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.

2.

3.

(a)(b)

(c)

(a)

(b)

What is degree of freedom of a mechanism? How is it determined?Define Grashof’s law. State how is it helpful in classifying the four-link mechanisms into different types?Find the maximum and minimum transmission angles for themechanisms shown in Fig. 1. The figures indicate the dimensions instandard units of length.

1

3

2

3

A D

C

B

d

cb

a

400

200

120o

350

700

300

A

O

P on slider

R

S

Q on AR

G

(mm)

Fig.1 Fig. 2

Fig. 2 shows the link mechanism of a quick-return mechanism of theslotted 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 cuttingtool at S and the angular acceleration of the link RS. The crank OProtates at 210 rpm.

What is Freudenstein’s equation? How is it helpful in designing a four-link mechanism when three positions of the input (θ1, θ2, θ3) and theoutput link (ϕ1, ϕ2, ϕ3) are known?Design a four-link mechanism when the motions of the input and theoutput links are governed by a function y = x2 and x varies from 0 to 2

5

5

5

15

5

4.

5.

6.

7.

8.

(a)

(b)

(a)

(b)

(a)

(b)(c)

(a)

(b)

(a)(b)

with an interval of 1. Assume � to vary from 50° to 150° and � from80° to 160°.

Prove that a Kempe’s mechanism traces an exact straight line usingtwo identical mechanisms.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 Bcarries a flywheel of mass 30 kg. If the radius of gyration of theflywheel is 100 mm, find the maximum torque in shaft B.

(Part – B)

Why is a cycloidal motion programme the most suitable for high-speedcams?The following data relate to a symmetrical circular cam operating aflat-faced follower:

Minimum radius of the cam 40 mmLift 24 mmAngle of lift 75o

Nose radius 8 mmSpeed of the cam 420 rpm

Determine the main dimensions of the cam and the acceleration of thefollower 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.

What are uniform pressure and uniform wear theories? Deduceexpressions for the friction torque considering both the theories for aflat collar.Explain the terms: friction circle, friction couple and friction axis.Describe the working of a mitchell thrust bearing.

Derive the relation, µθeT

T=

2

1 for a flat belt drive with usual notations.

A leather belt transmits 10 kW from a motor running at 600 rpm by anopen-belt drive. The diameter of the driving pulley of the motor is 350mm, centre distance between the pulleys 4 m and speed of the drivenpulley 180 rpm. The belt weighs 1100 kg/m3 and the maximumallowable tension in the belt is 2.5 N/mm2. µ = 0.25. Find the width ofthe belt assuming the thickness to be 10 mm. Neglect the belt thicknessto calculate the velocities.

State and prove the law of gearing.In the epicyclic gear train shown in Fig. 3, the compound wheels A andB as well as internal wheels C and D rotate independently about the

10

8

7

3

12

735

7

8

5

axis O. The wheels E and F rotate on the pins fixed to arm a. All thewheels are of the same module. The number of teeth on the wheels are

TA = 52, TB = 56, TE = TF = 36Determine 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.

a

A B C D

E

F

O

Fig. 3

10