The document provides an overview of dynamics of engine mechanisms. It discusses key topics like dynamics force analysis, inertia forces, D'Alembert's principle, velocity and acceleration analysis of reciprocating engines using graphical and analytical methods, turning moment diagrams, work done per cycle, flywheel analysis and cam dynamics. The document contains examples of force analysis on reciprocating parts of an engine, dimensions of flywheel rim, and operation of flywheel in punching press. It also provides questions for practice on related concepts.

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By
Dr. Manvandra Kumar Singh
(Ph.D., M.Tech. & B.Tech.)
Assistant Professor
Department of Mechanical Engineering
Amity School of Engineering & Technology
Amity University, Madhya Pradesh
12/23/2022
MODULE – I
DYNAMICS OF ENGINE MECHANISMS

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Introduction
The subject 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 a machine, and
forces which act on them.
The knowledge of this
essential for an engineer in designing
subject is very
the
various parts of a machine.
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Sub-divisions of Theory of
Machines
The Theory of Machines may be sub-
divided into the following four branches :
1. Kinematics
2. Dynamics
3. Kinetics
4. Statics
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1. Kinematics
It is that branch of Theory of Machines
which deals with the relative motion between
the various parts of the machines.
2. Dynamics
It is that branch of Theory of Machines
which deals with the forces and their effects,
while acting upon the machine parts in motion.
Sub-divisions of Theory of
Machines
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Sub-divisions of Theory of
Machines
3. Kinetics
It is that branch of Theory of Machines
which deals with the inertia forces which arise
from the combined effect of the mass and
motion of the machine parts.
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4. Statics
It is that branch of Theory of Machines
which deals with the forces and their effects
while the machine parts are at rest. The mass
of the parts is assumed to be negligible.
Sub-divisions of Theory of
Machines
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Fundamental Concepts
Space: Is a region which extends in all directions
and contains everything in it. The position of a
body in space is determined w.r.t. a reference
system
Time: to define the succession of events, it is not
sufficient to indicate their position. The time of
events is required, So time is as measure of the
succession of events.
Matter: Any substance, which occupies space. It is
made up of atoms and molecules
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Body: Any matter that is bounded by a closed
surface
Rigid body: Is that which does not change its shape
or size when subjected to external forces
Deformable body: is that which changes its shape
or size when subjected to external forces
Mass: Quantity of matter it contains. It does not
vary with the location and orientation of the body
Particle: Body of negligible dimension . It occupies
no space. i.e. no size, but has a definite mass
concentrated at a point
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Inertia: Resistance offered by a matter to any
change of its state of motion
Solid: Asubstance possessing a definite shape and a
definite volume
Force: It is a pull or push which acting on a body
changes or tends to change, the state of rest or
uniform motion of the body.
It is completely characterized by its point of
application, its magnitude and direction.
Forced System or system of forces: When a
number of forces act on a body
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Weight: Weight of a body is the force with which
the earth attracts the body towards its centre.
W = m.g
Equilibrium: A body acted upon by a system of
forces is said to be in equilibrium, if it either
