Theory of machines

Presented By:- Sourabh Kumar
THEORY OF MACHINES

THEORY OF MACHINES
Kinematics of machine
(KOM)
Dynamics of machine
(DOM)
 Kinematics: To study the
motion of bodies without
reference to the forces
which are cause this motion,
i.e it’s relate the motion
variables (displacement,
velocity, acceleration) with
the time.
Kinematics as a field of
study is often referred to as
the “Geometry of motion”
 Statics: which deals with the
forces and their effects,
while the machine parts are
rest.
 Dynamics: To study the
motion which deals with
the forces and their
effects, while acting upon
the machine parts in
motion.
 Kinetics: which deals with
relationship between the
motion of bodies and its
cause, namely “forces and
torque”.

SIMPLE MECHANISM ?
 Mechanism: is a combination of rigid bodies
which are formed and connected together by
some means, so that they are moved to perform
some functions, such as the crank- connecting
rod mechanism of the I.C. engines, steering
mechanisms of automobiles……. etc.
Can
crusher
Lift platform Front loader

Geneva Drive is
a Gear
Mechanism
Universal Knuckle
Joint
Mechanisam

When a mechanism is required to transmit power or to do
some particular type of work, then it becomes a Machine.
Working of an IC Engine (Machine)

Maufacturing In Industry by Machines

DIFFERENCE BETWEEN MACHINE AND
MECHANISM
• The similarity between machines and mechanisms is that
– they are both combinations of rigid bodies
– the relative motion among the rigid bodies are definite.
The difference between machine and mechanism is that
machines transform energy to do work, while
mechanisms do not necessarily perform this function.
“All machines are mechanisms. But all mechanisms are
not machines”.

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
Difference Between a Machine and a Structure

Kinematic Link or Element ?
 Each part of a machine, which having some relative
motion w.r.t some other part, is known as a
kinematic link (or simply link) or element.
A link may consist of several parts, which are rigidly
fastened together, so that they do not move relative
to one another.
For example, in a reciprocating steam engine, as
shown in Fig piston, piston rod and crosshead
constitute one link ; connecting rod with big and
small end bearings constitute a second link ; crank,
crank shaft and flywheel a third link and the
cylinder, engine frame and main bearings a fourth
link.

TYPES OF LINKS
In order to transmit motion, the driver and the follower may
be connected by the following three types of links :
1. Rigid link.
A rigid link is one which does not undergo any deformation
while transmitting motion. Strictly speaking, rigid links do
not exist. However, as the deformation of a connecting rod,
crank etc. of a reciprocating steam engine is not
appreciable, they can be considered as rigid links.
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.

Kinematic Pair ?
Kinematic Pair
The two links or elements of a machine, when in contact with
each other, are said to form a pair. If the relative motion
between them is completely or successfully constrained (i.e.
in a definite direction), the pair is known as kinematic pair.
Types of Constrained Motions
Following are the three 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.
For example, the piston and cylinder (in a steam engine)
form a pair and the motion of the piston is limited to a
definite direction (i.e. it will only reciprocate) relative to the
cylinder irrespective of the direction of motion of the crank.

The motion of a square bar in a square hole, as shown in Fig.
1, and the motion of a shaft with collars at each end in a
circular hole, as shown in Fig. 2, are also examples of
completely constrained motion.
Fig.
1
Fig.2

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.
A circular bar or shaft in a circular hole, as shown in Fig. 3, is an
example of an incompletely constrained motion as it may either
rotate or slide in a hole. These both motions have no relationship
with the other.
Fig.3

Incompletely constrained motion.

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.
Consider a shaft in a foot-step bearing as shown in Fig. 4.
The shaft may rotate in a bearing or it may move upwards.
This is a case of incompletely constrained motion. But if the
load is placed on the shaft to prevent axial upward
movement of the shaft, then the motion of the pair is said to
be successfully constrained motion.
The motion of an I.C. engine valve and the piston
reciprocating inside an engine cylinder are also the
examples of successfully constrained motion.
Fig.4

1. According to the type of relative motion
between the elements.
(a) 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.
Classification of Kinematic Pairs

(b) 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.
(c) Spherical pair.
When the two elements of a
pair are connected in such a
way that one element (with
spherical shape) turns or
swivels about the other fixed
element, the pair formed is
called a spherical pair. The
ball and socket joint,
attachment of a car mirror,
pen stand etc., are the
examples of a spherical pair.

