KOM-UNIT-1-BASICS OF MECHANISMS

KINEMATICS OF MACHINERY
UNIT I –BASICS OF
MECHANISMS
PAAVAI INSTITUTIONSDEPARTMENT OF MECHANICAL ENGINEERING
Present by:
S.Maniraj M.E.,(Ph.D)
Assistant Professor,
Department of Mechanical Engg.,
Paavai Engineering College,
Namakkal – 637018.

Mechanics is the branch of science which deals with the
behaviour of objects at rest or in motion, under the influence
of forces. Engineering mechanics involves the application of
the principles of mechanics to solve real-time engineering
problems.

Kinematics -Invented by Nicholas Oresme represented time and
velocity by lengths. It is the study of motion, without addressing any
of the forces that cause the motion.
Machine : machine originated with the Greek philosopher
Archimedes around the 3rd century, who studied the simple
machines: lever, pulley, and screw. “A machine is a combination of
rigid or resistant bodies, formed and connected do that they move
with definite relative motions and transmit force from the source of
power .A machine has two functions: transmitting definite relative
motion and transmitting force.

Kinematic Link or Element :Each part of a machine, which moves
relative to some other part, is known as a kinematic link. A link or
element need not to be a rigid.
Eg: Piston,Connecting rod etc.,
Types of Links
1. Rigid link. A rigid link is one which does not undergo any
deformation while transmitting motion. Eg: Piston,Connecting rod
etc.,
2. Flexible link. A flexible link is one which is partly deformed in a
manner not to affect the transmission of motion. For example, belts,
ropes, chains and wires are flexible links and transmit tensile
forces only.

3. Fluid link. A fluid link is one which is formed by having a fluid in a
receptacle and the motion is transmitted through the fluid by pressure
or compression only, as in the case of hydraulic presses, jacks and
brakes.
Structure : It is an assemblage of a number of resistant bodies (known
as members) having no relative motion between them. A railway
bridge, a roof truss, machine frames etc., are the examples of a
structure.
Difference Between a Machine and a Structure
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.

Kinematic Pair : The two links or elements of a machine, when in
contact with each other, are said to form a pair.
Eg: Connecting rod and Piston , Crank and connecting rod etc.,
Types of Constrained Motions
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.

Eg: Square bar in a square hole, Shaft with collars in a circular hole.
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.
Eg: Shaft in a circular hole

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.
Eg : The motion of an I.C. engine valve (these are kept on
their seat by a spring) and the piston reciprocating inside an
engine cylinder are also the examples of successfully
constrained motion.

Classification of Kinematic Pairs
1.According to the type of relative motion between
the elements.
(a)Sliding pair-one can only slide relative to the other.
Eg: The piston and cylinder.

(b) Turning pair-one can only turn or revolve about a fixed axis of
another link.
Eg: A shaft with collars.
(c) Rolling pair-one rolls over another fixed link.
Eg:Ball and roller bearings.

(d) Screw pair-one element can turn about the other by screw
threads.
Eg: Bolt with a nut.
(e) Spherical pair-one element (with spherical shape) turns
or swivels about the other fixed element.
Eg: Attachment of a car mirror

2. According to the type of contact between the
elements.
(a)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.
Eg : sliding pairs, turning pairs and screw pairs.
(b) Higher pair - When the two elements of a pair have a
line or point contact when relative motion takes place.
Eg : toothed gearing, belt and rope drives, ball and roller
bearings and cam and follower.

3. According to the type of closure
(a) Self closed pair - When the two elements of a
pair are connected together mechanically in such a
way that only required kind of relative motion
occurs.
Eg : Lower pairs.
(b) Force - closed pair - When the two elements of
a pair are not connected mechanically but are kept
in contact by the action of external forces.
Eg : cam and follower

Kinematic Chain
When the kinematic pairs are coupled in such a way that the last
link is joined to the first link to transmit definite motion (i.e.
completely or successfully constrained motion), it is called a
kinematic chain.
For example, the crankshaft of an engine forms a kinematic pair
with the bearings which are fixed in a pair, the connecting rod
with the crank forms a second kinematic pair, the piston with
the connecting rod forms a third pair and the piston with the
cylinder forms a fourth pair. The total combination of these
links is a kinematic chain.
If each link is assumed to form two pairs with two adjacent
links, then the relation between the number of pairs ( p ) forming
a kinematic chain and the number of links ( l ) may be expressed in the
form of an equation :
l = 2 p – 4

Another relation between the number of links (l) and the number
of joints ( j ) which constitute a kinematic chain is given by the
expression :
j = 3/2 l − 2
Let us apply the above equations to the following cases to
determine whether each of them is a kinematic chain or not.
(i)If L.H.S. > R.H.S., Such type of chain is called locked chain
and forms a rigid frame or structure which is used in bridges and
trusses.(eg : Three links)
(ii)If L.H.S. = R.H.S., constrained kinematic chain of one
degree of freedom.(eg: Four links)
(iii)If L.H.S. < R.H.S., Such a type of chain is called unconstrained
chain i.e. the relative motion is not completely constrained.

