kinematicsofmachinery-161110151759.pptx

KINEMATICS OF MACHINERY
BY
E SA I K R I SHNA
A SSI STANT P RO FESSOR
M ECHANICAL E N GG. D E PT.

UNIT – I
Mechanisms: Elements or Links – Classification – Rigid Link, flexible and
fluid link – Types of
kinematics pairs – sliding, turning, rolling, screw and spherical pairs – lower
and higher pairs – closed
and open pairs – constrained motion – completely, partially or successfully
and incompletely
constrained.
Mechanism and Machines – Mobility of Mechanisms: Grubler’s criterion,
classification of machines –
kinematics chain – inversions of mechanism – inversions of quadric cycle
chain, single and double slider
crank chains, Mechanical Advantage.

UNIT – II
Kinematics: Velocity and acceleration – Motion of link in machine –
Determination of Velocity and
acceleration – Graphical method – Application of relative velocity method.
Plane motion of body: Instantaneous center of rotation- centrodes and
axodes – Three centers in line
theorem – Graphical determination of instantaneous center, determination
of angular velocity of points
and links by instantaneous center method.
Kliens construction - Coriolis acceleration - determination of Coriolis
component of acceleration
Analysis of Mechanisms: Analysis of slider crank chain for displacement-
velocity and acceleration
of slider – Acceleration diagram for a given mechanism.

UNIT – III
Straight-line motion mechanisms: Exact and approximate copied and
generated types – Peaucellier
- Hart - Scott Russel – Grasshopper – Watt -Tchebicheff’s and Robert
Mechanism - Pantographs
Steering gears: Conditions for correct steering – Davis Steering gear,
Ackerman’s steering gear.
Hooke’s Joint: Single and double Hooke’s joint –velocity ratio –
application – problems.

UNIT – IV
Cams: Definitions of cam and followers – their uses – Types of followers
and cams – Terminology –
Types of follower motion - Uniform velocity, Simple harmonic motion
and uniform acceleration and
retardation. Maximum velocity and maximum acceleration during
outward and return strokes in the
above 3 cases.
Analysis of motion of followers: Tangent cam with Roller follower –
circular arc cam with straight,
concave and convex flanks.

UNIT – V
Higher pair: Friction wheels and toothed gears – types – law of gearing, condition for
constant velocity ratio for transmission of motion – velocity of sliding.
Forms of teeth, cycloidal and involutes profiles – phenomena of interferences –
Methods of interference.
Condition for minimum number of teeth to avoid interference – expressions for arc
of contact and path of contact of Pinion & Gear and Pinion & Rack Arrangements–
Introduction to Helical – Bevel and worm gearing
Gear Trains: Introduction – Types – Simple – compound and reverted gear trains –
Epicyclic gear
train. Methods of finding train value or velocity ratio of Epicyclic gear trains.
Selection of gear box -
Differential gear for an automobile.

TEXT BOOKS:
1. Theory of Machines and Mechanisms/JOSEPH E. SHIGLEY/ Oxford
2. Theory of Machines / S. S. Rattan / Mc Graw Hill Publishers.
REFERENCE BOOKS:
1. Theory of Machines / Sadhu Singh / Pearson.
2. Theory of Machines / Thomas Bevan/CBS.

11/10/2016 BY - T.S.SENTHILKUMAR/AP 8
INTRODUCTION

Mechanics
Dynamics
Kinetics Kinematics
Statics

• The branch of scientific analysis that deals
with motions, time and forces is called
mechanics.
• It is divided in to two parts statics and
dynamics.

STATICS
• It deals with the analysis of stationary systems.
But time is not considered.
DYNAMICS
• It deals with the systems that change with
time.

KINEMATICS
• It is the study of motion, quite apart from the
forces which produce that motion.
• It is the study of position, displacement,
rotation, speed, velocity and acceleration.
KINETICS
• It is the study of motion and its causes

The subject matter which deals with this
geometric constant of relative motion, without
any reference to the cause of the motion that is
the force is called kinematics.
For the study of kinematics, a machine may be
referred to as a mechanism, which is a
combination of inter connected rigid bodies
capable of relative motion.

