# C CO ON NT TE EN NT TS S

Mechanics

Oct 31, 2013 (4 years and 8 months ago)

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B
Tech

(Mechanical)

DYNAMICS LAB 4
th

sem

C
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1.

Study of Gyroscopic effect and determination of gyroscopic couple.

2.

Dynamic balancing of the rotating mass system.

3.

To determine radius of Gyration “K” of given pendulum.

4.

To study the free vibration and to

determine the natural frequency of
vibration of Tow
-
Rotor system.

5.

Study of longitudinal vibration and to determine the frequency of
vibration.

6.

Assembly and Working of 4
-
Bar, 6
-
Bar, 8
-
Bar Planar Mechanisms
.

2
2

Experiment No. 1
.

Title: Stud
y Of Gyroscopic effect and determination of gyroscopic
couple.

Equipment:
Motorized Gyroscope

Aim:
To study the gyroscopic principle and verify the relation between the
applied torque, Spin velocity and Precessional velocity in case of free
precession an
d forced precession.

Formula Used:

1. Gyroscopic couple C = I x w x w
p

2. Applied Torque (T) = W X r’

Procedure of Experiment:

Part I:

The spinning body exerts a torque or a couple in such a direction which tends
to make the axis of spin coincides with t
hat of the precession. To study the
phenomenon of forced precession following procedure is adopted.

1.

Balance initial horizontal position of rotor.

2.

Start the motor and adjust the voltage to get the constant speed.

3.

Press the yoke frame about the vertical axi
s by applying the necessary
force by hand in the clockwise direction viewed from the top.

4.

It will be observed that rotor frame swing about the horizontal axis so
that the motor side moves upwards.

5.

Rotating the yoke axis in the opposite direction causes the

rotor frame
to move in the opposite direction.

Part II:

The spinning body precesses in such a way that to make the axis of spin to
coincide with that of the applied couple. The direction is verified by following
the procedure given below and using the ap
paratus as well as the relation for
the magnitude of the couple.

1.

Balance the rotor in the horizontal plane.

2.

Start the motor and adjust the speed with the help of voltage regulation.
The speed is measured using a tachometer.

3.

Put weights on the side opposite

to the motor.

4.

The yoke start precessing.

5.

Note down the direction of precession.

6.

Verify this direction

7.

Measure the velocity of precession using the pointer provided the yoke
and stop watch.

8.

Verify the relation C = I X W X w
p

Observations:

Part I :

1.

Direct
ion of spin axis : CLOCKWISE/ANTICLOCKWISE

2.

Direction of forced precession : DOWNWORD

3
3

3.

Direction of couple acting on the frame :
CLOCKWISE/ANTICLOCKWISES

Part II:

1.

Mass of rotor (m) : 3kg

2.

Thickness of rotor : 19mm

3.

Rotor diameter (d) : 220mm

4.

Moment arm (r’) :

200mm

5.

Motor power : 120w

6.

Speed of motor : 0

500 rpm

Calculations:

1.

Moment of Inertia (I) = Kg.m²

2.

w = 2
π

3.

wp =
θ
/ t X
π

4.

Gyroscopic Couple © = I X w X wp = N

m.

5.

Applied Torque (T) = Wr’ = N

m.

Conclusions :

a)

are to be written based on the observations of direction
observed during Part I and Part II of the experiment.

b)

The values tabulated in the result table are to be compared (i.e. the
values of C & T are compared) and comments on the variation are to
be writt
en.

c)

Different case where the gyroscopic couple is observed is to be
mentioned.

4
4

Experiment No.
2

Title: Dynamic Balancing of Rotary Mass System

Equipment:
Dynamic Balancing Machine

Aim:

1. To obtain balancing mass for static balancing of rotary mass
system.

2. To obtain balancing mass for the rotating mass system

Formula Used:

Force = m x w² x r

Procedure of Experiment:

1.

Attached the balance frame to maintain frame firmly. Insert the card
with pan to the grooved pulley provided set the unit to 0 posi
tions.

2.

Values of static balancing for all the weights will be arrived when we
are conducting the experiment of dynamic balancing.

3.

Now keep the block in any suitable position as reference and fix the
second block in any convenient position say 3cm to left.

4.

Now hang the frame by chain and couple it with motor and run the
motor by using electric dimmer to a rated speed. By this way we can
balance the machine.

5.

If the calculation is not correct then the unit will vibrate. That indicates
there is some calculation

mistake at the time of drawing the force and
couple polygon.

6.

Attach any clock to the shaft at any position.

7.

Put steel balls in one of the pans to bring the block to original 90°
positions.

8.

Number of balls proportional to the ‘wr’ value o block.

9.

Repeat the

experiment for other three blocks.

10.

wr X No. of balls.