remains in a state of rest or continues to move in a
straight line with uniform velocity.
Motion: A body is said to be in motion, when it
changes its position w.r.t. other bodies. Thus the
relative change in position is called motion.
Motion involves both space and time.
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NEWTON’S LAW OF MOTION
1st Law: Every body continues in its state of rest
or uniform motion in a straight line unless an
external resultant forces acts on it.
2nd Law: The rate of change of momentum of a
body is directly proportional to the force acting
on it and takes place in the direction of force.
3rd Law: To every action there is an equal and
opposite reaction
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UNIT-I
FORCEANALYSIS
DYNAMICS OF MACHINES
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Static force analysis: When the inertia effect
due to the mass of the machine components are
neglected in the analysis of the mechanism
Dynamic force analysis: When the inertia
forces are considered in the analysis of the
mechanism
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Inertia force
A force equal in magnitude but opposite in
direction and collinear with the impressed
force producing the acceleration, is known as
inertia force.
Inertia force = – m x a
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Inertia torque
The inertia torque is an imaginary torque,
which when applied upon the rigid body,
brings it in equilibrium position. It is equal to
the accelerating couple in magnitude but
opposite in direction.
Inertia Torque = -I x α
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D-Alembert’s principle
D-Alembert’s principle states that the
resultant force acting on a body together with
the reversed effective force (or inertia force),
are in equilibrium.
٤F = 0
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Dynamic Analysis in reciprocating
engines
The velocity and acceleration of the reciprocating parts of
the steam engine or internal combustion engine may be
determined by graphical method or analytical method.
The velocity and acceleration, by graphical method, may
be determined by one of the following constructions:
1. Klien’s construction,
2. Ritterhaus’s construction, and
3. Bennett’s construction.
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19. Dynamic Analysis in reciprocating
engines - Analytical Method
Consider the motion of a crank and connecting rod of
a reciprocating steam engine as shown in Figure.
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Conti…
Let OC be the crank and PC the connecting rod. Let
the crank rotates with angular velocity of rad/s and
the crank turns through an angle θ from the inner
dead centre (briefly written as I.D.C).
Let x be the displacement of a reciprocating body P
from I.D.C. after time t seconds, during which the
crank has turned through an angle θ.
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Let
l = Length of connecting rod between the centres,
r = Radius of crank or crank pin circle,
θ = Inclination of crank to the line of stroke PO
n = Ratio of length of connecting rod to the radius of crank
= l/r.
Conti…
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22. Velocity of the piston
Conti…
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23. Conti…
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24. Conti…
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25. Conti…
Acceleration of the piston
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26. Conti…
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Forces on the Reciprocating Parts of an
Engine
1. Piston effort
It is the net force acting on the piston or
crosshead pin, along the line of stroke. It is denoted
by FP.
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28. Horizontal engine
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29. Conti…
2. Force acting along the connecting rod, FQ
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FQ