Machinery is defined as a mechanical device or
the parts that keep something working.
Machines or machine parts considered as a group.
The working parts of a particular machine.
An assemblage of machines.
The parts of a machine collectively.
An assemblage of machines or mechanical
apparatuses

• It is defined as the
combination of rigid or
resistance bodies assembled
in such a way that the motion
of one causes constrained and
predictable motion to others
is known as mechanism.
• If one of the links of a
kinematic chain is fixed,
then the chain is known as
mechanism. 15

 An assembly of moving parts performing a complete
functional motion.
A mechanism is a device designed to transform input
forces and movement into a desired set of output forces
and movement.
Mechanisms generally consist of moving components
such as gears and gear trains, belt and chain drives, cam
and follower mechanisms, and linkages as well as
friction devices such as brakes and clutches, and
structural components such as the frame, fasteners,
bearings, springs, lubricants and seals, as well as a
variety of specialized machine elements such as splines,
pins and keys.
16

• It is defined as a device which receives energy
and transforms it into some useful work.
• If the mechanism is used to transmit power
(or) to do work, then it is known as machine.
• The main function of the machine is to obtain
mechanical advantage.
BY - T.S.SENTHILKUMAR/AP 17

We can define machine as a device for
transferring and transforming motion and force
or power from the input that is, the source to
the output that is the load.
The motion needs to be transformed as it is
being transferred from the source to the load.

• It is a resistant body or assembly of resistant
body of a machine connecting other parts of
the machine with relative motion between
them.
• There are three types of links available in order
to transmit motion. They are as follows:
» Rigid link
» Flexible link
» Fluid link

Rigid link
A rigid link is one which does not undergo any
deformation while transmitting motion. Practically rigid
link does not exists. Ex : crank shaft, piston etc.,
Flexible link
A flexible link is one which undergoes partial deformation
without affecting the transfer motion. Ex : ropes, belts,
chains, springs etc.,
Fluid link
A fluid link is a link which has fluid inside the container
and motion is transmitted through the fluid by pressure or
compression. Ex: fluids used in hydraulic press, hydraulic
jack, hydraulic crane etc.,

Structure
It is an assemblage
of a number of
resistant bodies
(known as members)
having no relative
motion between
them and meant for
carrying loads
having straining
action. A railway
bridge, a roof truss,
machine frames etc.,
are the examples of a
structure.

Difference Between a Machine and a Structure
The following differences between a machine and a structure are important
from the subject point of view :
1. The parts of a machine move relative to one another,
whereas the members of a structure do not move relative to one another.
2. A machine transforms the available energy into some useful work, whereas
in a structure no energy is transformed into useful work.
3. The links of a machine may transmit both power and motion, while the
members of a structure transmit forces only.

• A joint of two links that permits relative motion
is called pair.
Types of kinematic pair
1. Nature of relative motion between the links.
2. Nature of contact between the links.
3. Nature of mechanical arrangement.

Nature of relative motion
» Sliding pair
» Turning pair
» Cylindrical pair
» Rolling pair
» Spherical pair
» Helical or screw pair
Nature of contact
» Lower pair
» Higher pair
Nature of mechanical constraint
» Closed pair
» Unclosed pair

Sliding pair

Turning pair

Cylindrical pair

Rolling pair

Spherical pair

Helical pair or screw pair

Lower pair
Lower pair. When the two elements of a pair have a
surface contact when relative motion takes place and
the surface of one element slides over the surface of
the other, the pair formed is known as lower pair.
It will be seen that sliding pairs, turning pairs and
screw pairs form lower pairs.

Higher pair
Higher pair.
When the two elements of a pair have a line or point contact when relative
motion takes place and the motion between the two elements is partly
turning and partly sliding, then the pair is known as higher pair.
A pair of friction discs, toothed gearing, belt and rope drives, ball and
roller bearings and cam and follower are the examples of higher pairs.

Closed pair
• When two elements of a pair are held together
mechanically, they constitute a closed pair.
Ex :All pair
Un closed pair
• When two elements of a pair are not held
together mechanically, they constitute a
unclosed pair.
Ex : cam and follower

• If the last link is joined to first link to transmit
definite motion, then it is known as kinematic
chain.
• To determine the given assemblage of links form
the kinematic chain or not:
• The two equations are: l = 2p – 4
j = (3/2) * l – 2
Where, l = number of links
p = number of pairs
j = number of joints

Example 1:
Can we form kinematics chain with 4 links and 4 pairs

Example 2:
Can we form kinematics chain with 4 links and 10 joints

Constrained
Motions
Completely
Constrained Motion
Uncompletely
Constrained Motion
Successfully
Constrained Motion

1. Completely constrained motion. When the motion between a
pair is limited to a definite direction irrespective of the direction
of force applied, then the motion is said to be a completely
constrained motion.

