Kom dom lab manual 2017 regulation

(Approved by AICTE New Delhi, Permanently Affiliated to Anna University, Chennai
DEPARTMENT OF
MECHANICAL ENGINEERING
ME8511 KINEMATICS AND DYNAMICS LABORATORY
V SEMESTER - R 2017
Name :
Reg. No. :
Section :
LABORATORY MANUAL
Oovery , kanchipuram(Dt). Pin: 631 502
P.T.Lee CHENGALVARAYA NAICKER COLLEGE
OF ENGINEERIN& TECHNOLOGY
Prepared by:N.KRISHNAMOORTHY,M.E,(Ph.D)

ME8511 KINEMATICS AND DYNAMICS LABORATORY
 To supplement the principles learnt in kinematics and Dynamics of Machinery.
 To understand how certain measuring devices are used for dynamic testing.
List of Experiments
1. a) Study of gear parameters.
b) Experimental study of velocity ratios of simple, compound, Epicyclic and differential gear
trains.
2. a)Kinematics of Four Bar, Slider Crank, Crank Rocker, Double crank, Double rocker,
Oscillating cylinder Mechanisms.
b) Kinematics of single and double universal joints.
3. a) Determination of Mass moment of inertia of Fly wheel and Axle system.
b)Determination of Mass Moment of Inertia of axisymmetric bodies using Turn Table
apparatus.
c) Determination of Mass Moment of Inertia using bifilar suspension and compound
pendulum.
4. Motorized gyroscope – Study of gyroscopic effect and couple.
5. Governor - Determination of range sensitivity, effort etc., for Watts, Porter, Proell, and
Hartnell Governors.
6. Cams – Cam profile drawing, Motion curves and study of jump phenomenon
7. a) Single degree of freedom Spring Mass System – Determination of natural Frequency and
verification of Laws of springs – Damping coefficient determination.
b) Multi degree freedom suspension system – Determination of influence coefficient.
8. a) Determination of torsional natural frequency of single and Double Rotor systems.-
Undamped and Damped Natural frequencies.
b) Vibration Absorber – Tuned vibration absorber.
9. Vibration of Equivalent Spring mass system – undamped and damped vibration.
10. Whirling of shafts – Determination of critical speeds of shafts with concentrated loads.
11. a) Balancing of rotating masses. (b) Balancing of reciprocating masses.
12. a) Transverse vibration of Free-Free beam – with and without concentrated masses.
b) Forced Vibration of Cantilever beam – Mode shapes and natural frequencies.
c) Determination of transmissibility ratio using vibrating table.
CO1 Explain gear parameters, kinematics of mechanisms, gyroscopic effect and working of
lab equipments.
CO2 Determine mass moment of inertia of mechanical element, governor effort and range
sensitivity, natural frequency and damping coefficient, torsional frequency, critical
speeds of shafts, balancing mass of rotating and reciprocating masses, and
transmissibility ratio.
COURSE OBJECTIVES
COURSE OUTCOMES

LIST OF EXPERIMENTS
S. No NAME OF EXPERIMENTS DATE
STAFF
SIGN
1 DETERMINATION OF MOMENT OF INERTIA BY
OSCILLATION METHOD FOR FLY WHEEL
2 WHIRLING SPEED OF SHAFT
3
SPRING MASS SYSTEM – SERIES (FREE
VIBRATION)(DAMPED AND UNDAMPED)
4 TRI FILAR
5 TRANSVERSE VIBRATION- SIMPLY SUPPORTED BEAM
6
DETERMINATION OF MOMENT OF INERTIA BY
OSCILLATION METHOD FOR CONNECTING ROD
7 TRANSVERSE VIBRATION- CANTILEVER BEAM
8 CAM PROFILE ANALYSIS
9 BALANCING OF ROTATING MASSES
10
SPRING MASS SYSTEM – PARALLEL (FREE
VIBRATION)(DAMPED AND UNDAMPED)
11 TURN TABLE
12 COMPOUND PENDULAM
13
DETERMINE THE CHARACTERISTICS OF WATT,
HARTNEL, PORTER AND PROELL GOVERNOR
14 SINGLE AND TWO ROTOR SYSTEM
15 MOTORISED GYROSCOPE
16
DETERMINATION OF TRANSMISSIBILITY RATIO BY USING
VIBRATING TABLE
17 BI FILAR
18 TRANSVERSE VIBRATION OF FREE-FREE BEAM
19 BALANCING OF RECIPROCATING MASSES
20 SLIDER CRANK MECHANISM
21 SCOTCH YOKE MACHANISM
22 CRANK ROCKER
23 EPICYCLIC GEAR TRAIN
24 SIMPLE GEAR TRAIN
25 COMPOUND GEAR TRAIN
26 KINEMATICS OF UNIVERCAL JOINT
27 STUDY OF DIFFERENTIAL GEAR MECHANISM
28 STUDY OF GEAR PARAMETERS

EX.NO:1 DETERMINATION OF MOMENT OF INERTIA BY OSCILLATION
METHOD FOR FLY WHEEL
DATE:
AIM:
To determine the moment of inertia by oscillation for fly wheel
APPARATUS REQUIRED:
1. Fly wheel
2. Stop watch
DIAGRAM:
FLY WHEEL
FORMULA USED:
(i) Time period, tp = Time taken for three oscillation / 3 in s
(ii) Equivalent Length of simple pendulum, L = (𝑓𝑛
2
×g)/4π2 in m
(iii) Radius of gyration, 𝑘𝑔 = √(𝐿 × ℎ) − ℎ2 in m
(iv) Moment of Inertia, I = m (kg
2
) in kg- m2
Where,
g- Acceleration due to gravity = 9.81 m/s2
L- Equivalent length of simple pendulum
PROCEDURE:
1. Dimensions of the fly wheel such as outer diameter and inner diameter
are measured.
2. Then the fly wheel is hanged on knife edge support.
3. Time taken for 3 oscillations of flywheel is noted for 3 times.
4. Radius of gyration is calculated by using formula.
5. Finally calculate the mass moment of Inertia of the flywheel.
 240
15

OBESERVATIONS & SPECIFICATIONS:
Mass of fly wheel (m) = 1kg
Rim diameter, (D) = 240 mm = 0.24 m
Bore Diameter (d) = 20 mm = 0.02 m
Rim thickness (t) = 15 mm = 0.015 m
h=Rim diameter /2 = 0.24/2 = 0.12 m
TABULATION:
S.No. Suspension Time taken for 3
oscillation
Time period (tp)
Frequency
fn = 1/ tp
1
Fly wheel
2
3
Average frequency (fn) = …………………Hz
RESULT:-
Moment of inertia of the fly wheel I=…………………kg-m2

VIVA-QUESTIONS:
1. What is flywheel?
A flywheel is used to control the variations in speed during each cycle of an engine. A flywheel
of suitable dimensions attached to the crankshaft, makes the moment of inertia of the rotating
parts quite large and thus acts as a reservoir of energy.
2. Write the equation for moment of inertia by oscillation method for flywheel.
I =
e
Kω2
Where, I=Moment of inertia of the flywheel, ω =mean speed, e =maximum fluctuation of
energy, K= Coefficient of fluctuation of speed
3.What are the functions of flywheel?
The flywheel absorbs energy, its speed increases and when it releases energy the speed
decreases.
4. What is the maximum fluctuation of energy?
The difference between the maximum and the minimum energies is known as maximum
fluctuation of energy.
5. What is the Coefficient of Fluctuation of Energy?
It may be defined as the ratio of the maximum fluctuation of energy to the work done per
cycle.
6. What is maximum fluctuation of speed?
The difference between the maximum and minimum speeds during a cycle is called the
Maximum fluctuation of speed.
7. What is coefficient of fluctuation of speed?
The ratio of the maximum fluctuation of speed to the mean speed is called the coefficient of
fluctuation of speed.
8. What is coefficient of steadiness?
The reciprocal of the coefficient of fluctuation of speed is known as coefficient of steadiness.
9. The maximum fluctuation of energy in a flywheel is equal to. 2E.CS

EX.NO: 2 DETERMINATION OF WHIRLING SPEED
OF THE SHAFT
DATE:
AIM: To determine the critical speed of the shaft or whirling speed of shaft with concentrated
load for given rod.
APPARATUS REQUIRED:
1. Whirling shaft apparatus
2. Various support and bearings.
3. Tachometer
4. Vernier caliper
5. Steel rule
6. Masses
FORMULA USED:
(i) Moment of Inertia, I =
𝜋
64
𝑑4
(in m4
)
(ii) Deflection, δ=
𝑚𝑔𝐿3
192𝐸𝐼
(in meter)
(iii) Critical speed of the shaft, N =
1
2𝜋
√
𝑔
𝛿
× 60 (in rpm)
Where,
g - Acceleration due to gravity 9.81(m/s2
)
m – Applied mass in kg
d – Diameter of the shaft in m
L – Length of the shaft in m
E – Young’s modulus of the shaft material in N/m2
.
THEORY:
The speed on which the shaft runs so that additional deflection of the shaft from the axis of
rotation becomes infinite is known as “critical speed”.
In actual practice, a rotating shaft carries different accessories and mountings. This shows that
the center of gravity of the pulley (or) gear is at the center distance from the axis of rotation
& due this the shaft is subjected to centrifugal force. This force will bend the shaft which will
further increase the distance of center of gravity. This increases the value of centrifugal forces
which further increases the distance of center of gravity. The bending of shaft only depends on
the speed at which it rotates.

DIAGRAM:
PROCEDURE:
1. Desired shaft is fixed between the chucks. The length of the shaft used for the experiment
can be changed and the sliding frame is locked.
2. Electric supply is given to the motors and slowly increases the speed. The speed of rotation
of the shaft can be measured by tachometer (or) stroboscope.
3. When the speed increases it can be very well observed that at critical speed, the shaft is
whirling.
4. The above procedure is repeated for various lengths between supports. The readings are
tabulated.
OBSERVATION SPECIFICATIONS:
Young’s modulus (E) = 200GPa = 200 x 109
N/m2
Length between support (L) = 1 m
Mass of the added weight (m) = 100 g = 0.1 kg
Dia of the wire (D) =4 mm = 4 x 10-3
m
TABULATION:
S.No.
Diameter of
rod(d)
(m)
Deflection (δ) in
(m)
Critical speed (rpm)
Actual
speed, NA
(or)
Experimental speed
(rpm)
Theoretical
speed, NT
(rpm)
1
2.
Weight

MODEL CALCULATION:
RESULT:
Thus the critical speed of the given shaft was calculated.
Actual speed calculated, NA= rpm
Theoretical speed calculated, NT= rpm

VIVA-QUESTIONS:
1. What is meant by critical speed of shaft?
Critical or whirling or whipping speed is the speed at which a rotating shaft tends to
vibrate violently in the transverse direction.
2.What do you meant by whirling of shaft?
When a rotor is mounted on a shaft, its center of mass does not usually coincide with
the center line of the shaft. Therefore, when the shaft rotates, it is subjected to a centrifugal
force which makes the shaft bend in the direction of eccentricity of the center of mass. This
is called as whirling of shaft.
3.What are the factors which influence the shaft bending?
a. The eccentricity of the center of mass of rotor,
b. Speed at which the shaft rotates.
4.List out the methods to determine the critical speed of shaft.
a. Rayleigh-Ritz method
b. Dunkerley's method
5.Name the mechanical elements which are usually undergoes whirling
phenomenon.
a. Turbines, b. Electric Motors, c. Heavy rotors d. Compressors e. Pumps
6. The normal operating speed of the shaft must be greater than it’s the critical
speed. Why?
When the rotational speed matches with this critical speed, the rotor undergoes large
deflection and the force transmitted to the bearings will be so enormous that they may fail.
8. What are the forces acting on the rotor during whirling of shaft?
1. The centrifugal force due to the spinning motion if the center of gravity of the
rotor about the bent up shaft axis.
2. The centrifugal force due to mass carried by the shaft and revolving with shaft
about the bearing center line at a radius of s.
3. The elastic restoring force in radially inward direction.
9. What are the types of shaft?
1. Solid shaft, 2.Hollow shaft.
10. What is stepped shaft?
When a shaft is made up of different lengths and of different diameters, it is termed as
shaft of varying section.