30. Conti…
3.Thrust on the sides of the cylinder walls (or)
normal reaction on the guide bars, FN
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FN

31. Conti…
4. Crank-pin effort, FT
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32. Conti…
5. Thrust on crank shaft bearings, FB
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Conti…
6. Crank effort or turning moment or torque on the
crank shaft.
The product of the crankpin effort (FT) and the crank
pin radius (r) is known as crank effort or turning moment
or torque on the crank shaft.
T = F × r
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Turning moment diagram
• The turning moment diagram (also known as
crank effort diagram) is the graphical
representation of the turning moment or crank-
effort for various positions of the crank. It is
plotted on cartesian co-ordinates, in which the
turning moment is taken as the ordinate and
crank angle as abscissa.
• It is also known as T-M diagram.
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35. The variation of torque (T) during one revolution of
the crankshaft of a steam engine or an I C Engine
is:
T = Ft ˟ r
= F* x r x [sin θ + (sin 2θ/2√n² - sin² θ)]
Where,
Ft -tangential force or force normal to crank
r-crank radius
F* - net force acting on the piston
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Conti…

36. Single cylinder engine
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37. Multi cylinder engine
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38. IC engine
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39. Work done per cycle
• The work done per cycle (in N-m or joules) may
be obtained by using the following two relations :
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40. Work done per cycle
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Fluctuation of Energy
• The variations of energy above and below the mean
resisting torque line are called fluctuations of energy.
• The difference between the maximum and the
minimum energies is known as maximum fluctuation of
energy.
Maximum fluctuation of energy,
E = Maximum energy – Minimum energy
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Coefficient of
Fluctuation of Energy
• It may be defined as the ratio of the maximum
fluctuation of energy to the work done per cycle.
CE = Maximum fluctuation of energy / Work done per cycle
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Flywheel
• 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.
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45. Coefficient of
Fluctuation of Speed
The
minimum
difference between the maximum and
speeds during a cycle is called the
maximum fluctuation of speed. The ratio of the
maximum fluctuation of speed to the mean speed is
called the coefficient of fluctuation of speed.
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Energy Stored in a
Flywheel
Energy stored, E = mk2ω2CS = mv2CS
Where,
m = Mass of the flywheel in kg,
k = Radius of gyration of the flywheel in metres
ω = angular speed in rad/s2
Cs = Coefficient of Fluctuation of Speed
v = Mean linear velocity
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47. Question.1. The maximum and minimum speed of flywheel is 242 rpm
and 238 rpm respectively. The mass of flywheel is 2600 kg and
radius of gyration is 1.8 m. Find the mean speed of the flywheel,
maximum fluctuation of energy and coefficient of fluctuation of
speed.
Question.2. Find the maximum and minimum speeds of a flywheel of
mass 5200 kg and radius of gyration 1.8 m when the fluctuation of
energy is 100800 Nm. The mean speed of engine is 180 r.p.m.
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Question 3:

50. Question. 4. The areas above and below the mean torque line for
an IC engine are -25, +200, -100, +150, -300, +150 and -75 mm²
taken in order. The scale for the turning moment diagram is 1 mm
vertical scale = 10 Nm and 1mm horizontal scale = 1.5°.the mass
of the rotating parts are 45 kg with a radius of gyration of 150
mm. if the engine speed is 1500 rpm, find the cof of speed.
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Dimensions of the
Flywheel Rim
Tensile stress or hoop stress,σ = ρR2ω2 = ρv2
Where,
ρ = Density of rim material in kg/m3,
N = Speed of the flywheel in r.p.m.,
ω =Angular velocity of the flywheel in rad/s,
v = Linear velocity at the mean radius in m/s
= ω R = DN/60
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Mass of the rim, m = Volume × density = πDA ρ
If the cross-section of the rim is a
rectangular, then
A = b × t
where b = Width of the rim, and
t = Thickness of the rim.
Conti…
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54. Question 5. The turning moment diagram as shown in figure, for a multi-cylinder
engine has been drawn to a scale of 1 mm to 500 N-m torque and 1 mm to 6° of
crank displacement. The intercepted area between o/p torque curve and mean
resistance line taken in order from one end, in sq. mm are: -30, +410, -280, +320, -
330, +250, -360, +280, -260 sq. mm when the engine is running at 800 rpm. The
engine has a stroke of 300 mm and fluctuation of speed is not to exceed 2% of the
mean speed.
Determine a suitable diameter and cross-section of the flywheel rim for a limiting
value of the some centrifugal stress of 7 N/mm³. the density of the material may be
assumed as 7200 kg/mm³. The width of the rim is to be 5 times the thickness.
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Operation of a Flywheel
in Punching Press
1. The function of a flywheel in an engine is to reduce
the fluctuations of speed, when the load on the crankshaft is
constant and the input torque varies during the cycle.
2. The flywheel can also be used to perform the same
function when the torque is constant and the load varies
during the cycle.
3. Such an application is found in punching press or in
a riveting machine.
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Dynamics of Cam
follower mechanism
Cam Dynamics
Cam dynamics is the study of cam follower systems
with considering the dynamic forces and torques developed
in it.
Types of cam systems
1. Rigid body cam systems
2. Elastic body cam systems
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Rigid cam system
If the members of the cam system are fairly rigid
and their speed is moderate, then the analysis of such
a cam system is known as analysis of rigid cam
system.
Elastic cam system
If the members of the cam system are elastic and
their speed is very high, then the analysis of such a
cam system is known as analysis of elastic cam
system
Conti…
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58. Thanking You!!!
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Disc W = 5000 N
100 mm
1 m

60. A
C
B
60 kg
800 mm
550 mm
250 mm