(d) Rolling pair.
When the two elements of a pair
are connected in such a way that one
rolls over another fixed link, the
pair is known as rolling pair. Ball and
roller bearings are examples of
rolling pair.
(e) Screw pair.
When the two elements
of a pair are connected
in such a way that one
element can turn about
the other by screw
threads, the pair is
known as screw pair.
The lead screw of a lathe
with nut, and bolt with a
nut are examples of a
screw pair.

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, the pair
formed is known as lower pair. It will be seen that sliding
pairs, turning pairs and screw pairs form lower pairs.
(b) 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.

Degrees of freedom (DOF):
• It is the number of independent coordinates required to
describe the position of a body in space.
• A free body in space in fig can have six degrees of
freedom. I.e., linear positions along x, y and z axes and
rotational/angular positions with respect to x, y and z
axes.
• In a kinematic pair, depending on the constraints
imposed on the motion, the links may loose some of the
six degrees of freedom.

Based On The Possible Motions
(Few Important Types Only)
Name of Pair Letter Symbol
D.O.F
1. Revolute / Turning Pair R 1
2. Prismatic / Sliding Pair P 1
3. Helical / Screw Pair H 1
4. Cylindrical Pair C 2
5. Spherical / Globular Pair S (or) G 3
6. Flat / Planar Pair E 3
7. Cylindric Plane Pair Cp 4
8. Spheric Plane Pair Sp 5
D.O.F.= 1
Example- In Turning PairRestraints motions = 3T+2R=5
D.O.F .= 6 (Total Possible motion)- Restraints to motion
D.O.F =6-5=1

Kinematic Chain ?
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.
• In other words, a kinematic chain may be defined as a
combination of kinematic pairs, joined in such a way that
each link forms a part of two pairs and the relative motion
between the links or elements is completely or
successfully constrained.

LINK / ELEMENT
KINEMATIC PAIR / JOINT
KINEMATIC CHAIN
MECHANISM
MACHINE

Gear ?
A gear is a wheel with teeth on its outer edge.
The teeth of one gear mesh (or engage) with the teeth of
another.
Above
Gears meshing or engaged

Driver and Driven
Two meshed gears always rotate in opposite directions.
Driven gear Driver gear

Idler gear
Driver
Idler gear
Driven

Generally, the Gear Ratio is calculated
by counting the teeth of the two gears,
and applying the following formula:
Gear ratio = Number of teeth on driven
gear
Number of teeth on driver
gear
Driver
Driven
Gear Ratio

Gear Ratio - Calculation
A 100 tooth gear drives a 25 tooth
gear. Calculate the gear ratio for the
meshing teeth.
Gear ratio = Number of teeth on driven
gear
Number of teeth on driver
gear
Gear ratio = driven25 = 1
driver 100 4
This is written as 1:4

Gear Speed :- Calculation
A motor gear has 28 teeth and
revolves at 100 rev/min. The driven
gear has 10 teeth.What is its
rotational speed?
28 teeth,
driver
10 teeth,
driven
Speed of driven gear = Number of teeth on driver gear
x 100
Number of teeth on driven gear
Speed of driven gear = driver = 28 x 100 = 280 rev/min
driven 10

TYPES OF GEARS
According to the position of axes of the shafts
 Parallel
Spur
Helical
Rack and Pinion
 Intersecting
Bevel Gear
 Neither Parallel nor Intersecting
Worm and worm wheel