Types of Joints in a Chain
1. Binary joint. When two links are joined at the same
connection, the joint is known as binary joint. For
example, a chain.
2. Ternary joint. When three links are joined at the same
connection, the joint is known as ternary joint.
3. Quaternary joint. When four links are joined at the
same connection, the joint is called a quaternary joint.

Mechanism
When one of the links of a kinematic chain is fixed, the
chain is known as mechanism. It may be used for transmitting
or transforming motion.
A mechanism with four links is known as simple mechanism,
and the mechanism with more than four links is known as
compound mechanism. When a mechanism is required to
transmit power or to do some particular type of work, it then
becomes a machine.
In such cases, the various links or elements have to be designed
to withstand the forces (both static and kinetic) safely.

Degrees of Freedom for Plane Mechanisms
It is defined as the number of input parameters (usually pair
variables) which must be independently controlled in order to
bring the mechanism into a useful engineering purpose.
The number of degrees of freedom of a mechanism is given by :
n = 3 (l – 1) – 2 j – h
This equation is called Kutzbach criterion for the movability of a
mechanism having plane motion.
It may be noted that
(a) When n = 0, then the mechanism forms a structure and no relative
motion between the links is possible.
(b) When n = 1, then the mechanism can be driven by a single input
motion.
(c) When n = 2, then two separate input motions are necessary to
produce constrained motion for the mechanism.
(d) When n = – 1 or less, then there are redundant constraints in the
chain and it forms a statically indeterminate structure.PAAVAI INSTITUTIONSDEPARTMENT OF MECHANICAL ENGINEERING

Inversion of Mechanism
The method of obtaining different mechanisms by fixing
different links in a kinematic chain, is known as inversion of the
mechanism.
Note: The part of a mechanism which initially moves with
respect to the frame or fixed link is called driver and that part of
the mechanism to which motion is transmitted is called follower.
Types of Kinematic Chains
The following three types of kinematic chains with four
lower pairs are important from the subject point of view :
1. Four bar chain or quadric cyclic chain,
2. Single slider crank chain, and
3. Double slider crank chain. PAAVAI INSTITUTIONSDEPARTMENT OF MECHANICAL ENGINEERING

Grashoff’s Law
(Four Bar Chain Or
Quadric Cycle Chain)
 Link 1 - Frame or Fixed link(AB):- The fixed link is
known as Frame
 Link 2 - lever or rocker or follower or output link
(BC):- The link which makes a partial rotation or
oscillates is known as lever.
 Link 3 - Connecting rod or coupler (CD):- The link
which connects the crank and lever is called as
connecting rod or coupler.
 Link 4 - Crank or driver or input link(AD): - In four bar
chain one of the links in particular the shortest link will
make a complete revolution relative to other three links,
is known as crank or driver.
 Definition: “Grashoff’s law states that the sum of the
shortest and longest link lengths should not be greater
than the sum of the remaining two link lengths, if there is
to be continuous relative motion between the two links”
 From fig ,
Let, Link 3 be the length of the longest link
Link 4 be the length of the shortest link
Link 1 & 2 be the lengths of the other two links
Acc to Grashoff’s law

Inversion of four bar chain
1.Beam engine ( Crank and lever mechanism)
2.Coupling rod of a locomotive ( Double crank mechanism)
3.Watt’s indicator mechanism ( Double lever mechanism)
Beam engine
( Crank and lever
mechanism ):-
The mechanism of a beam engine which
consist of four links as shown in fig.
 In this mechanism when crank rotates about
the fixed centre (A) , the lever oscillates about
a fixed centre (D).
 The end E of the lever CDE is connected to
a piston rod which reciprocates due to rotation
of the crank.
In other words the purpose of this
mechanisms is to convert rotary motion into
reciprocating motion

Coupling rod of a locomotive ( Double
crank mechanism)
 The mechanism of a coupling rod of a
locomotive which consist of a four links
as shown in fig.
 In this mechanism, the link AD and BC
(having equal length) act as crank and
are connected to the respective wheels.
 The link CD act as a coupling rod and
the link AB is fixed in order to maintain
a constant centre to centre distance
between them.
 This mechanism is meant for
transmitting rotary motion from one
wheel to the other wheel.

Watt’s indicator mechanism ( Double lever mechanism) A watt’s indicator mechanism which consists of
four links as shown in fig.
 It may be noted that BF and FD form one link
because these two parts have no relative motion
them.The link CE and BFD act as levers.
 The displacement of the link BFD is directly
proportional to the pressure of gas or steam
which act on indicator plunger.
 One any small displacement of a mechanism the
tracing point E at the end of the link CE traces
out approximately a straight line.

Inversion of Slider crank chain
Slider Crank Chain
When one of the turning pairs of a four bar chain is replaced
by a sliding pair, it is known as single slider chain or slider
crank chain.
1.Reciprocating engine
2.Reciprocating compressor
3.Pendulum pump or Bull engine
4.Oscillating cylinder engine
5.Rotary internal combustion engine
6.Crank and slotted lever quick return motion mechanism
7.Whitworth quick return motion mechanism
8.Hand pump

Reciprocating engine
 Link 1- Fixed link
 Link 2- Crank
 Link 3- Connecting rod
 Link 4- Slider or Piston
From fig,
It is a reciprocating
engine Link 4 is the driver.
Reciprocating compressor
 Link 1- Fixed link
 Link 2- Crank
 Link 3- Connecting rod
 Link 4- Slider or Piston
From fig,
It is a reciprocating
compressor Link 2 is the
driver.