EX.NO:3 SPRING MASS SYSTEM - SERIES FREE VIBRATION
(DAMPED AND UNDAMPED)
DATE:
AIM: To determine the experimental frequency and theoretical frequency.
APPARATUS REQUIRED:-
1. Mass
2. Tension spring
3. Spring mass system
DAIGRAM:
Spring 1
Spring 2
Mass adding
SPRING MASS SYSTEM
FORMULA:-
LOAD (w) in (newton) = mass added (m) × 9.81
DEFLECTION 1(δ1) = FINAL LENGTH OF SPRING 1 (FL1) –INITIAL LENGTH OF SPRING 1 (IL1)
STIFFNESS 1(s1) = LOAD (w) / DEFLECTION 1 (δ1)
DEFLECTION 2(δ2) = FINAL LENGTH OF SPRING 2(FL2) –INITIAL LENGTH OF SPRING 2(IL2)
STIFFNESS 2(s2) = LOAD (w) / DEFLECTION 2 (δ2)

EQUIVALENT STIFFNESS (seq) =
1 2
1 1
s s
 in N/m
THEORATICAL FREQUENCY (fth) = in Hz
EXPERIMENTAL FREQUENCY (fexp) =
1
𝑡𝑖𝑚𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 (𝑡𝑝)
in Hz
PROCEDURE:
 First measure the initial length of the spring 1 & 2.
 Adding one mass and oscillate the spring system.
 And also measure the final length of the spring 1 & 2.
 Note down the time period.
 Following the same procedure for different masses.
TABULATION:-
S.
no
Mass
Added
in kg
Load
in N
SPRING 1 SPRING 2 Equivalent
stiffness
(seq)
Theoretical
frequency
(ftheo)
Time
period
Experime
ntal
frequency
(fexp)
IL1 FL1 δ1 s1 IL2 FL2 δ1 s1
RESULT:
Experimental frequency = ………in Hz
Theoretical frequency=………in Hz
1
2
eq
s
m


VIVA QUESTION:
1. How does vibration of a body occurs?
A body is said to vibrate if it has a to and fro motion. These are caused due to elastic
forces.
2. What is free vibration?
Elastic vibrations in which there are no friction and external forces after the initial
release of the body are known as free or natural vibrations.
3. What is forced vibrations?
When a repeated force continuously acts on a system, the vibrations are said to be
forced.
4. Define frequency.
Frequency is the number of cycles of motion completed in one second, it is expressed
in hertz (Hz) and is equal to one cycle per second.
5. Define resonance.
When the frequency of the external force is the same as that of the natural frequency
of the system, a state if resonance is said to have been reached. Resonance results in large
amplitudes of vibrations and this may be dangerous.
6. What is mean by degrees of freedom?
The number if independent coordinates requires to describe a vibratory system is
known as its degree if freedom.
7. What are the types of vibrations?
Longitudinal vibration
Transverse vibration
Torsional vibration
fn = natural linear frequency, s = stiffness of the spring, m = mass.
8. Uses of spring?
Spring is used to store energy.
9. Types of spring?
1. Open coil spring
2. Closed coil spring

d
EX.NO:4 TRIFILAR
DATE:
AIM:
To determine the radius of gyration of the circular plate and hence its Mass Moment of
Inertia.
APPARATUS REQUIRED:
scale,
circular plate,
strings,
stop watch.
DIAGRAM:
Base
TRIFILAR
FORMULA USED:
Time period, T = t/N in seconds, Natural frequency, fn = 1/T Hz
Radius of gyration, K = (bT/2JI)(√𝑔/𝑙) in m.
Where b-distance of a string from center of gravity of the plate,
l- Length of string from chuck to plate surface.
Moment of inertia of the plate only, Ip=(R2
x W1) / (4π2
fn2
x l)
Moment of inertia with weight added ,It=R2
x (W1 + W) / 4π2
fn2
x l)
Where, R- Radius of the circular plate and W1-Weight of the circular plate = m1g in N
W- Weight of the added masses = mg in N
Moment of inertia of weight, Iw = It - Ip
OBSERVATIONS & SPECIFICATIONS
Mass of the disc, m1 = 2 kg
Acceleration due to gravity, g = 9.81m/s
2
Diameter of the wire,d =
Type of suspension:…………………,
No. of oscillations …………………….
Radius of circular plate, R=…….m,
Wire l Stand

PROCEDURE:
1. Hang the plate from chucks with 3 strings of equal lengths at equal angular intervals
(1200
each)
2. Give the plate a small twist about its polar axis
3. Measure the time taken, for 5 or 10 oscillations.
4. Repeat the experiment by changing the lengths of strings and adding weights.
TABULATION:
Sl.
No.
Length
of
string
l, m
Added,
mass,
m,
kg
Time for N
oscillations,
t, sec
Time
period
T, sec
Radius of
gyration,
k, m
Natural
frequency
fn, Hz
Moment of
inertia of
weight
in,kg-m
MODEL CALCULATION:
RESULT:
Thus the radius of gyration of the circular plate and hence its Mass Moment of Inertia were
tabulated.

VIVA-QUESTIONS:
1. What is meant by Rigidity modulus?
Modulus of Rigidity (or Shear Modulus) is the coefficient of elasticity for a shearing force.
It is defined as "the ratio of shear stress to the displacement per unit sample length
(shear strain)".
2. Define moment of inertia.
Moment of Inertia (Mass Moment of Inertia) depends on the mass of the object, its shape
and its relative point of rotation
3. Define the terms stress.
Stress is the internal force unit area associated with a strain
4. Define the terms strain.
Strain is the relative change in shape or size of an object due to externally applied forces
5.What is the relation between linear velocity and angular velocity?
The most intuitive measure of the rate at which the rider is traveling around the wheel
is what we call linear velocity.
6. What is angular acceleration?
Angular acceleration is the rate of change of angular Velocity with respect to time. It is a
vector quantity.
7. What is a rigid body?
In physics, a rigid body is nothing but a solid body of finite size in which change in original
shape (deformation in other words) is not allowed.

EX.NO:5 TRANSVERSE VIBRATION- SSB
DATE:
AIM:
To find the natural frequency of the simply supported beam.
APPARATUS REQUIRED:
1. Experimental setup
2. stop watch
3. weight
DIAGRAM: center point load (w)
L
Eccentric load
a b wshaft / length (UDL)
FORMULA:
For point load
For eccentric load
For UDL
4
5
384
wl
EI
 
Moment of inertia (I) =
3
48
wl
EI
 
2 2
3
wa b
EIl
 
3
12
bd

Theoretical frequency =
1
2
n
g
f
 
 in Hz
Time period = time taken for 3 oscillations / 3 in s
Experimental frequency = in Hz
PROCEDURE:
1. First the dimension of the beam is measured add point.
2. The point load is removed and add repeat experimental of UDL.
3. Calculate the theoretical value frequency for point load up.
SPECIFICATION:
Length l= 770 mm
Breadth b= 18 mm
Thickness t= 3mm
E=2 X 105
N/mm2
Mass (m) =0.1kg
Mass of the shaft (ms) = 0.34 kg
TABULATION:
FOR POINT LOAD:
s.no Mass
in kg
Load
in (N)
Time taken
for three
oscillations
Time
period
(tp)
Experimental
frequency
(fexp)
Deflection
(δ)
Theoretical
frequency
ftheo
FOR ECCENTRIC LOAD (a=…… m, b=…… m)
s.no Mass
in kg
Load
in (N)
Time taken
for three
oscillations
Time
period
(tp)
Experimental
frequency
(fexp)
Deflection
(δ)
Theoretical
frequency
ftheo
For UDL
s.no Mass
in kg
Load
in (N)
Time taken
for three
oscillations
Time
period
(tp)
Experimental
frequency
(fexp)
Deflection
(δ)
Theoretical
frequency
ftheo
RESULT:
Thus the natural frequency is determined by given transverse vibration.
1
n
p
f
t


VIVA- QUESTIONS:
1. Define the vibratory motion.
When elastic bodies such as a spring, a beam and a shaft are displaced from the equilibrium
position by the application of external forces, and then released, they execute a vibratory
motion.
2. Define time period.
It is the time interval after which the motion is repeated itself. The period of vibration is
usually expressed in seconds.
3. Define Cycle.
It is the motion completed during one time period.
4. Define Frequency.
It is the number of cycles described in one second. In S.I. units, the frequency is expressed
in hertz (briefly written as Hz) which is equal to one cycle per second.
5. What are the Types of Vibratory Motion?
1. Free or natural vibrations.
2. Forced vibrations.
3. Damped vibrations.
6. What are the Types of Free Vibrations?
1. Longitudinal vibrations, 2. Transverse vibrations, and 3. Torsional vibrations.
7. Explain the Transverse vibrations?
When the particles of the shaft or disc move approximately perpendicular to the axis of
the shaft.
8. Simply supported beam with an eccentric point load W.
9.Simply supported beam with a central point load W.
10. Simply supported beam with a uniformly distributed load of w per unit length.

30
EX.NO:6 DETERMINATION OF MOMENT OF INERTIA BY OSCILLATION
METHOD FOR CONNECTING ROD
DATE:
AIM:
To find out the mass moment of inertia of given connecting rod by oscillation method.
APPARATUS REQUIRED:
1. Connecting rod
2. Stop watch
DIAGRAM:
 60


CONNECTING ROD
FORMULA USED:
1 1 2
2 2 2
1 2
2 1
2 2
1 1 1 1
2 2
2 2 2 2
2 2
1 2
2 2
2 1 2
2
4
4
0.17
0.17
( )
2
n
n
G
G
G G
G G
G
G
g
L f
g
L f
h h
h h
k L h h
k L h h
k k assume
k k
k
I mk


 
 
 
 
 
 




L1, L2 – Equivalent length of simple pendulum when the axis of oscillation co-
ordinates with small and big end center respectively.
170
m

fn1, fn2 = frequency (or) oscillation of small and big end
TABULATION:
S.
No
.
Suspension
Time taken for 3 oscillations
Time
period(tp)
Frequency
(fn)
(Hz)
Trail 1
(Sec)
Trail 2
(Sec)
Average
1
2
Small end
Big
end
2 Big end
PROCEDURE:
1. Note down the various specifications of the connecting rod.
2. Suspend the connecting rod in the knife edge pointer with the smaller end.
3. Oscillate the connecting rod and note down the time taken for no of oscillation in
seconds.
4. Similarity suspends the connecting rod on the knife edge pointer with bigger end.
5. Oscillate it again and note down the time taken for no of oscillation.
OBSERVATION& SPECIFICATIONS:
1. Diameter of small end, d1 = 30 mm = 0.03 m
2. Diameter of big end, d2 = 60 mm = 0.06m
3. Mass of connecting rod = 1.5 kg
4. Distance between small end and big end Centre’s = h1 + h2 =170 mm = 0.17 m
RESULT:
The moment of inertia of connecting rod, I= in kg-m2

VIVA-QUESTIONS:
1. What is the formula for Thrust in the connecting rod?
2. What is the function of connecting rod?
It is used to covert rotation motion to reciprocation motion.
3. What are the two ends in connecting rod?
Big end and small end.
4. Where small end of connecting rod is connected?
Small end is connected to crank shaft.
5. Where big end of connecting rod is connected?
Big end is connected to piston.
6. Angular velocity of the connecting rod?
7. Angular acceleration of the connecting rod?
8. What is the material made of connecting rod?
Normally connecting rods are forge-manufactured and the material used is typically
mild and medium carbon.

