements is through the area
of contact. Its 6 types are:
? Revolute Pair
? Prismatic Pair
? Screw Pair
? Cylindrical Pair
? Spherical Pair
? Planar Pair.
Revolute Pair
A revolute allows only a relative rotation between
elements 1 and 2, which can be expressed by a single
coordinate angle '? ' .Thus a revolute pair has a
single degree of freedom.
Y
A
X
F=1
REVOLUTE (R)
?
Prismatic Pair
A prismatic pair allows only a relative translation
between elements 1 and 2, which can be expressed
by a single coordinate 'x'. Thus a prismatic pair has
a single degree of freedom.
Y
X
Screw Pair
A screw pair allows only a relative movement
between elements 1 and 2, which can be
expressed by a single coordinate angle '? ' or
=x‘. Thus a screw pair has a single degree of
freedom. Example-lead screw and nut of
lathe, screw jack.
Cylindrical Pair
A cylindrical pair allows both
rotation and translation between
elements 1 and 2, which can be
expressed as two independent
coordinate angle '? ' and =x‘. Thus a
cylindrical pair has two degrees of
freedom.
S
CYLINDRICAL (C)
f=2
?
Spherical Pair
A spherical pair allows three degrees of freedom since
the complete description of relative movement between
the connected elements needs three independent
coordinates. Two of the coordinates ' ? ' and ' ? ' are
required to specify the position of the axis OA and the
third coordinate '? ' describes the rotation about the
axis OA. e.g. – Mirror attachment of motor
cycle.
SPHERICAL (G)
f=3
X
Z
?
?
?
Planar Pair
A planar pair allows three degrees of freedom.
Two coordinates x and y describe the relative
translation in the xy-plane and the third '? '
describes the relative rotation about the z-axis.
Higher Pairs
A higher pair is defined as one in which the connection between two elements has only a point
or line of contact. A cylinder and a hole of equal radius and with axis parallel make contact
along a surface. Two cylinders with unequal radius and with axis parallel make contact along
a line. A point contact takes place when spheres rest on plane or curved surfaces (ball
bearings) or between teeth of a skew-helical gears. In roller bearings, between teeth of most of
the gears and in cam-follower motion. The degree of freedom of a kinetic pair is given by the
number independent coordinates required to completely specify the relative movement.
Wrapping Pairs
Wrapping Pairs comprise belts, chains, and other such devices
Sliding Pair
When the two elements of a pair are connected in such a way that one can only slide relative to
the other, the pair is known as a sliding pair. The piston and cylinder, cross-head and guides
of a reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed etc.
are the examples of a sliding pair. A little consideration will show that a sliding pair has a
completely constrained motion.
Turning pair
When the two elements of a pair are connected in such a way that one can only turn or revolve
about a fixed axis of another link, the pair is known as turning pair. A shaft with collars at
both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe
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