Calculations:

Force l = m x W² x r

Typical Result: (
For Illustration o Experimental Calculations)

Experiments :

To statically balance a four place rotating mass system, Block No. 2 is to be
positio
ned 90 anticlockwise and 3cms. Along the shaft from block No. 1
determine the angular and longitudinal positions of blocks 3 and 4 for perfect
balance.

Conclusions:

1. The force and the couple polygon coming to be close hence the force
produce

due to rotat
ing masses are completely balance.

5
5

Experiment No.
3

Title
:
To determine the radius of Gyration of a pendulum

Equipment:
.

Aim:

To determine the radius of Gyration of compound pendulum to verify relation

T = 2
π

K² +(OG)²/g(OG)²

Formula Used:

Force = m x w² x r

Procedure Of Experiment:

1.

Support the rod in any of the hole.

2.

Note the length of suspended pendulum.

3.

Allow the bar to oscillate and determine T by noting the time for say 10
oscillations.

4.

Repeat the exp
eriment with a small angular displacement
θ
, then
couple tending to restore the pendulum to the equilibrium position, T
=mgh sin
θ

Result Table:

Radius of gyration for pendulum are

K
th =

K
exp
=

6
6

Experiment No. 4

Title: To determine natural
frequency of torsional Vibration in two rotors
System.

Equipment:
Shaft, two rotor disc, chuck, stop watch.

Aim:
To determine natural frequency of torsional vibration theoretically

Experimentally in a two rotor system
.

Formula Used:

Procedure of Experi
ment:

1.

Fix two disc of the shaft and fit the shaft in the bearing.

2.

Deflect the disc in opposite direction by hand and then release.

3.

Note down the time required for particular number of oscillations.

4.

Fit cross arm to one end of the disc and again note down t
he time.

5.

Repeat the procedure with different and equal masses attached to the
ends of cross arm and note down
the time.

Observation:

Observations are to taken for copper and steel shafts.

Result:

The natural frequency of the torsional vibration in two

rotor system is
---
--
Hz

Conclusion:

It is studied to determine the natural frequency of vibration of the given
shaft. It is necessary to find out the natural frequency, so that during working
resonance will be taken care of
.

7
7

Experiment No.
5

T
itle: To study longitudinal vibration of a helical spring and to determine

the Frequency of vibration.

Equipment:
Helical spring, rigid support, scale, stop
-
watch
.

Formula Used:

K = W/S

T
exp =
Time
(t)
/ Oscillation(n)

T
th
= 2
π√
w/ K
mean

F = 1 / n

Proced
ure Of Experiment:

1.

Fix one end of the helical spring to upper screw.

2.

Determine the straight length of the helical spring at no load.

3.

Put the known height of the platform at same distance.

4.

For oscillations, Stretch the spring for some distance and leave it.

5.

Count the time for no. of oscillations.

6.

Determine the actual time period.

7.

Repeat the same procedure for different weights.

Result:

The mean actual frequency is found to be
-------

and theoretical frequency is
found to be
-------

Conclusion:

It is foun
d that the actual and the theoretical frequencies of the vibration close
to each other.

8
8

EXPERIMENT NO.
6

TITLE: ASSEMBLY AND WORKING OF 4
-
BAR, 6
-
BAR, 8
-
BAR PLANAR

MECHANISMS

Aim
:
-

To study of Assembly and working of 4
-
bar, 6
-
bar and 8
-
bar plan
ar

mechanism.

Theory:
-

A resistant body or group of resistant bodies with

rigid connections preventing their relative movement is known as link. A link

may

be defined as a member or a combination of members of a mechanism,

connecting oth
er members and having motion relative to them. Thus a link

may

consist of one or more resistant bodies. A slider crank mechanism

consist of

four links; Frame and guides, crank connecting rod and slider.

However, the

frame may consist of bearings for the cr
may have

crankshaft and flywheel also, forming one link having no relative

motion of

these.

Links can be classified into Binary, ternary, quaternary etc. depending upon

its ends on which revolute or turning can be placed.

Kine
matic pair:

A kinematic pair or simply a pair is a joint of two links having relative

motion
between them. In slider
-

1 and
constitutes a revolute or turning pair. Link 4 (slider) reciprocates relative

to lin
k
1 and is a sliding pair.

9
9

Type of kinematic pair:

Kinematic pairs can be classified according to

Kinematic pair according to nature of contact

a)
Lower pair:
A pair of links having surface or area contact between

the
members is known as a lower pair. The contact surfaces of the two

similar.

Ex
ample: Nut turning on a screw, shaft rotating in a bearing, all pairs of
a

slider
-
crank mechanism, universal joint etc.

b)
Higher pair:
When a pair has appoint or line contact between the

known as higher pair. The contact surfaces of the two

dissimilar.

