**GTU previous question papers**

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**BE SEM-V Examination-Nov/Dec.-2011**

**Subject code: 151902 **

**Subject Name: Theory of Machines **

**Instructions:**

**1. Attempt all questions.**

**2. Make suitable assumptions wherever necessary.**

**3. Figures to the right indicate full marks.**

**4. Illustrate your answer with neat sketches wherever required.**

**Q.1 (a) **Prove the Freudenstein’s equation for slider crank mechanism. ** **

**(b) **Synthesize a function generator to generate a function y = sin x in the region

0 ≤ x ≤

2

ð

, using Chebyshev spacing taking three precession points. Assume initial

crank angle, θi = 300, initial rocker angle, φi = 600 , *θ = 600 and *φ = 900. Take

fixed link length 50 mm. Also draw the mechanism.

**10**

**Q.2 (a) **Using Bloch’s method, synthesize and draw a four bar linkage to meet the following

specifications of angular positions. Velocities and accelerations at one of its positions

are

ω2 = 21 rad/sec , ω3 = – 6 rad/sec, ω4 = 12 rad/sec,

α2 = – 280 rad/sec2 , α3 = 200 rad/sec2 and α4 = 100 rad/sec2.** **

**(b) **Define (i) Hunting (ii) Sensitiveness (iii) Sleeve lift and (iv) Isochronisms for

governor.** **

**OR**

**(b) **A porter governor has all the four arms of 300 mm each. All the upper arms as well

as the sleeve arms are pivoted on the axis of rotation. The mass of each governor ball

is 1 kg. The mass of the sleeve is 20 kg. Find the speed of rotation, when the balls

rotate at a radius of 150 mm.** **

**Q.3 (a) **Derive an equation for gyro-couple with usual notations. ** **

**(b) **The turbine rotor of a ship has mass of 2000 kg and rotates at 25 rev./sec clockwise

when viewed from the stern. The radius of gyration of rotor is 0.30 meter. Determine

gyroscopic couple and its effect when

(i) The ship turns right at a radius of 250 m with a speed of 25 kM/hr.

(ii) The ship rolls at an angular velocity of 0.1 rad/sec.** **

**OR**

**Q.3 (a) **Explain dynamically equivalent two mass system. ** **

**(b) **A Hartnell governor having a central sleeve spring and two right angles bell crank

levers operates between 290 rpm and 310 rpm for a sleeve lift of 15 mm. The sleeve

arms and the ball arms are 80 mm and 120 mm respectively. The levers are pivoted at

120 mm from the governor axis and the mass of each ball is 2.5 kg. The ball arms are

parallel to the governor axis at the lowest equilibrium speed. Determine: (i) loads on

the spring at the lowest and highest equilibrium speeds and (ii) stiffness of the spring.** **

**Q.4 (a) **Distinguish between brakes and dynamometer. ** **

**(b) **Describe the construction and operation of a rope brake absorption dynamometer. ** **

**OR **

**Q.4 (a) **Differentiate between Flywheel and Governor. ** **

**(b) **A simple band brake is operated by a lever of length 500 mm. The brake drum has a

diameter of 500 mm and the brake band embraces 5/8 of the circumference. One end

of the band is attached to the fulcrum of the lever while the other end is attached to a

pin on the lever 100 mm from the fulcrum. If the effort applied to the end of the lever

is 2 kN and the coefficient of friction is 0.25, find the maximum braking torque on

the drum.

**Q.5 (a) **State and explain D’Alembert’s principle. ** **

**(b) **Draw and explain Klien’s construction for determining the velocity and acceleration

of the piston in a slider crank mechanism.** **

**OR**

**Q.5 (a) **Define the flywheel and state its importance. What are the functions of a flywheel? ** **

**(b) **In Internal combustion engine the crank radius is 400 mm and connecting rod is 950

mm long. The diameter of piston is 100 mm and net gas pressure acting on the piston

is 15 MPa. Find:

1. Thrust in connecting rod

2. Piston side exhaust

3. Torque acting on the crank shaft

4. Radial load on main bearings when the crank has made 450 from TDC.

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