2. Incompletely constrained motion. When the motion
between a pair can take place in more than one direction, then
the motion is called an incompletely constrained motion. The
change in the direction of impressed force may alter the
direction of relative motion between the pair.

3. Successfully constrained motion. When the motion between the
elements, forming a pair is such that the constrained motion is not
completed by itself, but by some other means, then the motion is said to
be successfully constrained motion.

JOINTS
Ternary
joint
Binary joint
Quaternary
joint

Binary link, Ternary link,
Quaternary link

The analysis of mechanism is the number of
degrees of freedom, also called the mobility of
the device.
The mobility of a mechanism is defined as the
number of input parameters which must be
controlled independently in order to bring the
device in to a particular position.
It is the number of independent coordinates
required to describe the position of a body in
space.

Movability includes the six degrees of freedom
of the device as a whole, as through the ground
link were not fixed and thus applies to a
kinematic chain.
Mobility neglects these and considers only the
internal motions, thus applying to a
mechanism.

A link is to have ‘n’ degree of
freedom if it has n independent
variables associated with its
position in the plane.

n = 3 (l-1) – 2j – h where,
l= number of links
Then the number of degree of freedom of a
mechanism (n) is given by,
j = number of binary joints
h = number of higher pairs
This equation is called kutzbach criterion for
the mobility of a mechanism.
If there is no higher pair, then h = 0. then
kutzbach criterion, n = 3 (l-1) – 2j

• Mechanism with lower pairs
– Three bar mechanism
– Four bar mechanism
– Five bar mechanism
– Six bar mechanism
• Mechanism with higher pairs

n = 6(l-1) – 5P1 – 4P2 – 3P3 – 2P4 – 1P5
Where, n = Number of degree of freedom
l = Number of links
P1 = Number of pair having one degree of
freedom
P2 = Number of pair having two degree of
freedom

• Grubler’s mechanism is obtained by substituting
n = 1 and h = 0 in Kutzbach criterion as below.
we know that,
n = 3 (l-1) – 2j – h
=>1= 3 (l -1) – 2j
=>3l – 2j – 4 = 0
This equation is known as Grubler’s criterion for
plane mechanism

We know that Kutzbach criterion for spatial
mechanism is
n = 6(l-1) – 5P1 – 4P2 – 3P3 – 2P4 – 1P5
substitute n = 1; P2, P3 , … P5 = 0
1 = 6(l-1) – 5P1 (or) 6l– 5P1 – 7 = 0
This equation is known as Grubler’s equation
for spatial mechanism.

• When one of the links of kinematic chain is
fixed, then the chain is known as mechanism.

1. Simple mechanism
2. Compound mechanism

Kinematic
Pair
When
ConnectedAs
Per Kutzbach’s
Criterion
Kinematic
Chain
When One Link
Is Fixed
Mechanism
When Forces
And Couples
Are Transmitted
Machine

The method of obtaining different mechanisms
by fixing different links in a kinematic chain,
is known as inversion of the mechanism.

Kinematic chain
Four bar chain
Slider crank
chain
Double crank
chain

Inversion
Of Four
Bar Chain
Beam
Engine
Coupled
Locomotive
Wheels
Watt’s
Indicator
Mechanism
Pantograph
Ackermann
Mechanism

Beam
Engine
second
Inversion
Third Inversion
Coupling rod
of locomotive
Watt’s Indicator
Mechanism
Pantograph
Ackermann
Steering
First
Inversion

Beam engine

Coupling rod of a locomotive

Watt’s indicator mechanism

Pantograph

ACKERMANN STEERING

Single
slider
crank
chain
Reciprocating
engine
Reciprocating
compressor
Whitworth quick
return mechanism
Rotary or Gnome
engine
Crank and slotted
lever mechanism
Oscillating
cylinder engine
Bull engine
Pump engine

First
Inversion
Reciprocating engine
Reciprocating compressor
Third
Inversion
Whitworth quick return mechanism
Second
Inversion
Rotary engine
Oscillating cylinder engine
Crank and slotted lever
mechanism
Fourth
Inversion
Bull Engine
Hand Pump

• Reciprocating engine

• Reciprocating compressor

• Whitworth Quick Return Mechanism

• Oscillating Cylinder Engine

•Crank and Slotted lever Quick return Mechanism

• Pendulum pump or bull engine

• Hand pump

Double Slider
Crank Chain
Elliptical
Trammel
ScotchYoke
Mechanism
Oldham
Coupling

Elliptical Trammel

Scotch Yoke Mechanism

Oldham's Coupling

• Oldham's Coupling

A crank and slotted lever mechanism used in a shaper has a centre distance of 300
mm between the centre of oscillation of the slotted lever and the centre of rotation
of the crank. The radius of the crank is 120 mm. Find the ratio of the time of cutting
to the time of return stroke.

