Theory of Machines

1. Prof A B Karpe
By
Prof. A B Karpe
Karpe.ajit@gmail.com
Department of Mechanical Engineering
STES’s, Smt. Kashibai Navale College of Engineering

2. Content
• Clutches (Theory and Numerical)
Pivot and collar friction, Classification of Clutches,
Torque Transmitting Capacity.
• Brakes (Theory and Numerical)
Different types of brakes, shoe brakes, external and internal
shoe brakes, block brakes, band brakes, Band and block
brakes, Braking torques
• Dynamometers (Theory)
Different types of absorption and transmission type

3. Clutches (Theory and Numerical)
• Uniform Pressure and Uniform Wear Theory
• Pivot and collar friction
• Plate clutches
• Cone clutches
• Centrifugal clutch

4. Uniform Pressure Theory
In a new bearing, the contact between the
shaft & bearing may be good over the whole
surface. So pressure over the rubbing surfaces
is uniformly distributed.
Here,
p = constant.

5. Uniform Wear Theory
When the bearing becomes old, all parts of
the rubbing surfaces will not move with the
same velocity. Velocity of rubbing increases
with distance from the axis of bearing. Hence,
wear may be different at different radii.
Rate of wear α p
Rate of wear α v

6. Uniform wear theory
But, v α r ………….. (v= r ω)
So,
Rate of wear α p .v
Rate of wear α p.r ……….(as v α r)
pr = constant (c)
P (max) x r(min) = P (min) x r(max) = c

7. Pivot Bearing
Flat Pivot Bearing
Collar Flat Pivot Bearing
Multiple Collars
Conical pivot
bearing
Trapezoidal or
Truncated conical pivot

9. Clutches
• Clutch is a mechanism to transmit rotary motion
from one shaft to another coincident shaft as and
when required without stopping the driver shaft.
• Types of clutches
1) Positive clutches
a) Jaw Clutch
2) Friction clutches
a) Disc or plate clutches
b) Cone clutches
c) Centrifugal clutches

10. Jaw clutch
These type of clutches are used in sprocket wheels, gears, pulleys etc.

11. Single plate clutch

12. Clutch Components

16. Diaphragm Coil
Spring Spring

18. Multi-plate Clutch

21. Cone clutch

23. Centrifugal Clutch

25. Derivations
m = Mass of each shoe,
n = Number of shoes,
r = Distance of centre of gravity of
the shoe from the centre of the
spider,
R = Inside radius of the pulley rim,
N = Running speed of the pulley in
r.p.m.,
ω = Angular running speed of the
pulley in rad/s = 2πN/60 rad/s,
ω1 = Angular speed at which the
engagement begins to take place,
μ = Coefficient of friction between
the shoe and rim

26. Torque
Pc = m.ω2.r
Ps = m (ω1)2 r
The net outward radial force= Pc – Ps
T = μ (Pc – Ps) R × n = n.F.R

27. Torque
l = Contact length of the
shoes,
b = Width of the shoes
R = Contact radius of the
shoes. It is same as the
inside radius of the rim
of the pulley.
θ = Angle subtended by the
shoes at the centre of the
spider in radians.
p = Intensity of pressure
exerted on the shoe.
θ = l/R rad
A = l.b
F= A × p = l.b.p
l.b.p = Pc – Ps

29. Unit 3
Brakes and Dynamometers
By
Karpe A B

30. Brakes
• A brake is a device by means of which artificial frictional
resistance is applied to a moving machine member, in order
to retard or stop the motion of a machine.
1) Hydraulic brakes e.g. pumps or hydrodynamic brake and
fluid agitator,
2) Electric brakes e.g. generators and eddy current brakes,
and
3) Mechanical brakes
a) Block brake
b) Band brake
c) Internal or external expanding shoe brake
d) Disc brake

31. Single Block or Shoe Brake

32. used on railway trains, bicycles and tram cars

33. the frictional force helps to apply the brake. Such type of brakes are said to be self
energizing brakes. When the frictional force is great enough to apply the brake with no
external force, then the brake is said to be self-locking brake
The frictional force assist the actuating force such brakes are called as self energizing or self
actuating brakes

34. Double Block or Shoe Brake
Used in electric cranes

35. Pivoted Block or Shoe Brake
when the angle of contact is less
than 60°, normal pressure between
the block and the wheel is uniform.
But greater than 60°, then the unit
pressure normal to the surface of
contact is less at the ends than at
the centre

37. Band brake
• A band brake consists of a flexible band of leather, one or more ropes, or a
steel lined with friction material, which embraces a part of the
circumference of the drum

39. Differential Band Brake

42. Band and Block Brake

45. Internal expanding brake

47. Dynamometers
• A dynamometer is a brake but in addition it has a device to measure the
frictional resistance. Knowing the frictional resistance, we may obtain the
torque transmitted and hence power of the engine.
1. Absorption dynamometers
a) Prony brake dynamometer
b) Rope brake dynamometer
c) Band Brake dynamometer
2. Transmission dynamometers.-the energy is not wasted in friction but is
used for doing work
a) Epicyclic-train dynamometer,
b) Belt transmission dynamometer
c) Torsion dynamometer

48. Prony brake dynamometer

50. Rope brake dynamometer

51. Rope brake dynamometer

52. Band brake dynamometer

53. Epicyclic-train Dynamometer

54. Belt Transmission Dynamometer-Froude or
Throneycroft Transmission
Dynamometer

55. Torsion Dynamometer
• A torsion dynamometer is used for measuring
large powers particularly the power
transmitted along the propeller shaft of a
turbine or motor vessel.

56. Bevis-Gibson Flash Light Torsion
Dynamometer