# Sample Question Paper (Kinematics of Machines) Maximum marks: 75 Time allowed: 3 Hours

```Sample Question Paper
(Kinematics of Machines)
Maximum marks: 75
Time allowed: 3 Hours
Note: Attempt any five questions selecting at least two from each part.
(Part – A)
1.
(a) What is degree of freedom of a mechanism? How is it determined?
(b) Define Grashof’s law. State how is it helpful in classifying the fourlink mechanisms into different types?
(c) Find the maximum and minimum transmission angles for the
mechanisms shown in Fig. 1. The figures indicate the dimensions in
standard units of length.
5
5
5
S
R
G
300
350
3
b
B
a
1
A
200
O
120 o
c
700
400
2
(mm)
3
Fig.1
2.
P on slider
Q on AR
C
d
D
A
Fig. 2
Fig. 2 shows the link mechanism of a quick-return mechanism of the
slotted lever type, the various dimensions of which are
OA = 400 mm, OP = 200 mm, AR = 700 mm, RS = 300 mm.
For the configuration shown determine the acceleration of the cutting
tool at S and the angular acceleration of the link RS. The crank OP
rotates at 210 rpm.
3.
(a) What is Freudenstein’s equation? How is it helpful in designing a fourlink mechanism when three positions of the input (θ1, θ2, θ3) and the
output link (ϕ1, ϕ2, ϕ3) are known?
(b) Design a four-link mechanism when the motions of the input and the
output links are governed by a function y = x2 and x varies from 0 to 2
15
5
with an interval of 1. Assume
80° to 160°.
4.
to vary from 50° to 150° and
from
(a) Prove that a Kempe’s mechanism traces an exact straight line using
two identical mechanisms.
(b) The two shafts of a Hooke’s coupling have their axes inclined at 20°.
The shaft A revolves at a uniform speed of 1000 rpm. The shaft B
carries a flywheel of mass 30 kg. If the radius of gyration of the
flywheel is 100 mm, find the maximum torque in shaft B.
10
8
7
(Part – B)
5.
6.
7.
8.
(a) Why is a cycloidal motion programme the most suitable for high-speed
cams?
(b) The following data relate to a symmetrical circular cam operating a
flat-faced follower:
40 mm
Lift
24 mm
Angle of lift
75o
8 mm
Speed of the cam
420 rpm
Determine the main dimensions of the cam and the acceleration of the
follower at
(i)
the beginning of the lift
(ii)
the end of contact with the circular flank
(iii) the beginning of contact with the nose
(iv)
the apex of nose.
(a) What are uniform pressure and uniform wear theories? Deduce
expressions for the friction torque considering both the theories for a
flat collar.
(b) Explain the terms: friction circle, friction couple and friction axis.
(c) Describe the working of a mitchell thrust bearing.
T1
= e µθ for a flat belt drive with usual notations.
(a) Derive the relation,
T2
(b) A leather belt transmits 10 kW from a motor running at 600 rpm by an
open-belt drive. The diameter of the driving pulley of the motor is 350
mm, centre distance between the pulleys 4 m and speed of the driven
pulley 180 rpm. The belt weighs 1100 kg/m3 and the maximum
allowable tension in the belt is 2.5 N/mm2. µ = 0.25. Find the width of
the belt assuming the thickness to be 10 mm. Neglect the belt thickness
to calculate the velocities.
(a) State and prove the law of gearing.
(b) In the epicyclic gear train shown in Fig. 3, the compound wheels A and
B as well as internal wheels C and D rotate independently about the
3
12
7
3
5
7
8
5
axis O. The wheels E and F rotate on the pins fixed to arm a. All the
wheels are of the same module. The number of teeth on the wheels are
TA = 52,
TB = 56,
TE = TF = 36
Determine the speed of C if
(i) the wheel D fixed and arm a rotates at 200 rpm clockwise
(ii) the wheel D rotates at 200 rpm counter-clockwise and the arm a
rotates at 20 rpm counter-clockwise.
10
E
a
A
O
F
Fig. 3
B
C
D
```