In a crank and slotted lever quick return motion mechanism, the distance between the fixed
centres is 240 mm and the length of the driving crank is 120 mm. Find the inclination of the
slotted bar with the vertical in the extreme position and the time ratio of cutting stroke to
the return stroke.
If the length of the slotted bar is 450 mm, find the length of the stroke if the line of stroke
passes through the extreme positions of the free end of the lever.

In a Whitworth quick return motion mechanism, as shown in Fig. 5.32, the distance
between the fixed centers is 50 mm and the length of the driving crank is 75 mm. The
length of the slotted lever is 150 mm and the length of the connecting rod is 135 mm.
Find the ratio of the time of cutting stroke to the time of return stroke and also the
effective stroke.

Few concepts
DOF Resultant
mechanism
Resultant Chain
> 1 Un constrained
mechanism
Unconstrained
chain
= 1 Constrained
mechanism
Constrained chain
= 0 Structure Locked chain
< 0 Redundant or
super structure
Redundant chain

Grashof’s rule
The Grashof condition for a four-bar linkage states: If
the sum of the shortest and longest link of a planar
quadrilateral linkage is less than or equal to the sum of
the remaining two links,
(S+L)<=(P+Q)
P
Q
L
S

Chain Type Inversio
n No.
Fixed Link Resultant
Mechanism
1. Class – I
(L + S)< (P +Q)
1.
2.
3.
4.
1. Shortest
2. Adjacent to Shortest
3. Adjacent to shortest
4. Opposite to shortest
1.Double crank
2. Crank rocker
3. Crank rocker
4. Double rocker
2. Class – II
(L + S) > (P +Q)
All Fix any link Double Rocker
3. Class – III
(L+S) = (P+Q)
Same as
Class - I
Same as Class - I
Same as Class – I
with dead centres

• Stationary screws with travelling nuts
• Stationary nuts with travelling screws
• Single and double acting hydraulic and
pneumatic cylinders.

• C-Clamp

• This type of mechanism produces a swinging or
rocking motion of a link. The motion is generally less
than 360o and is an oscillatory motion.
Toothed Rack System
• This is simply a rotating arm (b) with a link fitted with
a toothed rack (c) which meshes with a gear (d) to
produce a rocking motion of the gear.

Crank and Rocker Mechanism
• This is simply a four bar linkage (the frame
provides the first link). The operating
characteristics are dependent on the length of
the links and the design of the frame setting
the pivot points..Rotation of the arm (b)
produces a rocking motion of arm (d).

Crank and Rocker
Mechanism

Quick Return linkage
• The arm (b) rotates and results in a rocking
motion of arm (d)via the slider (c). The
action is a quick return action because the
angle (b) rotates through in one direction
,assumed to be the forward direction, is greater
than the angle which result in the return
motion.

Quick Return
linkage

Cam and Follower Mechanism
• Rotation of the cam (c) produces a rocking
motion of the lever (d) via the sliding interface
(b). The arrangement only identifies the
principle involved. In practice some means
would have to be provided to ensure the lever
is maintained in contact with the lever.

Cam and Follower
Mechanism

• This mechanism is for rectilinear motion

• This mechanism is used to regulate the
movement of clock.

• When a mechanism is desired which is capable
of delivering output rotation in the either
direction, some form of reversing mechanism
is required.
• Ex : gear shifting

• C:UserssenthilDesktopGeneva_mechanism
_6spoke_animation.gif

Application of the Geneva drive
• One is movie projectors : the film does not run
continuously through the projector. Instead, the
film is advanced frame by frame, each frame
standing still in front of the lens for 1/24 of a
second

• Peaucellier Mechanism
C:UserssenthilDesktopPeaucellier_linkage_anim
ation.gif

• Robert’s Mechanism
C:UserssenthilDesktopRoberts_linkage.gif

• Chebychev Mechanism
C:UserssenthilDesktopChebyshev_linkage.gif

• This connectors are used when one slider is to
drive another slider.

• In an automobile engine a valve must open,
remain open for a period of time, and then
close.
Ex : cam and follower

• The connecting rod of a planar four bar linkage
may be imagined as an infinite plane extending
in all directions but pin connected to the input
and output links.
• Then, during motion of the linkage, any point
attached to the plane of the coupler generates
some path with respect to the fixed link, this
path is called coupler curve.

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