B Tech (Mechanical)
DYNAMICS LAB 4th sem
CONTENTS
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.
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Experiment No. 1.
Title: Study 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 and forced precession.
Formula Used:
1. Gyroscopic couple C = I x w x wp
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 that 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 axis 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 apparatus 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 wp
Observations:
Part I :
1. Direction of spin axis : CLOCKWISE/ANTICLOCKWISE
2. Direction of forced precession : DOWNWORD
2
3. Direction
of
couple
acting
CLOCKWISE/ANTICLOCKWISES
on
the
frame
:
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 = 2πN / 60 = rad/s
3. wp = θ / t X π / 180 = rad/s
4. Gyroscopic Couple © = I X w X wp = N – m.
5. Applied Torque (T) = Wr’ = N – m.
Conclusions :
a) Comments 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 written.
c) Different case where the gyroscopic couple is observed is to be
mentioned.
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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 positions.
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
positioned 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 rotating masses are completely balance.
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Experiment No. 3
Title: To determine the radius of Gyration of a pendulum
Equipment: Compound Pendulum, Scale, Stopwatch, Thread.
Aim:
To determine the radius of Gyration of compound pendulum to verify relation
T = 2π √ 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 experiment with a small angular displacement θ, then
couple tending to restore the pendulum to the equilibrium position, T
=mgh sinθ
Result Table:
Radius of gyration for pendulum are
Kth =
Kexp =
5
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 Experiment:
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 the 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.
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Experiment No. 5
Title: 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
Texp = Time(t) / Oscillation(n)
Tth = 2π√ w/ Kmean
F=1/n
Procedure 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 found that the actual and the theoretical frequencies of the vibration close
to each other.
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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 planar
mechanism.
Theory: - Kinematic links: 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 other 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 crank shaft. The crank link
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.
Kinematic pair:
A kinematic pair or simply a pair is a joint of two links having relative motion
between them. In slider-crank mechanism, link 2 rotates relative to link 1 and
constitutes a revolute or turning pair. Link 4 (slider) reciprocates relative to link
1 and is a sliding pair.
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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 links are
similar.
Example: 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 links, it is
known as higher pair. The contact surfaces of the two links are 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 except 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 pair. This is achieved by cutting matching
threads on the two links. 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
link, it is spherical pair. 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 other links, it is a nonkinematic 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
the mechanism, it is necessary to know how many inputs are needed. In some
links and are said to have one degree of freedom. In other mechanism, two
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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 linkages. It
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
link is the coupler and the fourth link a lever or rocker if oscillates or an
another crank, if rotates. A four bar mechanism has the following
characteristics based on the lengths of its link.
1. It is impossible to have a four bar mechanism if length of the one of the
links is greater than 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 fixed, different
mechanisms are obtained known as Inversion
a. Shortest link is fixed
If the shortest link is fixed, the adjacent link b and d makes complete
revolutions. The mechanism thus obtained is known as crank- crank or double
crank or rotary- rotary mechanism.
b. Link adjacent to the shortest link is fixed;
If any of the link adjacent to the shortest link is fixed, the shortest link makes
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.
c. link opposite to shortest link is fixed:
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. The mechanism is known as a
rockerrocker or double rocker or double lever mechanism or oscillatingoscillating 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 class-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.
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4. Parallel-crank four-bar linkage: If in a four-bar linkage, two opposite links
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 in 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 links 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 seven
turning or revolute pairs is considered. There are two types of six-bar chains.
1. Watt chain: In watt chain the ternary links are adjacent for Watt sixbar
chain
2. Stephenson chain: In Stephenson chain ternary links separated by binary
links refer 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 triangular to indicate the possible path
of tracer points on floating links.
Conclusion: References:
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