EX.NO:7 TRANSVERSE VIBRATION- CANTILEVER BEAM
DATE:
AIM:-To determine the natural frequency of a cantilever beam.
1. Experimental setup.
DIAGRAM:
L Load
Motor with
eccentric load
Cantilever
Stepper
Adjustable Screw
RPM
Control Panel
Power Switch
TRANSVERSE VIBRATION – CANTILEVER BEAM

FORMULA:-
Actual natural work (ω act) =
% of deviation =
K= load acting length/total length of the beam
PROCEDURE:
1. Measure the cross section of beam.
2. Weight of mass of beam.
3. Calculate theoretical frequency (ϴn)
4. Actual frequency of system ω act=2πN/60
5. Compare the theoretical with actual valve.
TABULATION:-
Load acting
length
in mm
K factor
Actual
speed (N)
in (rpm)
Actual
frequency
(ωact)
Theoretical
frequency(ωn)
% Deviation
RESULT: Thus the natural frequency are determined by given transverse vibration
2
60
N

2 3
3 2
1 2
1000
[3 (0.026 ) ( ) ]
2 6
n
EI
k k
L m m
 
  
100
n act
n
 




VIVA QUESTION:-
1. Definition of cantilever beam?
A beam that is supported by only one fixed support at only one of its ends.
2. What are the Types of Beams based on geometry?
1. Straight beam – Beam with straight profile
2. Curved beam – Beam with curved profile
3. Tapered beam – Beam with tapered cross section
3. What are the type of beam based on the shape of cross section?
1. I-beam – Beam with ‘I’ cross section
2. T-beam – Beam with ‘T’ cross section
3. C-beam – Beam with ‘C’ cross section
4.What are the types of beam based on equilibrium conditions?
1. Statically determinate beam – For a statically determinate beam, equilibrium
conditions alone can be used to solve reactions.
2. Statically indeterminate beam – For a statically indeterminate beam,
equilibrium conditions are not enough to solve reactions. Additional deflections
are needed to solve reactions.
5.What are the type of beam based on the type of support?
1. Simply supported beam
2. Cantilever beam
3. Overhanging beam
4. Continuous beam
5. Fixed beam
6.Define simply supported beam?
A simply supported beam is a type of beam that has pinned support at one end
and roller support at the other end.
7.Define Overhanging beam?
An overhanging beam is a beam that has one or both end portions extending
beyond its supports.
8.Define Continuous beam?
A continuous beam has more than two supports distributed throughout its length.
It can be understood well from the image below.
9.Define fixed beam?
As the name suggests, fixed beam is a type of beam whose both ends are fixed.
10.What are the two types of waves?
There are two basic types of wave motion for mechanical waves: longitudinal
waves and transverse waves.

EX.NO:8 CAM PROFILE ANALYSIS
DATE:
AIM: -
To study about cam thus given motions to another know as follower and to find out
critical speed of cam and also draw the cam profile.
APPARATUS REQUIRED: -
1. Cam
2. semi-circle
3. follower
DIAGRAM:-
FORMULA:-
Where,
N1 – minimum speed in (rpm)
N2- maximum speed in (rpm)
PROCEDURE:-
1. Attach the cam with cam shaft
2. Switch on the motor and gradually increase the speed.
1
1
2
2
1 2
2
60
2
60
60
2
c
c
c
N
N
N




  




 



3. Measure the speed of cam shaft.
4. Table stroke reading and measure the maximum and minimum speed.
OBESERVATION:-
Base circle dia. = 50 mm
Nose circle dia. = 7 mm
Total lift = 10 mm
Total cam motion = 120o
TABULATION:
S.No Minimum
speed (rpm)
(N1)
Angular
velocity (ω1)
Maximum
speed (rpm)
(N2)
Angular
velocity (ω2) Critical speed (ωc)
S.NO CAM ANGLE TURNED in
degree
FOLLOWER DISPLACEMENT in
mm
S
.
N
O
JUMPING SPEED
RESULT:-
Thus the cam profile analysis is studied.

VIVA-QUESTIONS:
1. What is meant by cam?
A cam is a mechanical member used to impart desired motion to a follower by direct
contact.
2. Cam and follower belongs to which type of pair?
Higher pair
3. How cams are classified?
Cams are classified according to:
a. Shape,
b. Follower movement and
c. Manner of constraint of the follower.
4. How cams followers are classified?
Cams followers are classified according to:
a. Shape,
b. Movement and
c. Location of line of movement.
5. What is mean by dwell?
A dwell is the zero displacement or the absence of motion of the follower during the
motion of the cam.
6. What is base circle?
Base circle is the smallest circle tangent to the cam profile drawn to the centre of
rotation of a radial cam.
7. What is pitch curve?
Pitch curve is the curve drawn by the trace point assuming the cam to be fixed and
rotating the trace point of the follower around the cam.
8. What is meant by pressure angle?
The pressure angle, representing the steepness of the cam profile, is the angle
between the normal to the pitch curve at a point and the direction of the follower motion. It
varies in magnitude at all instants if the follower motion.
9. What are the basic follower motion programs available?
Simple harmonic motion (SHM)
Constant acceleration and deceleration
Constant velocity
Cycloid
10. Which type of motion program is ideal for high speed follower motion?
Cycloid motion is the most ideal program for high speed follower motion.
11. State some application of cam.
IC engines, printing control mechanisms, machine tools, automatic machines.

EX.NO:9 BALANCING OF ROTATING MASS
DATE:
AIM:
To verify the balancing using the rotating machine element.
1. Balancing rotary system 2. Masses
DIAGRAM:
Reference Plane
FORMULA:-
PROCEDURE:
1. To order of the basic operation involved with respect to static balancing as
following
2. Then the mass should be fixed in one side of the stud and its angle to be adjusted
with the help of angular scale and its radii can be corrected with the help of vernier caliper.
3. Angular displacement between the masses is calculated by force diagram through
known value of mass and radii.
4. Fix the masses to the calculated angular displacement using angular scale.
5. Now switch on the motor.
Centrifugal force= mass*radius
Centrifugal couple= centrifugal force* Length
A B C D
10
20
29
3

6. By changing the sped of the motor, check it out for vibration for running
7. Add by changing the mass with different radii and find out the angular
displacement among the mass for balancing the system
DATA REQUIRED:
Mass of rotor=0.1kg
Radius of rotor=3x 10-2
m
TABULATION:
Plane
Mass
( m) Kg
Radius
( r) m
Force
(m x r) Kg-m
Distance
( l ) m
Couple
(m x r x l)
Kg-m2
DIAGRAMS
ANGULAR POSITIONS OF PLANES

COUPLE POLYGON (SCALE RATIO: )
FORCE POLYGON (SCALE RATIO: )
RESULT: Thus the relative angular settings of masses are calculated and the balancing was
made.

VIVA QUESTION:-
1.What is balancing of rotating masses?
Balancing is the process of designing or modifying machinery so that the unbalance is
reduced to an acceptable level and if possible is eliminated entirely.
2. How does the unbalanced force produced?
When the center of mass does not lie on the axis or there is an eccentricity, an
unbalanced force is produced.
3. What are the two types of unbalancing?
Rotating unbalance and reciprocating unbalance.
4. List some example where the unbalance of rotating masses occurs.
Steam turbine rotors, engine crankshafts, rotary compressor, centrifugal pumps.
5. At which speed the balancing of rotating masses is needed?
At high speed.
6. What are the different cases in balancing of rotating masses?
a. Balancing of a single rotating mass by a single mass rotating in the same plane.
b. Balancing of a single rotating mass by two masses rotating in different planes.
c. Balancing of different masses rotating in the same plane.
7. State the condition for static balancing.
The net dynamic force acting on the shaft is equal to zero.
8. State the condition for dynamic balancing.
The net dynamic force acting on the shaft and the net couple due to the dynamic forces
acting on the shaft is equal to zero.
9. How can we find the balancing mass and its angular position in graphical
method?
In graphical method, by drawing vector polygon and couple polygon, we can find the
balancing mass and its angular position.
10. The balancing of rotating bodies is important to avoid vibration. Why?
In heavy industrial machines such as gas turbines and electric generators, vibration
can cause catastrophic failure, as well as noise and discomfort. In the case of a simple wheel,
balancing simply involves moving the center of gravity to the center of rotation.

EX.NO:10 SPRING MASS SYSTEM – PARALLEL (FREE & FORCED VIBRATION)
(DAMPED AND UNDAMPED)
DATE:
AIM: To determine the experimental frequency and theoretical frequency.
1. Mass
2. Tension spring
3. Spring mass system
DAIGRAM:
Spring 1
SPRING MASS SYSTEM
FORMULA:-
LOAD (w) in (newton) = mass added (m) × 9.81
DEFLECTION (δ) = FINAL LENGTH OF SPRING (FL) –INITIAL LENGTH OF SPRING (IL)
STIFFNESS 1(s1) = LOAD (w) / DEFLECTION (δ)
STIFFNESS 2(s2) = LOAD (w) / DEFLECTION (δ)
EQUIVALENT STIFFNESS (seq) = s1+s2 in N/m
THEORATICAL FREQUENCY (fth) = in Hz
Time period= time taken for 3 oscillations/ 3
EXPERIMENTAL FREQUENCY (fexp) =
1
𝑡𝑖𝑚𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 (𝑡𝑝)
in Hz
1
2
eq
s
m

Exciter
Spring 2
Mass
Frame

PROCEDURE:
FREE VIBRATION:
 First measure the initial length of the spring 1 & 2.
 Adding one mass and oscillate the spring system.
 And also measure the final length of the spring 1 & 2.
 Note down the time period.
 Following the same procedure for different masses.
FORCED VIBRATION:
 Now switch on the motors.
 Regulate the requirement speeds.
 Take the reading for forced vibration.
TABULATION:-
FREE VIBRATION & FORCED VIBRATION:
S
.
n
o
Mass
Added
in kg
Load
in N
Final
length
of the
spring
Initial
length
of the
spring
Defle
ction
(δ)
Stiffne
ss-
1(s1)
Stiffne
ss-
2(s2)
Equivalent
stiffness
(seq)
Theoretical
frequency
(ftheo)
Time
taken
for
three
oscillat
ions
Time
period
Experimental
frequency
(fexp)
RESULT:
FREE VIBRATION
Experimental frequency =
Theoretical frequency=
FORECD VIBRATION
Experimental frequency =

VIVA QUESTION:
1. How does vibration of a body occurs?
A body is said to vibrate if it has a to and fro motion. These are caused due to elastic
forces.
Elastic vibrations in which there are no friction and external forces after the initial release
of the body are known as free or natural vibrations.
3. What is forced vibrations?
When a repeated force continuously acts on a system, the vibrations are said to be
forced.
4. Define frequency.
Frequency is the number of cycles of motion completed in one second, it is expressed in
hertz (Hz) and is equal to one cycle per second.
5. Define resonance.
When the frequency of the external force is the same as that of the natural frequency
of the system, a state if resonance is said to have been reached. Resonance results in large
amplitudes of vibrations and this may be dangerous.
6. What is mean by degrees of freedom?
The number if independent coordinates requires to describe a vibratory system is known
as its degree if freedom.
7. What are the types of vibrations?
Longitudinal vibration
Transverse vibration
Torsional vibration
8. Write the formula for natural circular frequency and natural linear frequency.
𝜔𝑛 = √
𝑠
𝑚
,
𝑓𝑛
=
1
2𝜋
√
𝑠
𝑚
, where 𝜔𝑛 = natural circular frequency,
𝑓𝑛
= natural linear frequency, s = stiffness of the spring, m = mass.
9. Uses of spring?
Spring is used to store energy.
10. Types of spring?
1. Open coil spring
2. Closed coil spring.