Example: wheel rolling on a surface, cam and follower pair, tooth gears,

balls
and roller bearings, etc.

Kinematic pairs according Nature of relative motion

a)
Sliding pair:
If two links have a sliding motion relative to each

other,
they
form a sliding pair.

A rectangular rod in a prism is a sliding pair.

b)
Turning pair:
when one link has a turning or revolving motion relative

to each other, they constitute a turning pair or revolving pair.

In slider
-
crank
mechanism, all pairs excep
t the slider and guide pair are turning

pairs. A
circular shaft revolving inside a bearing is a turning pair.

c) Rolling pair:
when the links of a pair have a rolling motion relative to

each
other, they form a rolling pair, e.g. a rolling wheel on a flat
surface,

ball and

roller bearing, the ball and the shaft constitute one rolling pair

whereas the ball
and the bearing is the second rolling pair.

d) Screw pair:
If two mating links have turning as well as sliding

motion

between them, they form a screw pai
r. This is achieved by cutting

matching

The lead screw and the nut of a lathe is a screw pair.

e)
Spherical pair:
when one link in the form of a sphere turns inside a

fixed

The ball and socket joint is
a spherical pair.

Kinematic Chain:

A kinematic chain is an assembly of links in which the relative motions of the

links is possible and the motion of each relative to the others is definite.

In
case, the motion of a link results in indefinite motions of o

a non
-
kinematic chain.

Mechanism:

If one of the links of a kinematic chain is fixed to the ground and if motions of

each link results in definite motions of the others, the linkage is known as

mechanism.

To obtain constrained or definite

motions of some of the links of
t
he

mechanism, it is necessary to know how many inputs are needed. In some

and are said to have one degree of freedom. In other mechanism, two

1
1
0
0

inputs

may be necessary to get a constrained motions of the another links
and
are said

to have two degrees of freedom and so on.

Four bar mechanism:

A
four bar mechanism is the most fundamental of the lane kinematic

is much preferred mechanical device for the mechanization and

control of

motion due to its simplicity

and versatility. Basically it consists of

four rigid
links which are connected in the form of a quadrilateral by four pin

joints.

A
link that make complete revolutions is the crank, the link opposite to the

fixed
lever or rocker if oscillates or an

another crank, if rotates.

A four bar mechanism has the following

characteristics based on the lengths of

1. It is impossible to have a four bar mechanism if length of the one of the

sum of the other three.

2. If the sum of the lengths of the largest and the shortest links is less than

the
sum of the other two links, the linkage is known as class
-
I, four
-

bar

mechanism.

If the links of the four bar mechanism obtained above, are fixe
d, different

mechanisms are obtained known as Inversion

revolutions. The mechanism thus obtained is known as crank
-

crank or double

crank or rotary
-

rotary m
echanism.

complete revolution and acts as a crank, and the link opposite to the crank is

oscillates. The mechanism is known
as a crank
-
rocker or crank
-
lever

mechanism

or a rotary
-
oscillating converter.

If the shortest link a is made coupler and the link opposite to it, i.e. c, is fixed,

the other two links b and d would oscillate. Th
e mechanism is known as a

rockerrocker

or double rocker or double lever mechanism or oscillating
-
o
scillating

mechanism.

3. When the sum of the lengths of the shortest and largest links is more

than
the sum of the lengths of the other two links known as cla
ss
-
II, four bar

mechanism. In such mechanism, fixing any of the links always results in a

rocker
-

rocker mechanism. In other words, the mechanism and its inversions

give the same type of motion i.e. double
-
rocker mechanism.

1
1
1
1

4. Parallel
-
crank four
-
bar linkage: If in a four
-

are parallel and equal in length, then any of the links can be made fixed. The

four links form a parallelogram in all the positions of the cranks, provided the

crank rotates i
n the same sense.

The use of such a mechanism is made in the
coupled wheels of locomotive in

which the rotary motion of one wheel is
transmitted to the other wheel. For

kinematic analysis, link d is treated as fixed
and the relative motions of the

other li
nks are found. However, in fact, d has a
translator motion parallel to the

trails.

6
-
bar planar mechanism:

In case of four
-
bar chain does not provide the required performance of an

application, one of the two single
-
degree of freedom six bar chain with se
ven

turning or revolute pairs is considered. There are two types of six
-
bar chains.

1. Watt chain:

chain

2.
Stephenson chain:
In Stephenson chain ternary links separated by binary

fig. for Stephenson
-
I six
-
bar mechanism, For Stephenson
-
II six
-
bar

mechanism and For Stephenson
-
III six
-
bar mechanism. It may be noted that

in

both these types of mechanism some triangular shaped links are truly
ternary

links while other are known as tria
ngular to indicate the possible path
of tracer