Pendulum pump or Bull engine
 In this mechanism, the inversion is obtained by
Fixing the cylinder or link 4 (Sliding pair) as
shown in fig.
 In this case when the crank (Link 2) rotates, the
connecting rod (Link 3) oscillates about a pin
pivoted to the fixed link 4 at A and the piston
attached to the piston rod (Link 1) reciprocates.
 In this mechanism is used to supply feed water to
boilers.

Oscillating cylinder engine
 The arrangement of oscillating cylinder engine mechanism as shown in fig.
Which is used to reciprocating motion into rotary motion.
 When the crank (Link 2) rotates, the piston attached to piston rod (Link 1)
reciprocates and the cylinder (Link 4) oscillates about a pin pivoted to the
fixed Link 3 at B

Rotary internal combustion engine or
Gnome engine
 In this mechanism a crank 2 is fixed, Link 3 is connecting rod,
Link 4 is piston and Link 1 is cylinder.
 From fig it can be observed that with the rotation of Link 3, the
Link 1(cylinders) rotates about point O and piston 4 reciprocates
on it.
 This also implies that if the piston is made to reciprocates on the
Link 1(Cylinder) the crank 3 will rotate about A and the Link 1
about point O.
 In a rotary engine the crank 2 is fixed and the body 1 (Link 1 or
cylinder) rotates where as in reciprocating engine the body 1 is
fixed and crank 2 rotates about point O.

Crank and slotted lever quick return motion
mechanism  This mechanism is mostly used in shaper and
slotting machine, which is shown in fig.
 In this mechanism link3 is fixed, and the driving
crank 2 rotates with uniform angular speed
about fixed centre a.
 A slider is attached at the end of driving crank
which also reciprocates in slotted link 4 and thus
causes oscillate the slotted link about point c.
 The link 5 transmit the motion from link ce to
ram which carries the tool.
 Since driving crank rotates at uniform angular
speed, the ratio of cutting stroke to return stroke
time will be given by,
 Since φ is less than θ the time required for return
stroke is less than cutting stroke. Hence this
mechanism is called as quick return mechanism.

Whitworth quick return motion mechanism The withworth quick return mechanism is
used in shaper machine which is shown in
fig.
 In this mechanism driving crank 3 is rotates
in clockwise direction with uniform angular
speed.
 The slider c which attached at the end of
driving link is also reciprocates in slotted
link 1 and cause to oscillate the slotted link
1 about pivot point b.
 The link 5 is attached at the end of slotted
link 1 which carries the ram and tool.

Hand pump
 In this mechanism, the link
1 reciprocate vertically in
fixed link 4, at the same time
link 2 and link 3 will
oscillates about the pin joint
‘a’ and ‘b’ respectively.

Double slider crank chain
Inversion of double slider crank chain
Double slider crank chain:
 A kinematic chain which consists of two
turning pairs and two sliding pairs is known
as double slider crank chain. From fig. the
link 2 and 3 form two turning pairs, the link
2 and 1 form one sliding pair and link 4 and
1 form the second sliding pair.
1.Elliptical trammels.
2.Scotch yoke mechanism,
3.Oldham’s coupling. PAAVAI INSTITUTIONSDEPARTMENT OF MECHANICAL ENGINEERING

Elliptical trammels:
 The elliptical trammels is an instrument
used for drawing ellipse.
 When the link 1 and 3 slide along their
respective grooves, any point on the link
2 such as P traces out an ellipse on the
surface of link 4 as shown in fig.
Scotch yoke mechanism
 This mechanism is used for converting
rotary motion into a reciprocating
motion which is shown in fig.
 When the crank rotates about B as centre
the link 1 reciprocates in the fixed link 4.

Oldham’s coupling
 An oldham’s coupling is used
for connecting two parallel
shafts whose axes are at a
small distance apart, is shown
in fig.
 The link 1 and link 3 form
turning pair with link 2 and
these flanges have diametrical
slots cut in their inner faces,
which is shown in fig.
 The intermediate piece (link 4)
which is a circular disc have
two tongue (diametrical
projections) T1 and T2 on each
face at right angles to each
other as shown in fig.

MECHANICAL ADVANTAGE
The mechanical advantage may also be defined as the ratio of
output torque to the input torque.
Let TA = Driving torque, TB = Resisting torque,
A and B = Angular velocity of the driving and driven links
respectively.
 Ideal mechanical advantage, M.A. (ideal) = TB / TA
TRANSMISSION ANGLE
For a 4bar linkage, the transmission angle ( ) is defined as theμ
acute angle between the coupler and the follower.

UNIVERSAL OR HOOKE’S JOINT
A Hooke’s joint is used to connect two shafts, which are
intersecting at a small angle.

Machine :

KOM-UNIT-1-BASICS OF MECHANISMS

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