EX.NO:11 TURN TABLE
DATE:
AIM:-To determine moment of inertia unknown member by using torsional apparatus.
2. Connecting rod.
3. Vernier caliper
DIAGRAM:
TURN TABLE
FORMULA:-
Theoretical mass moment of inertia=
Experimental mass moment of inertia=
4
32
CJ
q
l
J d



2
2
mR
I 
2
2
4
p
qt
I



OBSERVATION:
Disk diameter (D) =300 mm
Radius of the disk(R) =150 mm
Diameter of the shaft (d) =6mm=0.006 m
Length of the shaft (l) =600 mm=0.6m
Mass (without member) m =15 kg
Mass (with member) m =17.12 kg
PROCEDURE:
 Give the angular twist to the disc and measure period for oscillation.
 And out the mass moment of inertia of the disc using formula.
 Compare the theoretical valve of disc using formula.
 Mass moment of inertia I= mr2
/2
 Find out the mass moment of inertial of the disc and test object using formula
TABULATION:-
s.no Condition Time period(tp)
Theoretical mass
moment of inertia
(Itheo)
Experimental mass
moment of inertia
(Iexp)
1. Without member
2. With member
RESULT:
Thus the theoretical oscillation equipment is tested and moment of inertia of
unknown object is found out.

VIVA QUESTION:-
1. Explain Torsional vibration?
Torsional vibration is an oscillatory angular motion causing twisting in the shaft of a
system; the oscillatory motion is superimposed on the steady rotational motion of a
rotating/reciprocating machine.
2. What are the causes of torsional moment?
Torsional or twisting moment is caused by forces whose resultant does not pass
through the axis of rotation (called the shear center) of the structural member.
3. Where the torsional moments are induced?
Typically, significant torsions are induced in shafts of rotating motors, structural
members subjected to eccentric loading (e.g., edge beams) or curved in the horizontal plane
(e.g., curved bridges, helical stairs).
4. Torsional Rotation of Circular Section Calculation of torsional rotation is
necessary to?
1. Design structures not only to be strong enough (to withstand torsional stress), but
also stiff enough (i.e., they should not deform too much due to torsional moments),
2. Design machineries for torsional vibrations,
3. Analyze statically indeterminate structures
5. Define moment of inertia?
Moment of inertia is a property of rotating bodies that defines its resistance to a
change in angular velocity about an axis of rotation.
6.Where the moment of inertia is applied?
Moment of inertia applies to an extended body in which the mass is constrained to
rotate around an axis. It arises as a combination of mass and geometry in the study of the
movement of continuous bodies, or assemblies of particles, known as rigid body dynamics.
7.Moment of Inertia Examples?
Moment of inertia is defined with respect to a specific rotation axis. The moment of
inertia of a point mass with respect to an axis is defined as the product of the mass times the
distance from the axis squared. The moment of inertia of any extended object is built up from
that basic definition. The general form of the moment of inertia involves an integral.
8. What is the use of turn table apparatus?
The set-up is solely designed & developed for the students of Mechanical Engg., to
experimentally determine the Moment of Inertia of a Disk & Ring in rotational motion.
9. What are the main parts of turn table?
A turntable apparatus bears and rotates a disc inserted into a reproducing apparatus for signals
recorded on the disc through a casing inlet opening. The turntable apparatus comprises a
turntable rotatable supported on a chassis to move vertically and a center spindle rotatable
supported coaxially with an axis of rotation of the turntable and received in a recess at the
center portion of the turntable to move vertically.

EX.NO:12 COMPOUND PENDULAM
DATE:
AIM:
To find the radius of gyration and natural frequency of the compound pendulum.
APPARATUS REQUIRED:
Experimental setup
Stop watch
DIAGRAM:
Compound pendulum
FORMULAE:
Theoretical radius of gyration= in meter
Theoretical frequency= in Hz.
Experimental radius of gyration= in meter
Experimental frequency= in Hz.
OBSERVATION:
2 3
theo
L
k 
2 2
1 .
2
theo
theo
g OG
f
k OG



2
2
exp
. .
2
p
t g OG
k OG

 
 
 
 
exp
1
p
f
t


Length of the compound pendulum (L) =110 cm=1.1 m
TABULATION:
s
.
n
o
Distance
between
center of
gravity and
point of
suspension
(OG)
Time
taken
for 3
oscillati
ons
Time
period
(tp)
Experimental
radius of
gyration
(kexp)
Experimental
Frequency
(fexp)
Theoretical
radius of
gyration
(ktheo)
Theoretical
frequency
(ktheo)
1
2
3
PROCEDURE:
 Measure the length of the pendulum and fix the pendulum at one point.
 Take that point as a point of suspension.
 Measure the distance between the point of suspension and center of gravity.
 Create oscillations by hand and take down the time taken for 3 oscillations.
 Repeat the same procedure for different readings.
RESULT:
The experiment was carried out and the following things are found.
1. Theoretical radius of gyration =
2. Theoretical frequency (ktheo) =
3. Experimental radius of gyration (ktheo) =
1. Experimental Frequency (fexp) =
EX.NO:13 DETERMINE THE CHARACTERISTICS OF GOVERNOR

USING UNIVERSAL GOVERNOR APPARATUS
DATE:
AIM:
To determine the sensitivity and effort of Watt, Porter, Proell and Hartnell governor.
APPARATUS REQUIRED:
1. Universal governor apparatus
2. Tachometer
3. Measuring scale
4. Sleeve weights
DIAGRAM:
PORTER GOVERNOR WATT GOVERNOR
PROELL GOVERNOR HARTNELL GOVERNOR

PROCEDURE FOR WATT GOVERNOR:
1. Arrange the setup as a watt governor. This can be done by removing the upper sleeve on the
vertical spindle of the governor and using proper linkage provided.
2. Make proper connections of the motor.
3. Increase the motor speed gradually.
4. Note the sleeve displacement on the scale provided and speed by tachometer.
5. Plot the graph for speed vs governor height for watt governor.
6. Plot the graph of speed vs sleeve displacement for watt governor.
PROCEDURE FOR PORTER, PROELL &HARTNELL GOVERNOR
1. Initially the radius of rotation of the governor, height of the governor and length of the link are
measured and are recorded.
2. The given sleeve weights are added to the sleeve through the central spindle and the auto
transformer is switched on.
3. The speed of the governor is gradually increased to get sleeve displacement.
4. At four different speed of the governor say 200, 250, 300 and 350 rpm and the corresponding
sleeve displacements are noted and tabulated.
5. The sleeve weights are removed in success and the procedure is repeated.
6. Thus the effect of sleeve weight on sleeve displacement, radius of rotation and hence the force
can be observed.
SPECIFICATIONS:
Length of each link (l) =130 mm=0.13 m
Initial height of governor (h0) =120 mm=0.12 m
Mass of sleeve load (M) = 1 kg
Mass of ball (m) = 0.2 kg
Formulae Used for watt governor:

FORMULA USED FOR PORTER, PROELL &HARTNELL GOVERNOR:
Sensitivity (s) = (Max speed-Min speed) / Mean Equilibrium speed=2(N1-N2)/ (N1+N2)
Mean Equilibrium speed = (Max speed + Min speed)/2 = (N1+ N2)/2
Effort (P) = s (M+m).g in N.
Where, s- Sensitivity (or) sensitiveness
g – Acceleration due to gravity, (9.81 m/s2)
TABULATION FOR WATT GOVERNOR
S.
No
Speed (N)
(rpm)
Angular
velocity
(ω) in
rad/s
Sleeve
displace
ment
„x‟
(mm)
Height “h‟
(mm)
Angle (ϴ) Radius of
rotation
“r‟ (mm)
Force
(KN)
1
2
3
4
TABULATION FOR PORTER, PROELL AND HARTNELL GOVERNOR
S.No
Types of
governor Load
(Kg)
Minimum
speed
(N2)
(rpm)
Maximum
speed
(N1)
(rpm)
Equilibrium
speed (rpm) Sensitivity
(s)
Effort
(P)
(N)
1 Porter
2 Proell
3 Hartnell

MODEL CALCULATION:
Graph for porter governor:
1. Load Vs Sensitivity
2. Load Vs Effort
Graph for proell governor:
1. Load Vs Height of the governor
2. Load Vs % of increase in speed (rpm)
3. Load Vs Sensitivity
4. Load Vs Effort
Result:
1. Thus the characteristics of the watt governor are studied and its characteristics
Curves are drawn.
2. Thus the sensitivity and effort of Porter, Proell, hartnell governor were tabulated.

VIVA – QUESTIONS:
1. State the function of governor as applied to the I.C. Engines?
It is used to adjust the supply of fuel according to the load requirements so as to keep the speeds
at various, loads , as close to the mean speed as possible , over long range of working of the
engines.
2. Define height of governor?
It is the vertical distance between the center of the governor halls and the point of intersection
between the upper arms on the axis of spindle is known as governor height. It is generally
denoted by h.
3. Define sleeve lift?
The vertical distance the sleeve travels due to change in the equilibrium speed is called the sleeve
lift. The vertical downward travel may be termed as negative lift.
4.What is the function of governor?
a) To control the engine speed
b) To maintain the speed of an engine
c) To maintain constant speed of the piston
d) To maintain constant engine speed
5. What is meant by Equilibrium speeds in case of governors?
The speeds at which the governor balls, the arms etc. are in complete equilibrium and the
sleeve does not tend to move upward or downward are called the equilibrium speeds.
6.Define Governor Effort.
The mean force acting on the sleeve for a given change of speed or lift of the sleeve is known as
the governor effort.
7. What is meant by controlling force in case of governors?
The force acting radially upon the rotating balls to counter act its centrifugal force is called the
controlling force.
8.What is Isochronism?
When the equilibrium speed is constant for all radii of rotation of the balls within the working
range, the governor is said to be in isochronism.
9. What is Stability?
Stability is the ability to maintain a desired engine speed without fluctuating.
10.What is hunting?
The phenomenon of continuous fluctuation of the engine speed above and below the mean speed
is termed as hunting.

A B
EX.NO:14 SINGLE AND TWO ROTOR SYSTEM
DATE:
AIM:-To determine the natural frequency of single and the rotor system
2. Scale
3. Vernier caliper
4. Sensor setup with timer
DIAGRAM:
I1 I2
SINGLE AND TWO ROTOR SYSTEM
FORMULA:-
FOR SINGLE ROTOR:
Mass moment of inertia=
2 2
1
1
( )
12
m a b
I

 in kg-m2
Polar moment of inertia=
4
32
J d

 in m4
Experimental frequency= exp
1
p
f
t
 in Hz
1 1
1
2
theo
CJ
f
I L

 in Hz
FOR TWO ROTOR:
Polar moment of inertia=
4
32
J d

 in m4
Moment of inertia=
2 2
2
1
2
( )
12
m a b
I m k

  in kg-m2
Length of the shaft=L=L1+L2 in m
1
p
f
t
 in Hz
1
2
theo
CJ
f
IL

 in Hz
L1 L2

PROCEDURE:
FOR SINGLE ROTOR:
 First measure the rod diameter, width and length of the single rotor.
 Fix the top side rotor as stationery and oscillate the lower end of the rotor.
 Take down the time period.
 Find the theoretical and experimental frequency by using formula.
FOR TWO ROTOR:
 Oscillate two rotors in opposite direction and note down the time period.
OBSERVATIONS:
Modulus of rigidity of shaft (C) =0.8×1011
N/m2
Mass of the rotors=m1=m2=0.33 kg
Length of the shaft=L1=L2=37.5 cm=0.375 m
So, L=L1+L2=0.75 m
Diameter of the shaft (d) = 3×10-3
m
Width of the rotor (a) = 5 cm=0.05 m
Length of the rotor (b) = 60 cm=0.6 m
Radius of gyration (k) =
TABULATION:-
s.no Type of rotor Time period
(tp)
Experimental
frequency (fexp)
Theoretical frequency
(ftheo)
1 Single rotor
2 Two rotor
MODEL CALCULATION:
RESULT:
Thus the natural frequency of single and two rotor are found out and compare with
theoretical.

