KOM_20-21.pdf

202047 - Kinematics of Machinery
(K.O.M.)
SE Mechanical- Term II(Semester 4)
Prof. Ami Barot PVG's COET & GKPIM

What is Machine?

What is Machine?
 A machine is device which receives energy in some
available form & utilizes it to do some useful work.
 Car, lathe, shaper, washing machine, mixer grinder,
cycle, motor bike etc…

Kinematics of Machinery

A machine is device which receives energy in some
available form & utilizes it to do some useful work.
A machine is a device that transfers and
transforms motion and force from source to the
load.
Machine is a device consisting of fixed and
moving parts(Rigid body) that modifies
mechanical energy and transmit it in more useful
form.

Machines are composed of different
types of mechanisms.
• Rotational motion transforms to rectilinear
• Rotational motion transforms to oscillation
• Rotational motion transforms to angular
oscillation
• Rotational motion transforms to intermittent
And vice versa…

Theory of Machines
Theory of Machines: may be defined as that
branch of engineering science, which deals
with the study of relative motion between the
various parts of machine, and forces which act
on them.
In establishing these relations and design of
the machine, theory of machines uses
principles from physics, kinematics, statics and
kinetics.

The branch of scientific analysis that deals with
motion, time and forces are called mechanics or
TOM.
(TOM)Mechanics
Kinematics Dynamics
Statics Kinetics

Kinematics:- It is a branch of theory of
machines, deals with the study of only motion
in the machine members (displacement,
velocity, acceleration are motion
characteristics)
Dynamics:- It is that branch of Theory of
Machines which deals with the forces and
their effects impressed upon the different
parts of the machine

Statics
It is that branch of Theory of Machines which
deals with the forces & their effects while
machine parts are at rest.
Kinetics
It is that branch of Theory of Machines which
deals with the inertia forces which arise from
combined effect of the mass and motion of the
machine parts.
Kinetics deals with the forces that produce
motion
[deals with both motion and the forces]

 Study of mechanism involves both analysis and
synthesis
 Analysis involves the study of motions and forces
concerning different parts of the existing mechanism
 Synthesis involves the design of various parts of
machine concerning its shape and size, material to be
used and the arrangement of the parts so that the
resulting machine can perform the desired tasks

(K.O.M.)
 Subject scheme and Syllabus

(K.O.M.)
 Examination Scheme
 Theory : 03 Hr./Week
 Practical : 02 Hr./Week
 Theory : 03
 Practical : 01
 In-Semester : 30 Marks
 End-Semester : 70 Marks
 Oral : 25 Marks

Unit I Fundamentals of Mechanism
 Kinematic link, Types of links, Kinematic pair,
Types of constrained motions, Types of Kinematic
pairs, Kinematic chain, Types of joints,
Mechanism, Machine, Degree of freedom,
Mobility of Mechanism, Inversion, Grashoff’s law,
Four-Bar Chain and its Inversions, Slider crank
Chain and its Inversions, Double slider crank
Chain and its Conversions, Mechanisms with
Higher pairs, Equivalent Linkages and its Cases -
Sliding Pairs in Place of Turning Pairs, Spring in
Place of Turning Pairs, Cam Pair in Place of
Turning Pairs

Unit II Kinematic Analysis of Mechanisms:
Analytical Method
 Analytical methods for displacement, velocity and
acceleration analysis of slider crank Mechanism,
Velocity and acceleration analysis of Four-Bar and
Slider crank mechanisms using Vector and
Complex Algebra Methods.
 Computer-aided Kinematic Analysis of Mechanism
like Slider crank and Four-Bar mechanism,
 Analysis of Single and Double Hook’s joint

Unit III Kinematic Analysis of Mechanisms:
Graphical Method
 Displacement, velocity and acceleration analysis
mechanisms by Relative Velocity Method
(Mechanisms up to 6 Links), Instantaneous Centre of
Velocity, Kennedy’s Theorem, Angular Velocity ratio
Theorem, Analysis of mechanism by ICR method
(Mechanisms up to 6 Links), Coriolis component of
Acceleration (Theoretical treatment only)

Unit IV Synthesis of Mechanisms
 Steps in Synthesis: Type synthesis, Number Synthesis,
Dimensional synthesis, Tasks of Kinematic synthesis -
Path, function and motion generation (Body
guidance), Precision Positions, Chebychev spacing,
Mechanical and structural errors
 Graphical Synthesis: Inversion and relative pole
method for three position synthesis of Four-Bar and
Single Slider Crank Mechanisms
 Analytical Synthesis: Three position synthesis of Four-
Bar mechanism using Freudenstein’s equation, Blotch
synthesis

