Kinematics of machinery

11/10/2016 By - T.S.SENTHILKUMAR/AP 1

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.

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.

• 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.

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.,

Binary link, Ternary link, Quaternary link

• 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 pair
Nature of contact
» Lower pair
» Higher pair
Nature of mechanical constraint
» Closed pair
» Unclosed pair11/10/2016 By - T.S.SENTHILKUMAR/AP 17

Sliding pair

Turning pair

Cylindrical pair

Rolling pair

Spherical pair

Helical pair or screw pair

Lower pair

Higher pair

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

Constrained
Motions
Completely
Constrained Motion
Uncompletely
Constrained Motion
Successfully
Constrained Motion

JOINTS
Ternary
joint
Binary joint
Quaternary
joint

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.

Then the number of degree of freedom of a
mechanism (n) is given by,
n = 3 (l-1) – 2j – h
where, l = number of links
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
l = 3 (l -1) – 2j
or
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
Connected As
Per Kutzbach’s
Criterion
Kinematic
Chain
When One Link
Is FixedMechanism
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
Locomotiv
e Wheels
Watt’s
Indicator
Mechanis
m
Pantograph
Ackerman
n
Mechanis
m

First
inversion
Beam
Engine
second
Inversion
Coupling rod
of locomotive
Third Inversion
Watt’s Indicator
Mechanism
Pantograph
Ackermann
Steering11/10/2016 By - T.S.SENTHILKUMAR/AP 46

Beam engine
• Mechanism.Gifinversion of four bar chainbeam-
engine-o.Gif

Coupling rod of a locomotive

Watt’s indicator mechanism

Pantograph

ACKERMANN STEERING

Singleslidercrank
chain
Reciprocating
engine
Reciprocating
compressor
Whitworth quick
return mechanism
Rotary or Gnome
engine
Crank and slotted
lever mechanism
Oscillating
cylinder engine
Bull engine
Pump engine11/10/2016 By - T.S.SENTHILKUMAR/AP 53

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

• Reciprocating engine

• Reciprocating compressor

• Whitworth Quick Return Mechanism

• Rotary Engine

• Oscillating Cylinder Engine

• Crank and Slotted lever Quick return Mechanism
basic1_quickreturn.gif

• Pendulum pump or bull engine

• Hand pump

Double Slider
Crank Chain
Elliptical
Trammel
Scotch Yoke
Mechanism
Oldham
Coupling

Elliptical Trammel

Scotch Yoke Mechanism

Oldham's Coupling

• Oldham's Coupling

• 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.gif11/10/2016 By - T.S.SENTHILKUMAR/AP 92

• 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.

Kinematics of machinery

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