VIVA QUESTION:-
1. Where the rotors are used?
The rotor system found on helicopters can consist of a single main rotor or dual rotors.
With most dual rotors, the rotors turn in opposite directions so the torque from one rotor is
opposed by the torque of the other. This cancels the turning tendencies
2. Define Periodic Motion?
The motion which repeats after a regular interval of time is called periodic motion
3. Define Frequency?
The number of cycles completed in a unit time is called frequency. Its unit is cycles per
second (cps) or Hertz (Hz)
.
4. Define Time Period?
Time taken to complete one cycle is called periodic time. It is represented in
seconds/cycle
5. Define amplitude?
The maximum displacement of a vibrating system or body from the mean equilibrium
position is called amplitude
When a system is disturbed, it starts vibrating and keeps on vibrating thereafter
without the action of external force. Such vibrations are called free vibrations
7. What is natural frequency?
When a system executes free vibrations which are undamped the frequency of such a
system is called natural frequency.
8. What is forced vibration?
The vibrations of the system under the influence of an external force are called forced
vibrations.
9. Define resonance?
When frequency of the exciting force is equal to the natural frequency of the system
it is called resonance. Under such conditions the amplitude of vibration builds up dangerously.
10. Explain the degree of freedom?
The degree of freedom of a vibrating body or system implies the number of
independent coordinates which are required to define the motion of the body or system at
given instant.

EX.NO:15 MOTORISED GYROSCOPE
DATE:
AIM:-To verify the gyroscope rule and find out gyroscopic value of a plane rotating disc.
1. Gyroscopic setup. 2. Weight 3. Tachometer
DIAGRAM:
Plane of
Spinning
Axis of
precision
Axis of active
gyroscopic
couple
Plane of active
gyroscopic
couple
Plane of
precision
disc
Axis of spin
Axis of reactive
gyroscopic
couple

FORMULA:
Angular velocity of spin=
2
60
N

  in rad/s
Angular velocity of precision= p
d
dt

  in rad/s
Gyroscopic couple= p
C I
 in N-m
Torque= T W l
  in N-m
% of error=

SPECIFICATION:-
 Rotor Mass moment of inertia (I)=0.05 kg m2
 Distance between both center to weight pan from disc center(l)=23cm=0.23 m
 Constant speed (N) =………. rpm.
PROCEDURE:-
1. Initially check the balance of the motor and weight plate.
2. Switch on the motor and wait for obtaining the speed of the disc constant.
3. Place the weights that are given like is 1/2, 1 and 2 kg on the platform.
4. Note down the angular motion of the fork with a fixed time or angle, the time is
noted down.
5. calculate the ω and ωp values.
6. Compare above values with applied torque and find percentage loss in torque
due to friction.
TABULATION:
Constant speed N=………..rpm , Angular velocity (ω) =……….rad/s
s.
n
o.
Mass
applied
(kg)
Weight
applied(W)
in N
Torque
(T)
(N-m)
Angle of
precision
Time
taken
(dt)
Precision
angular
velocity
(ω p)
rad/sec
gyroscope
couple
(C) in N-m
% of error
degree Radian
(dϴ)
100
T C
T

 

 
 

MODEL CALCULATION:
RESULT: Thus the gyroscope rule of plane rotating disc was verified.

VIVA QUESTIONS:-
1. What is mean by gyroscope?
A gyroscope is a spinning body which is free to move in other directions under the
action of external forces.
2. Define active gyroscopic torque.
The torque required to cause the axis of spin to precess in a plane is known as the
active torque.
3. Define active gyroscopic torque.
A reactive gyroscope torque tends to rotate the axis of spin in the opposite direction.
4. On which principle the gyroscope works?
Principle of angular momentum.
5. What is mean by gyroscopic effect?
The effect of gyroscopic couple on a rotating body is known as the gyroscope effect on
the body.
6. How does the axis of spin, the axis of precession and the axis of gyroscope couple
oriented?
The axis of spin, the axis of precession and the axis of gyroscope couple are in three
perpendicular axis.
7. A four wheel vehicle tends to turn outwards when taking a turn. Why?
Due to the effects of gyroscopic couple and the centrifugal force.
8. How the two wheel vehicle does stabilize while taking a turn?
A two wheel vehicle stabilizes itself by tilting towards inside while taking a turn to
nullify the effects of gyroscopic couple and the centrifugal force.
9. Where do we use the gyroscopic principle?
Ships, Airplanes and Automobile etc.
10. What is the effect of gyroscopic torque, when an automobile vehicle takes the
left turn?
The gyroscopic torque increases the forces on the outer wheels.

EX.NO:16 DETERMINATION OF TRANSMISSIBILITY RATIO & NATURAL FREQUENCY
USING VIBRATING TABLE
DATE: AIM:-
To find natural frequency of free vibration and forced vibration using vibration table.
1) Spring 2) mass 3) damper 4) stopwatch 5) steel rule
DIAGRAM:
VIBRATING TABLE
FORMULA:
Angular velocity=
2
60
N

  in rad/s
Force excited=
2
e
F m e

 in N
Force transmitted= max
.
t
F s X
 in N
Transmissibility ratio = t
e
F
F
 
1
2
theo
s
f
m

 in Hz
1
p
f
t
 in Hz
PROCEDURE:-
Free Vibration:
 Remove the damper from the experimental setup.
 Then strike the beam by taken 5 oscillation time required.
 Repeat the procedure for different length of beam to adjust the beam set up.
Forced Vibration:
1) Fit the spring, mass damper in proper position note down the spring stiffness, mass of the
beam, length of the beam from one point and measure the exciter mass.

2).The electrical motor is switched ON, using stop watch note down 3 oscillation time for small
jerk.
3).Then repeat the procedure for different length of beam.
SPECIFICATIONS:
Stiffness of spring(s) =280 N/m
Mass of the exciter (m) = 7.5 kg
Turning end (e) =7.5x 10-2
m
TABULATION:-
Exciter
position
(Xmax)
Time
taken for
three
oscillations
Time
period
(tp)
Speed
‘N’
(rpm)
Angular
velocity
(ω) rad/s
Force
Transmitted
(Ft)
Force
Excited
(Fe)
Transmissibility
ratio(Є)
Exp.
freq
Theo.
freq
MODEL CALCULATION:
RESULT:-
Thus the transmitting of forced vibration and all the types of vibration with frequency
and amplitude was adjusted and determined.

VIVA QUESTIONS:-
1. Define viscous damping?
The motion of a body is resisted by frictional forces. In vibrating systems, the effect
of friction is referred to as damping. The damping provided by fluid resistance is known as
viscous damping.
2. Define critical damping?
The critical damping is said to occur when frequency of damped vibration (fd) is zero
(i.e. motion is aperiodic). This type of damping is also avoided because the mass moves back
rapidly to its equilibrium position, in the shortest possible time.
3. Define damping factor?
The ratio of the actual damping coefficient (c) to the critical damping coefficient is
known as damping factor or damping ratio.
4. Define Logarithmic Decrement?
It is defined as the natural logarithm of the amplitude reduction factor.
5. Define Dynamic Magnifier?
It is the ratio of maximum displacement of the forced vibration (Xmax) to the deflection
due to the static force F(xo).
6. Define transmissibility ratio?
The ratio of the force transmitted (FT) to the force applied (F) is known as the isolation
factor or transmissibility ratio of the spring support.
7. In vibration isolation system, if ω/ωn> 1, then the phase difference between
the transmitted force and the disturbing force is?
180°
8. Define Amplitude?
It is the maximum displacement of a body from its mean position.
9. Define Periodic time?
It is the time taken for one complete revolution of the particle.
10. Define Frequency?
It is the number of cycles per second and is the reciprocal of time period.

EX.NO:17 BIFILAR SUSPENSION
DATE:
AIM:
 To determine moment of inertia of object by bifilar suspension.
APPARATUS REQUIRED:
 Experimental setup
DIAGRAM:
cord
bar
FORMULA:
Theoretical mass moment of inertia=
2 2
2
( )
12
theo
M a b
I mk

  in kg-m2
Experimental mass moment of inertia=
2 2
exp 2
. . .
.4
p
M g c t
I
L 
 in kg-m2
PROCEDURE:
 Place the bar by using two equal cords.
 And also arrange the sensor and timer setup correctly.
 Oscillate the bar and note down the time period.
 Repeat the above steps for various cord length or adding masses.
SPECIFICATIONS:
 Mass of the bar (M) = 1.2 kg

Acceleration due to gravity (g) =9.81 m/s2
 Distance between center of the bar to the one end of rope (c) = 10 cm=0.1 m
 Length of the bar (a) = 59.5 cm =0.595 m
 Width of the bar (b) = 3 cm =0.03 m

TABULATION:
s.no. Length of
the cord
(L) in m
Mass
added (m)
in kg
Time
period
(tp) in s
Distance
between
center
and mass
applied
(k) in m
Experimental mass
moment of inertia
(Iexp)
in kg-m2
Theoretical
mass
moment of
inertia (Itheo)
in kg-m2
MODEL CALCULATION:
RESULT:
Thus the value of Mass moment of Inertia of body with and without mass are found out
experimentally and compared with theoretically.

EX.NO:18 TRANSVERSE VIBRATION OF FREE-FREE BEAM
DATE:
AIM:
 To Find the Natural frequency of beam by deflection method.
APPARATUS REQUIRED:
 Experimental setup.
DIAGRAM:
FORMULA:
Theoretical frequency =
1
2
theo
s
f
m

 in Hz
Stiffness=
centre
load P
s
deflection y
  in N/m
Deflection = 2 2
(3 4 )
24
center
Pa
y L a
EI
  in m
Experimental frequency = exp
1
2
g
f
 
 in Hz
PROCEDURE:
1. Measure cross section of beam.
2. Weigh the mass on the beam.
3. Fix at known distance.
4. Fix the dial gauge in particular position.
5. Now place the hanger and find deflection of beam.
6. Do it for various weights and various position of hangers.
OBSERVATIONS:
Length of the bar (L) =100 cm =1 m
Young’s modulus of the bar (E) =200×109
N/m2
Moment of inertia =
3 3
9 4
0.03 0.008
1.28 10
12 12
bd
I m


   
Acceleration due to gravity (g) = 9.81 m/s2

TABULATION:
s.no mass
of the
bar+
mass
of the
hanger
in kg
mass
added
in the
hanger
in kg
Total
mass
(m)
in kg
Load
in N
Distance
between
support
and load
applied
(a) in m
Actual
deflection
(δ) in m
Theoretical
deflection
(ycenter) in
m
Stiffness
(s) in
N/m
ftheo
in Hz
fexp
in Hz
1 2.89
2 2.89
3 2.89
4 2.89
MODEL CALCULATION:
RESULT:
Thus the natural frequency are determined by given free beam setup.