Unit V Kinematics of Gears
 Gear: Classification
 Spur Gear: Terminology, law of gearing, Involute and cycloidal
tooth profile, path of contact, arc of contact, sliding velocity,
Interference and undercutting, Minimum number of teeth to
avoid interference, Force Analysis (theoretical treatment only)
 Helical and Spiral Gears: Terminology, Geometrical
Relationships, virtual number of teeth for helical gears
 Bevel Gear & Worm and Worm Wheel: Terminology,
Geometrical Relationships
 Gear Train: Types, Analysis of Epicyclic gear Trains, Holding
torque - simple, compound and Epicyclic gear Trains, Torque on
Sun and Planetary gear Train, compound Epicyclic gear Train

Unit VI Mechanisms in Automation Systems
 Cams & Followers: Introduction, Classification of Followers and Cams,
Terminology of Cam Displacement diagram for the Motion of follower
as Uniform velocity, Simple Harmonic Motion (SHM), Uniform
Acceleration and Retardation Motion (UARM), Cycloid motion, Cam
Profile construction for Knife-edge Follower and Roller Follower, Cam
jump Phenomenon
 Automation: Introductions, Types of Automation
 Method of Work Part Transport: Continuous transfer, Intermittent or
Synchronous Transfer, Asynchronous transfer, Different type of transfer
mechanisms - Linear transfer mechanisms and Rotary transfer
mechanisms
 Automated Assembly-Line: Types, Assembly line balancing Buffer
Storages, Automated assembly line for car manufacturing, Artificial
intelligence in automation

Kinematics of Machinery:
Unit 1

 Kinematic Link:
 Each part of machine which has relative
motion to some other part of the machine is
known as kinematic link or kinematic element.
 Link may be rigid, flexible, fluid
 Link may be Binary, Ternary and Quaternary

 Rigid link does not undergo any deformation
while transmitting motion. Ex connecting rod,
crank

Flexible link deforms partly while transmitting
motion but does not affect transmission of motion.
Belts, springs, chain, ropes.

Fluid link is formed by having the motion which is
transmitted through the fluid by pressure or
by compression.
Hydraulic jack and fluid brake
Hydraulic press and hydraulic brakes in vehicles

• Links which are attached to two different points in
a mechanism means containing two pair element
connections are called Binary links.
• Links containing three pair element connections
are called Ternary links.
• Links containing four pair element connections
are called Quaternary links.

Rigid body and resistant body
 A body is said to be rigid if under the action of
forces, it does not suffer any appreciable
distortion or change in physical form by the forces
acting on them are known as a Rigid body.
 Distance between any two points on rigid body
remains constant. Ex. Piston, connecting rod,
crank
 The component of a machine which do not suffer
appreciable distortion or change in physical form
by the forces acting on them for the purpose they
have to serve are known as a Resistant body.
 Spring, chain, belt are example of resistant
body. Prof. Ami Barot PVG's COET & GKPIM

Rigid body and Resistant body
 A body is said to be rigid if under the action of
forces, it does not suffer any appreciable
distortion or change in physical form by the forces
acting on them are known as a Rigid body.
 Distance between any two points on rigid body
remains constant. Ex. Piston, connecting rod,
crank

 Resistant body are those which are rigid for
the purpose they serve.
 A resistant body or rigid body which is a part
of machine and has motion relative to the
other connected components is known as
kinematic link.

 Kinematic Pair:-
 There always exists a relative motion between
every two links.
 If this relative motion between the pair of links
is constrained or successfully constrained
then the pair is called as Kinematic pair.
 Constrained Motion:- one element has got only
one definite motion relative to the other.

Constrained Motion
Types:
 Completely constrained motion
 Incompletely constrained motion
 Successfully constrained or partially constrained
motion

(a) Completely constrained motion:
 The motion between two elements of a pair is in a
definite direction irrespective of the direction of force
applied
 The constrained motion is completed by its own links
 Square bar in square hole, shaft with collar in a circular
hole , piston and cylinder in steam engine

(b) Incompletely constrained motion:
• If the links are so connected that motion can take place
in more than one direction
• Circular bar moving in the round hole, because bar can
rotate and reciprocate independently

(c) Successfully constrained or partially constrained
motion:
• When the motion between two elements of a pair is
possible in more than one direction but is made to have
motion only in one direction by using some external
means
• A definite constrained motion is not completed by itself
but by some other means.