Spur Gears
 Used in transmitting torque between parallel shafts.
 Teeth are cut parallel to shaft axis.
 Spur gears have high power transmission efficiency.
 They are compact, easy to install & offer constant velocity ratio.
 Spur gears produce a lot of noise when operating at high
speeds & Gear teeth experience a large amount of stress.
 They cannot be used for long distance power transmission.
 If one of the gears has infinite diameter, Rack and pinion
arrangement

Applications:-
-Spur gears have a wide range of applications. They are used in:
-Metal cutting machines
-Power plants
-Marine engines
-Mechanical clocks and watches
-Fuel pumps
-Washing Machines
-Gear motors and gear pumps
-Rack and pinion mechanisms
-Material handling equipments
-Automobile gear boxes
-Steel mills
-Rolling mills

Helical Gear
 Helical gears have their teeth inclined to the axis of the shafts
in the form of a helix, hence the name helical gears.
Used in transmitting torque between parallel shafts
 Teeth are cut at an angle with the shaft axis
 Helical gears can be meshed in
parallel or crossed orientations.
 When two of the teeth start to engage, the contact is gradual-
starting at one end of the tooth and maintaining contact as the
gear rotates into full engagement.

 The typical range of the helix angle is about 15 to
30 deg. The thrust load varies directly with the
magnitude of tangent of helix angle. Single helical
gears impose both radial loads and thrust loads
on their bearings and so require the use of thrust
bearings.
In order to reduce the axial thurst, hence to
protect the shaft bearing so, we introduce Double
Helical Gear (Herringbore Gear)

Applications:-
•Helical gears are normally preferred to work under heavy
load efficiently.
•When we need silent operation such as in automobile
applications, we prefer to use helical gears as such gears
work silently and smoothly.
•Helical gears are used in fertilizer industries, Printing
industries and earth moving industries, Rolling mills, section
rolling mills, power and port industries, textile industries,
plastic industries, food industries, conveyors, elevators,
blowers, compressors, oil industries & cutters.

Bevel Gears
 Used to transmit rotary motion between intersecting shafts.
 Tooth-bearing faces of the gears are conically shaped.
 Bevel gears are most often mounted on shafts that are 90
degrees apart, but can be designed to work at other angles
as well.
 The pitch surface of bevel gears is a cone.
 Straight Bevel gear teeth have similar characteristics to spur
gears and also have a large impact when engaged. Like spur
gears, the normal gear ratio range for straight bevel gears is
3:2 to 5:1.
 Spiral Bevel gears the teeth are oblique. They are quieter and
can take up more load as compared to straight bevel gears.

Straight Bevel
Gear
Spiral Bevel Gear
Mitre
Gears

Applications:-
• Due to their ability to change the direction of force and the
operating angle of the machinery, bevel gears are used in many
diverse applications such as locomotives, marine applications,
automobiles, printing presses, cooling towers, power plants,
steel plants, railway track inspection machines, etc.
• One of the most common uses is in the
hand drill.
• In differential drives of motor vehicles,
where bevel gears enable the transmission
of power to two axles spinning at different
speeds, such as those on a cornering
automobile.
• Helicopter engines utilize bevel gears to
redirect the shaft of the engine to the vertical
turn of the rotors. These gears are also used in
the functioning of mechanical garage doors.

Worm and Worm Wheel/Gear
 Worm gears are used to transmit power at 90° and where
high reductions are required.
 The axes of worm gears shafts cross in space.
 The shafts of worm gears lie in parallel planes and may be
skewed at any angle between zero and a right angle.
 In worm gears, one gear has screw threads. Due to this,
worm gears are quiet, vibration free and give a smooth
output. Worm gears and worm gear shafts are almost
invariably at right angles.
Worm (Driver)
Very high spiral
angle with less
diameter
Worm Wheel
(Driven)
Very less spiral
angle
With more
diameter

Applications:-
Worm and Worm Wheel/Gear can be used for reducing
speed and increasing torque.
Worm gears are used in large gear reductions. Gear ratio
ranges of 5:1 to 300:1 are typical.
High velocity ratio of the order of 100 can be obtained in a
single step.
Due to self-locking & less space, it used
in many applications & they are
•Gate control mechanisms
•Hoisting machines
•Automobile steering mechanisms
•Lifts
•Conveyors
•Presses
•Used in Wiper motor
•Shutter lifting mechanism at
opining and closing times at stores

Gear Train
Definition:
When two or more gears are made to mesh with each
other to transmit power from one shaft to another, such
a combination is called ‘gear train or train of toothed
wheels’.
Types of gear trains:
1. Simple gear train,
2. Compound gear train,
3. Reverted gear train, and
4. Epicyclic gear train.