EX.NO:19 BALANCING OF RECIPROCATING MASSES
DATE:
AIM:-To determine the reciprocating masses
Balancing of reciprocating mass system
DIAGRAM:
BALANCING OF RECIPROCATING MASSES
FORMULA:-
PROCEDURE:
1. Initially all weights and bolts are removed then the motor is started. The speed of the
motor is increased due to the unbalanced masses, the vibration will be created. The vibration is
observed.
2. The speed is noted down. Now the speed is increased and the vibrations are all so
noted down. The motor is switched off then some weights added on the piston top. The weights
may be added on the piston top. The weights may be added either eccentrically (or) coaxially.
Now the motor is started the vibrations are observed at the tested speed noted in the previous
B = m1+m2 (N)
ω=2πN/60
Motor
Shaft
Vibrating Plate
Spring
Mass

case. If still the vibration are observed. One of the following has to be done to eliminate the
unbalance forces
3. Some weights are added in opposites direction of crank and the engine run and the
vibration, are observed at the tested speed.
4. Combination of both the above cases. The speeds, the weight added on piston,
diameter at which the weights are added are noted down at different case.
TABULATION:-
S. No
Crank
speed(N)
rpm
mass (grams)
Angular
velocity
Vibration
(comments)
1
m 2
m B
RESULT:
Thus the balancing of the reciprocating masses was determined.

VIVA QUESTION:-
1. State the condition for complete balancing of reciprocating mass.
For complete balancing of the reciprocating parts, the primary forces and primary couples
as well as the secondary forces and secondary couples must balance.
2. Write the expression for primary and secondary unbalanced force.
Primary unbalanced force = m ω2
r cos θ, Secondary unbalanced force = m ω2
r
𝑐𝑜𝑠2𝜃
𝑛
3. State the condition of magnitude and direction of unbalanced force due to
reciprocating masses.
The unbalanced force due to reciprocating masses varies in magnitude and constant in
direction.
4. When the primary unbalanced force is maximum?
When θ = 0o
and 180o
, the primary unbalanced force is maximum, thus the primary
unbalanced force is maximum twice in one revolution of the crank.
5. When the secondary unbalanced force is maximum?
When θ = 0o
, 90o
, 180o
and 360o
, the secondary unbalanced force is maximum, thus the
secondary unbalanced force is maximum four times in one revolution of the crank.
6. What is meant by hammer blow?
The maximum magnitude of unbalanced force along the perpendicular line of stroke is
called as hammer blow.
7. Why multi cylinder engines are desired over others?
Both balancing problem and the six of the flywheel are reduced.
8. What are Inline engines?
The multi-cylinder engine with the cylinder center lines in the same plane and on the
same side of the center line of the crankshaft, are known as In-line engines.
9. What is meant by tractive force?
The resultant unbalanced force due to the two cylinders, along the line of stroke, is
known as tractive force.
10. What is meant by swaying couple?
The unbalanced forces along the line of stroke for the two cylinders constitute a couple
about the center line between the cylinders. This couple has swaying effect about a vertical axis,
and tends to sway the engine alternately in clockwise and anticlockwise directions. Hence the
couple is known as swaying couple.

EX.NO:20 SLIDER CRANK MECHANISM
DATE:
AIM: -
To find the angular velocity of connecting rod, slider velocity, slider acceleration and
compare with its theoretical value
APPARATUS REQUIRED: -
1. Slider crank setup
DIAGRAM:-
SLIDER CRANK MECHANISM
FORMULA:-
Ø=sin-1
[r cos / L]
PROCEDURE:-
TESTING PROCEDURE:
1) This model consist of a slider crank mechanism with following features
2. A) crank length is adjustable
3. B) connecting rod length is adjustable
4. Crank and connecting rod and are hinged by ball bearings
5. Angular position of crank in measured of an accurately of 0%
6. Slider position can be measured to correction is needed.
EXPERIMENTAL PROCEDURE:
 Set the length of scale and the connecting rod.
 Ensure zero reading is crank angle for outer dead centre of crank
 Measure value of position of slider x for various values of crank angle Ø from 0, 10, 20
...180.
 Calculate indication of connecting rod
Ø = sin-1
[r sinØ/L]
Plot graph Ø-x and Ø-Ø
Find slope of Ø-x curve at the required point dx/dØ
Velocity of slider d/dx = dx/dØ. dØ/dt
dx/dØ × w compare velocity of slider for one angle ø.
× [wr [sinØ +sin2Ø/2n]]
N = 1/r
x
r L
 
Slider
Crank

 Angular velocity of connecting rod wcr/w = cosØ/r cosØ
 This can be calculating for a particular value of Ø and cam is compressed with slope of
graph.
 Wc12 = dØ/dØ
TABULATION: -
Crank
angle
(Ø)
Measured value from
scale
Distance between
crank centre and
slider
X = m + xo
Angle between slider
and connecting rod
Ø=sin-1
[r Cos / L]
xo m
RESULT:
Thus the angular velocity is verified and this theoretical value is compared with its
practical value.

VIVA-QUESTIONS:-
1. What are the applications of slider crank mechanisms?
Reciprocating engine, Rotary engine, Oscillating cylinder engine, Hand Pump, Scotch
Yoke, Oldham's coupling, Elliptical Trammel.
2. What is the operation for slider-crank mechanism?
It is the conversion of rotary to reciprocating motion
3. Where is a crank and slider mechanism used?
Crank and Slider mechanism is used in Engines which is used to raise and lower auto
windows.
4. What is double slider-crank mechanism?
A four-bar chain having two turning and two sliding pairs such that two pairs of the same
kind are adjacent is known as double-slider crank chain.
5. What is slider crank chain?
When one of the turning pairs of a four-bar chain is replaced by a sliding pair, it becomes
a single slider-crank chain or slider crank chain.
6. What is double slider crank chain?
It is also possible to replace two sliding pairs of a four-bar chain to get a double slider
crank chain.
7. Define offset.
The distance between the fixed pivot and the straight line path of the slider is called the
offset and the chain so formed an offset slider-crank chain.
8. What is Inversions?
Different mechanisms obtained by fixing different kinks of a kinematic chain are known
as its inversions.
9. What are the inversions of single slider–crank chain?
First inversion (i.e; Reciprocating engine and compressor)
Second inversion(i.e., Whitworth quick return mechanism and Rotary engine)
10.What are theinversions of double-slider crank-chain?
First inversion (i.e., Elliptical trammel)
Second inversion (i.e., Scotch yoke)

EX.NO:21 SCOTCH YOKE MACHANISM
DATE:
AIM:-To study the scotch yoke mechanism and also to measure the displacement of angle.
1. Scotch yoke mechanism
DIAGRAM:
SCOTCH YOKE MECHANISM
FORMULA:-
Displacement of piston x =x1 – x0
Velocity of piston v = ω√r2
– x2
Acceleration of piston a =
2

PROCEDURE:
1. Make the crank angle on line with the axis of mechanism
2. Twist the crank angle such that it makes an angle 10o
with the angle
3. Note down the displacement of the slider
4. Repeat the procedure for only 10o
of crank rotation
5. Apply formula to get the velocity of piston
SPECFICATION:
ω =10 rad / sec
X0 = 0
r = 9cm
A
r
B

TABULATION:-
RESULT:
Thus the scotch yoke mechanism has been studied and the displacement for the angle
of term has been measured.
VIVA QUESTION:-
1. What is scotch yoke mechanism?
A scotch yoke mechanism is used to convert the rotary motion into a sliding motion.
2. What is crank rocker?
In a four-link mechanism, a link that makes complete revolution is known as crank, the link
opposite to the fixed link the coupler and the fourth link, a lever or rocker if oscillates or another
crank, if rotates.
3. What is Universal joint?
A Hooke’s joint commonly known as a Universal joint, is used to connect two non-parallel and
intersecting shafts. It is also used for shafts with angular misalignment.
4. What is the application of Universal joint?
A common application of this joint is in an automobile where it is used to transmit power from
the gear box to the rear axle.
5. What is the difference between driving and driven speed?
The driving shaft rotates at the uniform angular speed.
The driven shaft rotates at the varying angular speed.
6. What is differentials?
Differentials means to differentiate which may be between two speeds or two values or two
readings, etc. Differentials are usually two-degree of freedom mechanisms in which two inputs
or coordinates must be defined to obtain a definite output.
7. Explain Double Slider Crank Chain?
A four bar chain having two turning and two sliding pairs such that two pairs of the same kind
are adjacent is known as double slider crank chain.
8. Explain Inversions of Double slider Crank chain?
It consists of two sliding pairs and two turning pairs. There are three important inversions of
double slider crank chain. 1) Elliptical trammel. 2) Scotch yoke mechanism. 3) Oldham’s
coupling.
9. Uses of Elliptical Trammel?
This is an instrument for drawing ellipses.
10. What is the inversion of Rotary engine mechanism?
Rotary engine mechanism or gnome engine is another application of third inversion.
S. No Crank angle (Deg) Displacement (x)

EX.NO:22 CRANK ROCKER
DATE:
AIM:-To determine the angular velocity ratio 4
2


for various angular position and link sizes
DIAGRAM:
CRANK ROCKER
FORMULA:-
Angle between link 2 and link 3
3
 = tan-1
[ 4
r sin 4
 – 2
r sin 2
 /r1- r2 cos 2
 + r4cos 4
 ]
Velocity ratio between links 2, 4
4
2


=r2 sin ( 3
 – 2
 )/r4 sin ( 3
 – 4
 )
Velocity ratio of between links 2, 3
3
2


=r2 sin ( 4
 – 2
 )/r3 sin ( 3
 – 4
 )
PROCEDURE:-
1. Check the position of gear screw in crank
2. And also check the position of couple and rocker
3. Check the angular position of crank and rocker cam be measured with accuracy of
0.1
OBSERVATION:-
Crank length = 80 – 120 mm
Couple length = 180 – 320 mm
Rocker length = 130 – 320 mm
Overall size = 600 × 300 mm
Weight = 2 kg, Resolution = 0.1
r1 = 250 mm r3 = 320 mm
r2 = 145 mm r4 = 180 mm
r2
3
r3
4
2
r4
r1

TABULATION:-
S.No 2
 4
 3

4
2


3
2


MODEL CALCULATION:
RESULT:-
Thus the angular velocity of 4
2


& 3
2


was found out and compared with the graphical
value.

VIVA QUESTIONS:-
1.Define simple mechanism?
A mechanism with four links is known as simple mechanism.
2. Define compound mechanism?
the mechanism with more than four links is known as compound mechanism.
3.Define machine?
When a mechanism is required to transmit power or to do some particular type of work, it then
becomes a machine
4.Define mechanism?
When one of the links of a kinematic chain is fixed, the chain is known as mechanism.
5. Define 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
6.Types of Joints in a Chain?
1. Binary joint 2. Ternary joint.
7.Define Binary joint?
When two links are joined at the same connection, the joint is known as binary joint.
8.Define Ternary joint?
When three links are joined at the same connection, the joint is known as ternary joint
9.Define Quaternary joint?
When four links are joined at the same connection, the joint is called aquaternary joint
10.Grubler’s Criterion for Plane Mechanisms?
A plane mechanism with a movability of 1 and only single degree of freedom joints can not have
odd number of links. The simplest possible machanisms of this type are a four bar mechanism
and a slider-crank mechanism in which l = 4 and j = 4.

EX.NO: 23 EPICYCLIC GEAR TRAIN
DATE:
AIM: To determine the speed for annular, arm and compare with the theoretical value.
Experimental setup
DIAGRAM:
EPICYCLIC GEAR TRAIN
FORMULA:-
 Annular speed / sun speed = NA/NS = S/A
 Annular fixed
Annular speed/arm speed = NA/NS =
1
1
A
s
 

 
 
 Sun fixed
Annular speed/arm speed = Nu/Ns = s/A
Where,
s- No of teeth of sun wheel = 33
A-no of teeth of annular = 63
q-no of teeth of planet gear = 15
PROCEDURE:-
 Find the arm c by align the give some x degree by annulus and vertically that annulus
resolution in s/n towing of run wheel.
 Find annulus by align the screw in annulus outer given n degree rotation run wheel and
measure angle.
 Find the above value and verify its theoretical value.