(c) Successfully constrained or partially constrained
motion:
e.g.
A shaft in a footstep bearing have vertical motion apart
from rotary motion. Load applied on a shaft constrained
to move in vertical direction.
In a petrol engine the piston and cylinder form a
successfully constrained pair.
In cam and follower, the successfully constrained motion
is obtained by the gravity of follower and the spring force

When the two kinematic links are connected such a way that
their motion is either completely or successfully
constrained then these two links are said to form pair.
Types of Kinematic Pairs
 Based on relative motion between pairing elements
 Based on contract between the links
 Based on mechanical constraint or mechanical arrangement
between the links
KINEMATIC PAIRS

Based on relative motion between pairing elements
(1) Sliding pair (Prismatic pair or sliding joint) :
Two links have a sliding motion relative to each other, they
form a sliding pair
eg. Piston and cylinder in reciprocating engine
TYPES OF KINEMATIC PAIRS

(2) Turning pair (revolute pair or pin joint)
When one link has a turning of revolving
motion relative to each other, they
constitute a turning pair.
eg. Crankshaft and the frame of engine

(3) Helical pair or screw pair
If two links have a turning as well as sliding motion
between them, they form a screw pair.
This is achieved by cutting machine threads on
the two links.
Eg. The lead screw and nut of the lathe, screw
jack, C-clamp, fitting vice.

(4) Spherical pair or globular pair
When one link in the form of a sphere turns inside a
fixed link, it is a spherical pair.
Eg. Ball and socket joint, Attachment of a mirror
for motorcycle, joystick

(3) Rolling pair
When links of a pair have a rolling motion
relative to each other, they form a rolling pair.
Eg. Ball and roller bearings, wheel rolling of
flat surface, toothed gear, cam follower mechanism,
Belt drive

Rolling pair
Exa. Wheel Rolling on the flat surface

(1) Sliding pair (Prismatic pair or sliding joint)
(4) Spherical pair
(5) Rolling pair

Based on nature of contact between elements
 (i) Lower pair : The joint by which two members
are connected has surface or area contact.
In a slider crank mechanism all pairs are lower
pair
Shaft revolving in a bearing

(ii) Higher pair: The contact between the pairing
elements takes place at a point or along a line.
Cam and follower mechanism, toothed gears, ball and
roller bearing, wheel rolling on a surface.
Toothed gear

53
 Higher pair
 Have line and point contact between the
pairing elements.
CAM Follower Gears
Pin and slot

Based on the nature of mechanical
constraint
(a) Closed pair : Two elements of a pair
are held together mechanically, it
forms closed pair.
contact between the two can be broken
only by destruction of at least one of the
members
sliding pairs, turning pairs, spherical
pairs and screw pairs i.e. all lower pairs.

Based on the nature of mechanical
constraint
(b) Unclosed or force closed pair
Two elements of a pair
are in contact either due to force of
gravity or some spring action, they
constitute an unclosed pair.
Cam and follower mechanism held
together by the forces exerted by spring
and gravity not mechanically.

(1) Siding pair (Prismatic pair or sliding joint)
(3) Rolling pair
(4) Spherical pair
Based on nature of contact between elements
(1) Lower pair
(2) Higher pair
Based on the nature of mechanical constraint
(1) Closed pair
(2) Unclosed or force closed pair

57

58
 Lower pair
 Have surface contact between the surfaces.
Revolute (pin) joints
prismatic joints
Helical joints Cylindrical joint Spherical joint

59

60
 Higher pair
 Have line and point contact between the pairing
elements.
CAM Follower Gears
Pin and slot

62
 Kinematic chain
 When kinematics pairs are so coupled that the last
link is joined to the first link.
 It is assembly of the links in which the relative motion
of the links is possible and the motion of each link is
relative to the others is definite.

 Kinematic chain
 A combination of links and pairs without a
fixed link.
No element is fixed to the ground or frame

MECHANISM
- When one of the links of a kinematic chain is fixed, the
result is 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

Fixed
Mechanisms

Kinematic Link
Kinematic pair
Kinematic chain
Mechanism
Machine

Difference Between a Machine and a
Structure
The members of a structure
1. Do not move relative to one another.
2. Do not transform energy into useful work.
3. The links of a machine may transmit both power
and motion, while the members of a structure
transmit forces only.
Examples:
Structure: Roof trusses used in buildings.
Machine: screw jack , I.C. engine

KOM_20-21.pdf

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