Simple gear train
Definition:
When there is only one gear
on each shaft as shown in
fig., it is known as simple
gear train.
When the distance between
two shafts is small, the two
gears 1 and 2 are made to
mesh with each other to
transmit motion from one
shaft to other as shown in fig.
Since the gear 1 drives 2,
therefore gear 1 is called the
driver and the gear 2 is called

Compound gear train
Definition:
When there are more than one gear
a shaft as shown in fig., it is known
as compound gear train.
Compound gear trains are useful
in bridging over the space between
the driver and the driven.

Reverted gear train
Definition:
When the axes of the first gear
and the last gear are co-axial, then
the gear train is known as
reverted gear train as shown in
figure.
Here the gear 1 drives the gear 2 in
the opposite direction.
Since the gear 2 and 3 form a
compound gear and the gear 3 will
rotate in the same direction as of
gear 2.
the gear 3 will drive the gear 4 in the
same direction as of gear 1.
hence the motion of the first gear

Epicyclic gear train
In an epicyclic gear train, the axes
of the shafts, over which the gears
are mounted, may move relative to
a fixed axis.
A simple epicyclic gear train is
shown in figure.
When a gear 1 and arm 3 and gear
2 and arm 3 have a common axis.
If the arm is fixed, the gear train is
simple and gear 1 can drive gear 2
or vice-versa, but is gear 1 is fixed
and the arm is rotated about the
axis then the gear 2 is forced to
rotate upon and around the gear 1.
Such a motion is called epicyclic.

Compound Epicyclic gear train-sun and
planet gear

What is a Governor??
A speed-sensitive device, designed to maintain a
constant engine speed regardless of load variation.

Functions of Governor
 To provide the engine with the feedback
mechanism to change speed as needed and to
maintain a speed once reached.
 To control the engine speed by regulating the
quantity of fuel as per the variation of load.
 When the load on an engine increases, its speed
decreases, then the governor increases the
supply of fuel & vice-versa in case of decrease of
load.
 Governor has no control over the change in speed
within the cycle and they are not able to store the
energy as well.

Types of Governor
1. Centrifugal Governor- The centrifugal
governors are based on the balancing of centrifugal
force on the rotating balls for an equal and opposite
radial force, known as the controlling force. It
consist of two fly balls of equal mass, which are
attached to the arms.
2. Inertia Governor- In inertia governor the fly balls
are arranged in such a manner that the angular
acceleration or retardation of the governor shaft
will change the position of these balls.
Inertia governors gives more rapid response to the effect of change of
load but they are practically difficult to make because of partial
balancing of the rotating parts of governors, therefore centrifugal
governors are used widely.

Centrifugal governor
Pendulum type Loaded type
Watt governor
Dead weight
governor
Spring controlled
governor
Porter governor Proell governor
Pickering
governor
Hartung
governor
Wilson - Hartnel
governor
Hartnell
governor
Types of Centrifugal Governor

Working of Centrifugal Governor

 Governor balls or fly balls revolve with a spindle,
which is driven by the engine through bevel gears.
 The upper ends of the arms are pivoted to the
spindle, so that the balls may rise up or fall down as
they revolve about the vertical axis.
 The sleeve revolves with the spindle but can slide up
& down.
 The balls and the sleeve rises when the spindle
speed increases, and falls when the speed
decreases.
 The sleeve is connected by a bell crank lever to a
throttle valve.
 The supply of the working fluid decreases when the
sleeve rises and increases when it falls.
 When the load on the engine increases, the engine
and the governor speed decreases, this results in the
decrease of centrifugal force on the balls. Hence the
balls move inwards and the sleeve moves down-

The downward movement of the sleeve operates a
throttle to increase the supply of working fluid and
thus the engine speed is increased.