TABULATION:-
Fixed
position
Angle rotated Actual speed of sun
Theoretical ratio of
sun
sun annular arm annular arm annular arm
Annular
Arm
RESULT:-
Thus the annular and arm speed ratio are determined by experiment in epicyclic gear box
and compared with its theoretical value.
VIVA QUESTIONS:-
1. Define epicyclic gear train?
An epicyclic gear train, the axes of the shafts, over which the gears are mounted, may
move relative to a fixed axis.
2. Advantage epicyclic gear train?
The epicyclic gear trains are useful for transmitting high velocity ratios with gears of
moderate size in a comparatively lesser space.
3. Uses of epicyclic gear train?
The epicyclic gear trains are used in the back gear of lathe, differential gears of the
automobiles, hoists, pulley blocks, and wrist watches etc1.Define epicyclic gear train?
4. Methods may be used for finding out the velocity ratio of an epicyclic gear train?
The following two methods may be used for finding out the velocity ratio of an epicyclic
gear train. 1. Tabular method 2.Algebraic method.
5. Define gear train?
Sometimes, 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.
6. Types of Gear Trains?
1. Simple gear train, 2. Compound gear train, 3. Reverted gear train, and 4. Epicyclic
gear train
7. Define simple gear train?
When there is only one gear on each shaft, it is known as simple gear train.
8. Define train value?
Ratio of the speed of the driven or follower to the speed of the driver is known as train
value of the gear train
9. Define idle gears?
Intermediate gears are called idle gears
10. Define compound train of gear?
When there are more than one gear on a shaft, it is called a compound train of gear.

EX.NO:24 SIMPLE GEAR TRAIN
DATE:
AIM:-To draw the speed diagram, ray diagram by using the simple gear train.
DIAGRAM:
SIMPLE GEAR TRAIN
1
T =40 2
T =20 3
T =20
4
T =40
FORMULA:-
GEAR RATIO=
𝑁𝑈𝑀𝐵𝐸𝑅𝑂𝐹𝑅𝐸𝑉𝑂𝐿𝑈𝑇𝐼𝑂𝑁 𝐼𝑁 𝑂𝑈𝑇𝑃𝑈𝑇 𝑆𝐻𝐴𝐹𝑇
𝑁𝑂 𝑂𝐹 𝑅𝐸𝑉𝑂𝐿𝑈𝑇𝐼𝑂𝑁 𝐼𝑁 𝐼𝑁𝑃𝑈0𝑇 𝑆𝐻𝐴𝐹𝑇
DEVATION=
𝑃𝑅𝐸𝐹𝐸𝑅𝐷 𝐺𝐸𝐴𝑅 𝑅𝐴𝑇𝐼𝑂−𝐴𝐶𝑇𝑈𝐴𝐿 𝐺𝐸𝐴𝑅 𝑅𝐴𝑇𝐼𝑂
𝑃𝑅𝐸𝐹𝐸𝑅𝐸𝐷 𝐺𝐸𝐴𝑅 𝑅𝐴𝑇𝐼𝑂
∗ 100
PROCEDURE:
1. Count no of offset in each gear.
2. Calculate the module of gear same of all the gear.
3. Module=
𝑂𝑈𝑇𝐸𝑅 𝐷𝐼𝐴𝑀𝐸𝑇𝑅 𝐴𝑁 𝐺𝐸𝐴𝑅 𝑇𝐸𝐸𝑇𝐻
𝑁𝑂 𝑂𝐹 𝑇𝐸𝐸𝑇𝐻+2
4. Find out the mass moment of inertia of the disc and test object using formula.
SPECIFICATION:
Number of speed=2
Number of shaft=2
Overall size=250x60x300 mm
Approximate weight=5kg

TABULATION:-
Gear
position
Calculation of gear ratio
Actual ratio Deviation
I/P rev O/P rev Output/input
RESULT:
Thus the speed ratio of simple gear train was verified
VIVA QUESTION:-
1. Define driver?
When the distance between the two shafts is small, the two gears 1 and 2 are made to
mesh with each other to. Transmit motion from one shaft to the other, since the gear 1 drives
the gear 2, therefore gear 1 is called the driver
2. Define driven?
When the distance between the two shafts is small, the two gears 1 and 2 are made to
mesh with each other to. Transmit motion from one shaft to the other, since the gear 1 drives
the gear 2, therefore gear 1 is called the driver and the gear 2 is called the driven or follower.
3. Define Speed ratio?
The speed ratio (or velocity ratio) of gear train is the ratio of the speed of the driver to
the speed of the driven or follower.
4. Methods may be used for finding out the velocity ratio of an epicyclic gear train?
The following two methods may be used for finding out the velocity ratio of an epicyclic
gear train. 1. Tabular method, 2.Algeberic method.
5. Define gear train?
Sometimes, 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.
6. Types of Gear Trains?
gear train
7. Define simple gear train?
When there is only one gear on each shaft, it is known as simple gear train.
8. Define train value?
Ratio of the speed of the driven or follower to the speed of the driver is known as train
value of the gear train
9. Define idle gears?
Intermediate gears are called idle gears
10. Define compound train of gear?
When there are more than one gear on a shaft, it is called a compound train of gear.

EX.NO:25 COMPOUND GEAR TRAIN
DATE:
AIM:-
To draw the speed diagram or phase diagram by using gear train.
1. No of shaft =2
2. Overall size = 600*300*300
3. Approximate weight =10 kg
4. Apparatus weight = 10 kg
5. Resolution = P for angular measurement
DIAGRAM:
COMPOUND GEAR TRAIN
FORMULA:-
GEAR RATIO=
𝑁𝑂𝑂𝐹 𝑅𝐸𝑉𝑂𝐿𝑈𝑇𝐼𝑂𝑁 𝑂𝑈𝑇𝑃𝑈𝑇
𝑁𝑂 𝑂𝐹 𝑅𝐸𝑉𝑂𝐿𝑈𝑇𝐼𝑂𝑁 𝐼𝑁𝑃𝑈𝑇
DEVIATION=
𝑃𝑅𝐸𝐹𝐸𝑅𝐷 𝐺𝐸𝐴𝑅 𝑅𝐴𝑇𝐼𝑂−𝐴𝐶𝑇𝑈𝐴𝐿 𝐺𝐸𝐴𝑅 𝑅𝐴𝑇𝐼𝑂
𝑃𝑅𝐸𝐹𝐸𝑅𝐷 𝐺𝐸𝐴𝑅 𝑅𝐴𝑇𝐼𝑂
*100
PROCEDURE:
1. Check the sliding gear in mesh with its meshing gears.
2. Check the numbers of teeth for all the gear.
3. Check the bearings shafted keys positive check the gear number are perfectly.
4. Draw the speed diagram.
Z
1
Z
2
Z
3
Z
5
Z
Z
6 Z
7
Z
9
Z10
Z
8 Z12
Z11
Input
Output

TABULATION:-
Gear
position
calculation gear ratio output/input Theoretical gear
ratio
deviation
%
I/P O/P
RESULT:
Thus the speed ratio are found for the gear train and couponed with its actual valve.

VIVA QUESTION:
1.What uses a compound gear train?
Any power plant that uses more than a single steam turbine as a prime mover. It could be a
power plant, or a ship for instance. They use a compound gear train to get everything going.
2.What is simple gear train and compound gear train?
A simple gear train is basically the same as a compound gear train, but the compound gear
train usually has more gears closer together.
3.Give general use of gears?
•To reverse the direction of rotation
•To increase or decrease the speed of rotation
•To increase or decrease the speed of rotation
4.What is difference between simple and compound gear train?
A simple gear train is one in which each gear is fastened to a separate shaft, If at least
one shaft has two or more gears fastened to it, the train is said to be compound.
5. Explain gear train?
A gear train is formed by mounting gears on a frame so that the teeth of the gears
engage.
6. What are the Types of Gear Trains?
gear train.
7. What is the advantage of a compound train over a simple gear train?
The advantage of a compound train over a simple gear train is that a much larger speed
reduction from the first shaft to the last shaft can be obtained with small gears.
9. Explain Worm gears?
This connects at 90° to a large gear (the thread shaft points along the outside edge of
the larger gear). Each time the shaft spins one revolution, the gear turns forward by only one
tooth. If the gear has 50 teeth, this creates a gear ratio of 50:1.
10. Explain Bevel gears?
Bevel gears, like worm gears, change the axis of rotation through 90°. The teeth have
been specially cut so the gears will mesh at right-angles to each other, where spur gears must
be parallel.

EX.NO:26 KINEMATICS OF UNIVERSAL JOINT
DATE:
AIM:-To determine the angular velocity ratio for single and double joint
DIAGRAM:
UNIVERSAL JOINT
FORMULA:-
Angular velocity ratio is single joint
ω2 /ω1 =cos∝/1-(cos2
α-sin2
α)
Experimental velocity ratio for single joint
ω2 /ω1 =( 2
d /dt) /( 1
d /dt)= 2
d / 1
d
Where,
ω2, ω1 angular velocity of output and input.
TESTING PROCEDURE:
 Check the joints are perfect.
 Check the measuring scale is connected or not.
 Check the initial connection.
EXPERIMENTAL SETUP:
 Get α=0 initial measure valve of ϴ and ϴ for several of ϴ starting from 0 to 360.
 More output shaft for perpendicular valve of given α-25 and α0 is step 2.
 Calculate dϴ = about experimental angular velocity ratio ω2 /ω1 =cos α/1-
(cos2
α+sin2
α)
 Calculate theoretical angular velocity ratio ω2 /ω1 =cos α/1-(cos2
α+sin2
α)
 Draw the graph for b/w follow data same graph sheet.
 At this for X=30, 35, 40 and verify with the theoretical one.

TABULATION:-
α ϴ1 ϴ2 ϴ3 dϴ2
Experimental ω2 /ω1
=
dϴ2 /dt1
Theoretical
ω2 /ω1
cosα/1-(cos2
α+sin2
α)
RESULT:
Thus the angular velocity ratio of single and double joint was determined.

VIVA QUESTION:
1. Explain the Kinematics of Universal Joints?
If two shafts bent at angles to each other are connected with a universal joint and the
drive shaft moves at constant angular velocity, the driven shaft runs with uneven angular
velocity.
2. What are the objectives of this experiment?
(1)To investigate the kinematic characteristics of a universal joint (a Hooke's joint).
(2)To determine the effect of using this type of joint to transmit uniform motion
3. Explain Single Joint?
For this section the intermediate shaft ant the output shaft are always aligned in a
straight line. Determine the angular displacement ratio between the input and output shaft for
five different angles between the input and output shaft.
4. Explain the Two Joints - Parallel Output Shaft?
Adjust the Hooke's joints on either end of the center shaft such that the axes of the pins
(for the two portions on the center shaft) are parallel.
5. Explain the Two Joints - Perpendicular Output Shaft?
Adjust the Hooke's joints on either end of the center shafts such that the axes of the
pins are perpendicular.
6. What are the Applications?
Typical applications of universal joints include aircraft, appliances, control mechanisms,
electronics, Instrumentation, medical and optical devices, ordnance, radio, sewing machines,
textile machinery and tool drives.
7. What are the materials it is made up of?
Universal joints are available in steel or in thermoplastic body members. Universal joints
made of steel have maximum load-carrying capacity for a given size. Universal joints with
thermoplastic body members are used in light industrial applications.
8. What are the other types of joints?
Universal joints of special construction, such as ball-jointed universals are also available.
These are used for high-speed operation and for carrying large torques. They are available both
in miniature and standard sizes.
9. What are the advantages of Single Cardan joints?
 Low side thrust on bearings.
 Large angular displacements are possible.
 High torsional stiffness.
High torque capacity.

