**GTU previous question papers**

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**B. E. Sem. – V – Examination – June- 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.**

**Q.1 (a) **(i) Explain: Function generation, path generation & motion generation.

(ii) Derive Freudenstein’s Equation.** **

**(b) **Using relative pole method synthesize a four bar mechanism by taking

θ12 = 500 ϕ12= 300, θ13 = 600 ϕ13= 400.

Draw again your mechanism by taking fixed link length = 60 mm.** **

**Q.2 (a) **State Chebyshev theorem and find three precession points for the function

f(x) = x1.2 in the interval 0 ≤ x ≤ 6.

Take θi = 600, 4 θ = 900, ϕi=500, and 4 ϕ=1000.** **

**(b) **A porter governor has equal arms each 200 mm in length and pivoted on the

axis of rotation. The mass of each ball is 5 kg and the mass of sleeve is 25 kg.

The radius of governor is 100 mm when governor begins to lift. If the

frictional increase of speed is 1%, then determine the governor effort and

power.** **

**OR**

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

crank lever operates between 290 r.p.m. and 310 r.p.m. 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 mass of each

ball is 2.5 kg. The ball arms are parallel to the governor axis at the lowest

equilibrium speed. Determine stiffness of the spring.** **

**Q.3 (a) **List and explain mechanical brakes and also derive condition of self locking for simple shoe or block brake.** **

**(b) **A torsion dynamometer is fitted to a propeller shaft of a marine engine. It is

found that the shaft twists 20 in a length of 20 m at 120 r.p.m. If the shaft is

hollow with O.D. = 400 mm and I. D. =300 mm, and modulus of rigidity of

shaft material is 8×1010 N/mm2.Find the power of the engine.** **

**OR**

**Q.3 (a) **Classify ‘governors’ and prove for Watt governor, height of the governor h = 895/ N 2.where N is speed of rotation of sleeve.** **

**(b) **Find the angle of inclination with respect to the vertical of a two wheeler

negotiating a turn .Following data is given: combined mass of the vehicle with

its rider 250 kg, moment of inertia of the engine flywheel 0.3 kg.m 2, moment

of inertia of each road wheel 1 kg.m 2,speed of engine flywheel five times that

of road wheels and in the same directions, height of centre of gravity of rider

with vehicle 0.6 m ,two wheeler speed 90 km/h, wheel radius 300 mm ,radius

of turn 50 m.** **

**Q.4 (a) **Explain gyroscopic couple and discuss its effect on an aeroplane taking turns when viewed from rear.** **

**(b) **The turbine of rotor of a ship has mass of 3000 kg. & radius of gyration of 0.4

m, and clockwise speed of 2500 r.p.m. when looking from stern. Determine

gyroscopic couple and its effect when

(i) The ship steers to the left on curve of 100 m radius at a speed of 36

km/hr. and

(ii) When the ship is pitching in S.H.M., the bow falling with its

maximum velocity .The period of pitching is 40 Sec. and the total

angular displacement between the bow extreme positions of pitching

is 12 0.** **

**OR**

**Q.4 (a) **Explain the term ‘turning moment diagram’, ’Coefficient of fluctuation of speed and ‘’Coefficient of fluctuation of energy’.** **

**(b) **A flywheel, which is rotating at a maximum speed of 250 r.p.m. and is

having radius of gyration as 0.5 m , is attached to a punching press. The press

is driven by a constant torque electric motor and punches 750 holes per hour.

Each punching operation requires 14000 N-m of energy and takes 1.8

seconds. If the speed of the flywheel is not to fall below 225 r.p.m. Find:

(i) power of the motor and

(ii) mass of the flywheel** **

**Q.5 (a) **What is meant by dynamically equivalent system? State and prove conditions for it.** **

**(b) **The lengths of crank and the connecting rod of a horizontal reciprocating

engine are 300 mm and 1.5 m respectively. The crank is rotating at 120 r.p.m.

clockwise .The mass of the reciprocating parts of the engine is 290 kg whereas

the mass of the connecting rod is 250 kg. The C.G. of the connecting rod is

475 mm from the crank pin centre and the radius of gyration of the connecting

rod about an axis passing through the C.G. is 625 mm .Find the inertia torque

on the crank shaft analytically, when θ = 400.** **

**OR**

**Q.5 (a) **A single cylinder vertical engine has a bore of 150 mm and a stroke of 200

mm. The connecting rod is 350 mm long. The mass of piston is 1.6 kg and

engine speed is 1800 r.p.m. On the expansion stroke with a crank at 30 0 from

the top dead centre, the gas pressure is 750 kN/m 2. Determine the net thrust

on the engine.

**(b) **Solve the problem of Que. 5 (b) above, graphically using Klein’s construction

method.