Flywheel
• In practice, there are two following types of cases where reciprocating
engine mechanism is used :
1) An internal combustion engine or a steam engine which is used as a
prime mover to drive generators, centrifugal pumps, etc.
2) A punching machine which is driven by a prime mover like electric
motor.
• In both these cases either a variable torque is supplied where demand
is a constant torque or demand is variable torque whereas constant
torque is supplied.
• In both these cases there is mismatch between the supply and
demand. This results in speed variation.
• In case of generators, speed variation results in change in frequency
and variation in voltage.

Cont…
 On the other hand, punching machine requires energy at
small interval only when punching is done.
 To supply such large energy at the time of punching, motor
of high power shall be required.
 At the same time, there will be large variation in speed.
 To smoothen these variations in torque, flywheel is used
which works as an energy storage.
 This results in usage of low power motor in punching
machine.
 A flywheel is an inertial energy-storage device. It absorbs
mechanical energy and serves as a reservoir, storing energy
during the period when the supply of energy is more than the
requirement and releases it during the period when the
requirement of energy is more than the supply.

Rim
Type Flywheel
Tapered
Disc Flywheel

Flywheel’s-Function, need and
Operation
 The main function of a flywheel is to smoothen out variations in the
speed of a shaft caused by torque fluctuations.
 If the source of the driving torque or load torque is fluctuating in
nature, then a flywheel is usually called for.
 Many machines have load patterns that cause the torque time function
to vary over the cycle.
 Internal combustion engines with one or two cylinders are a typical
example. Piston compressors, punch presses, rock crushers etc. are
the other systems that have flywheel.
 Flywheel absorbs mechanical energy by increasing its angular
velocity and delivers the stored energy by decreasing its velocity
 A flywheel used in machines serves as a reservoir, which stores
energy during the period when the supply of energy is more than the
requirement, and releases it during the period when the requirement
of energy is more than the supply.

Cont…
 In case of steam engines, internal combustion engines, reciprocating
compressors and pumps, the energy is developed during one stroke
and the engine is to run for the whole cycle on the energy produced
during this one stroke.
 For example, in internal combustion engines, the energy is developed
only during expansion or power stroke which is much more than the
engine load and no energy is being developed during suction,
compression and exhaust strokes in case of four stroke engines and
during compression in case of two stroke engines.
 The excess energy developed during power stroke is absorbed by the
flywheel and releases it to the crankshaft during other strokes in
which no energy is developed, thus rotating the crankshaft at a
uniform speed.
 Hence a flywheel does not maintain a constant speed; it simply
reduces the fluctuation of speed.

Cont…
 In other words, a flywheel controls the speed variations caused by the
fluctuation of the engine turning moment during each cycle of
operation.
 In machines where the operation is intermittent like punching
machines, shearing machines, riveting machines, crushers, etc., the
flywheel stores energy from the power source during the greater
portion of the operating cycle and gives it up during a small period of
the cycle.
 Thus, the energy from the power source to the machines is supplied
practically at a constant rate throughout the operation.

Difference between Flywheel and
Governor??
FLYWHEEL GOVERNOR
 used because of variation of
speed due to variation in the
output torque of engine
during a cycle.
 Limits the inertiable
fluctuation of speed during
each cycle which arises due
to fluctuation of turning
moment on crank shaft.
 Stores excess of rotational
energy from the power
stroke and supply back
during non- power strokes
of the cycle.
 It controls the speed for one
cycle only so it is
continuous.
 used because of variation of
speed due to variation in the
load on the engine.
 Controls the mean speed of
engine by varying the fuel
supply which arises due to
variation of load.
 When load on the engine
increases, speed decreases,
it increases the flow of fuel
to keep the mean speed
constant.
 It maintains constant mean
speed over a period of time
so it is discrete.

Theory of machines

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