EX.NO:27 STUDY OF DIFFERENTIAL GEAR MECHANISM
DATE:
AIM:-
To study about the arrangement of gear automotive differential mechanism.
DESCRIPTION:
DIFFERENTIAL GEAR:-
When a vehicle takes a turn, the outer wheels must travel farther than the inner wheels. In
automobiles, the front wheels can rotate freely on their axis and thus can adapt themselves to
the conditions. Both rear wheels are driven by the engine through gearing. Therefore, some of
automatic device is necessary so that the two rear wheels are driven at slightly different speeds.
This is accomplished by fitting a differential gear on the rear axle. This consist of drive shaft
driving ring gears through a special level gear normally this will provide uniform rotation to both
gear wheels. Outer wheels have to rotate in near wheel to avoid any slip. This made possible
by the differential provided by differential unit provided.
DIAGRAM:
AUTOMOBILE STEERING GEAR
RESULT: Thus the arrangement of automatic differential mechanism is studied.
w
l
a
θ
θ
φ
φ

VIVA QUESTION:-
1.Why we use a Differential?
When a car turns a corner, one wheel is on the "inside" of a turning arc, and the other
wheel is on the "outside." Consequently, the outside wheel has to turn faster than the inside
one in order to cover the greater distance in the same amount of time. Thus, because the two
wheels are not driven with the same speed, a differential is necessary. A car differential is placed
halfway between the driving wheels, on either the front, rear, or both axes (depending on
whether it’s a front-, rear-, or 4-wheel-drive car). In rear-wheel drive cars, the differential
converts rotational motion of the transmission shaft which lies parallel to the car’s motion to
rotational motion of the half-shafts (on the ends of which are the wheels), which lie
perpendicular to the car’s motion.
2. How Differential works?
Assuming the wheels do no slip and spin out of control, the following two examples of
car motion describe how the differential works when the car is going forward and when it is
turning.
3. What is differential Ratios?
The ratio of speeds between gears is dependent upon the ratio of teeth between the two
adjoining gears such that
w1 x N1 = w2 x N2
4.What is differentialVelocity?
When two gears are in contact and there is no slipping, v = w1 x r1 = w2 x r2, where v is the
tangential velocity at the point of contact between the gears, and r is the respective pitch radius
of the gear. In a differential, since the speed transmitted by the crown gear is shared by both
of the wheels (not necessarily traveling at the same speed),
win = (w1 + w2) / 2
5. What is differential Power?
Typically, each gear mesh will have 1%-2% loss in efficiency, so with three different
meshes from the transmission shaft to each of the half shafts, the system will actually be 94%
to 97% efficient.
6.What is called Limiting physics?
Things that might limit or disrupt the behavior of the differential include contact stresses
between the gears, which limits the torque transmission, as well as fatigue and losses due to
friction between the gears.
7.What islimited slip differential?
If one of the wheels attached to a differential decides to hit some ice, for example, it
slips and spins with all of the speed the differential has to distribute. Thus, a locking mechanism,
or "limited slip differential" allows one wheel to slip or spin freely while some torque is delivered
to the other wheel
8. Where to find differentials?
In the rear axles of most cars and trucks.
9. A differential gear in an automobile is a?
Epicyclic gear train.
10. A differential gear in automobiles is used to?
Help in turning.

Expt. No.28 STUDY OF GEAR PARAMETERS
Date:
Aim:
To study the various types of gears and its parameter
Apparatus required:
Arrangement of gear system
Introduction:
Gears are used to transmit motion from one shaft to another or between a shaft. This is
accomplished by successful engaging of tooth. Gears are intermediate links or
connections and transmit the motion by direct contact. In this method the surface of two
bodies have either a rolling or sliding motion along the tangent at the point of contact to
transmit the definite motion of one disc to another or to prevent slip between the surface
projection and recession on two discs can be made which can mesh with each other. The
discs with teeth are known as gears or gear wheel.
Classification of gear:
The different kinds of gears are:
1. Based on the peripheral velocity of gears
a. Low velocity gears – Gears with peripheral velocity < 3 m/s
b. Medium velocity gears – Gears with peripheral velocity = 3-15 m/s
c. High velocity gears – Gears with peripheral velocity > 15 m/s
2. Based on the position of axes of revolution
a. Gears with parallel axes
i. Spur gear
ii. Helical Gear
a) Single Helical Gear
b) Double Helical Gear (or) Herringbone Gear
b. Gears with intersecting axes
i. Bevel Gear
a) Straight bevel gear
b) Spiral bevel gear
c) Zerol bevel gear
d) Hypoid bevel gear
ii. Angular gear
iii. Miter gear
c. Gears with non-parallel and non-intersecting axes
i. Worm gear
a) Non-throated worm gear
b) Single-throated worm gear
c) Double-throated worm gear
ii. Hypoid gear
iii. Screw gear (or crossed helical gear)
3. Based on the type of gearing
a. Internal gear
b. External gear

c. Rack and Pinion
4. Based on the tooth profile on the gear surface
a. Gears with straight teeth
b. Gears with curved teeth
c. Gears with inclined teeth
1. Spur Gear:
Spur gears have straight teeth parallel to the rotating axis and thus are not subjected to
axial thrust due to teeth load. Spur gears are the most common type of gears. They
have straight teeth, and are mounted on parallel shafts. Sometimes, many spur gears
are used at once to create very large gear reductions.
Each time a gear tooth engages a tooth on the other gear, the teeth collide, and this
impact makes a noise. It also increases the stress on the gear teeth. Spur gears are the
most commonly used gear type. They are characterized by teeth, which are
perpendicular to the face of the gear. Spur gears are most commonly available, and are
generally the least expensive.

Spur Gear Terminology:
Fig. Spur Gear Terminology

The following terms, which are mostly used to describe a gear, are as follow:
 Face of tooth: It is defined as the surface of the tooth above the pitch circle is
known as face.
 Flank of tooth: The surface of the tooth below the pitch circle is known as flank.
 Top land: The top most surface of the tooth is known as the top land of the tooth.
 Face width: Width of the tooth is known as face width.
 Pitch Circle: It is an imaginary circle which is in pure rolling action. The motion
of the gear is describe by the pitch circle motion.
 Pitch Circle diameter: The diameter of the pitch circle from the center of the
gear is known as pitch circle diameter. The gear diameter is described by its pitch
circle diameter.
 Pitch point: When the two gears are in contact, the common point of both of
pitch circle of meshing gears is known as pitch point.
 Pressure angle or angle of obliquity: Pressure angle is the angle between
common normal to the pitch circle to the common tangent to the pitch point.
 Addendum: Distance between the pitch circle to the top of the tooth in radial
direction is known as addendum.
 Dedendum: Distance between the pitch circle to the bottom of the tooth in
radial direction, is known as dedendum of the gear.
 Addendum circle: The circle passes from the top of the tooth is known as
addendum circle. This circle is concentric with pitch circle.
 Dedendum circle: The circle passes from the bottom of the tooth is known as
dedendum circle. This circle is also concentric with pitch circle and addendum
circle.
 Circular pitch: The distance between a point of a tooth to the same point of the
adjacent tooth, measured along circumference of the pitch circle is known as
circular pitch. It is plays measure role in gear meshing. Two gears will mesh
together correctly if and only they have same circular pitch.
 Diametrical pitch: The ratio of the number of teeth to the diameter of pitch
circle in millimeter is known as diametrical pitch.
 Module: The ratio of the pitch circle diameter in millimeters to the total number
of teeth is known as module. It is reciprocal of the diametrical pitch.
 Clearance: When two gears are in meshing condition, the radial distance from
top of a tooth of one gear to the bottom of the tooth of another gear is known
as clearance. The circle passes from the top of the tooth in meshing condition is
known as clearance angle.
 Total depth: The sum of the addendum and dedendum of a gear is known as
total depth. It is the distance between addendum circle to the dedendum circle
measure along radial direction.
 Working depth: The distance between addendum circle to the clearance circle
measured along radial direction is known as working depth of the gear.
 Tooth thickness: Distance of the tooth measured along the circumference of the
pitch circle is known as tooth thickness.
 Tooth space: Distance between the two adjacent tooth measured along the
circumference of the pitch circle is known as the tooth space.
 Backlash: It is the difference between the tooth thickness and the tooth space.
It prevents jamming of the gears in meshing condition.
 Profile: It is the curved formed by the face and flank is known as profile of the
tooth. Gear tooth are generally have cycloidal or involute profile.
 Path of contact: The curved traced by the point of contact of two teeth form
beginning to the end of engagement is known as path of contact.

 Arc of contact: It is the curve traced by the pitch point form the beginning to
the end of engagement is known as arc of contact.
 Arc of approach: The portion of the path of contact from beginning of
engagement to the pitch point is known as arc of approach.
 Arc of recess: The portion of the path of contact form pitch point to the end of
the engagement is known as arc of recess.
2. Helical Gear:
The helical gear is used to connect two parallel shafts and teeth inclined or unused
to the axis of the shafts. The leading edges of the teeth are not parallel to the axis
of rotation, but are set at an angle. Since the gear is curved, this angling causes
the tooth shape to be a segment of a helix. Helical gears can be meshed in a
parallel or crossed orientations.
Fig. Helical Gear Fig. Bevel Gear
3. Bevel Gear:
Bevel gears transmit power between two intersecting shafts at any angle or between
non- intersecting shafts. They are classified as straight and spiral tooth bevel and hypoid
gears. When intersecting shafts are connected by gears, the pitch cones (analogous to
the pitch cylinders of spur and helical gears) are tangent along an element, with their
apexes at the intersection of the shafts where two bevel gears are in mesh. The size and
shape of the teeth are defined at the large end, where they intersect the back cones.
Pitch cone and back cone elements are perpendicular to each other. The tooth profiles
resemble those of spur gears having pitch radii equal to the developed back cone radii.
4. Worm Gear:
Worm gears are usually used when large speed reductions are needed. The reduction
ratio is determined by the number of starts of the worm and number of teeth on the
worm gear. But worm gears have sliding contact which is quiet but tends to produce
heat and have relatively low transmission efficiency.
The applications for worm gears include gear boxes, fishing pole reels, guitar string
tuning pegs, and where a delicate speed adjustment by utilizing a large speed reduction
is needed.

5. Screw gears:
Screw gears, also sometimes called crossed helical gears, are helical gears used in
motion transmission between non-intersecting shafts. The helical gears used in parallel
shafts have the same helix angle but in the opposite directions.
6. Miter gears:
Miter gears are one type of bevel gears where the two rotational axes intersect. When
speaking of narrow definition of bevel gears with ability to increase or decrease speed,
miter gears do not have that ability due to the pair’s same number of teeth. Their
purpose is limited to the change in transmission direction. Because they are a type of
bevel gears, the basic characteristic of bevel gears exist such as presence of gear forms
of straight cut, spiral cut and zerol types.

Result:
Thus gear, types and its parameters were studied.
Outcome:
Able to demonstrate the principles of gear, types and its parameters
Application:
1. They are used in back gear of the lathe, hoists, pulley blocks, clock, wrist watches
and precision equipment.
2. They are popular for automatic transmission in automobiles.
3. They are used for power train between internal combustion engine and an electric
motor.
4. They are also used in speed drives in textile and Jute machineries.
1. Define – Pitch circle
2. Define – Pitch point
3. Define – Circular pitch
4. Define – Module
5. Define – Backlash
7. What is axial of a helical gear?
8. Define – Cycloid
9. Define – Undercutting gear
10. What is meant by contact ratio?
11. Define – Gear tooth system
12. State law of gearing.
13. What is an angle of obliquity in gears?
14. What is bevel gearing? Mention its types.
15. What are the methods to avoid interference?
16. What do you know about tumbler gear?
17. Define – Interference
18. Define – Backlash
19. What is meant by non – standard gear teeth?
20. Define – Cycloidal tooth profile
Viva-voce

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