JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II THEORY OF MACHINES Previous Question Paper (August/September - 2022 - R13)
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Main
What are the different Inversions of a four – bar chain? Describe the working of any one inversion, with the help of relevant sketch.
Answer
The inversions of a four-bar chain are obtained by fixing different links in the kinematic chain. The three primary inversions are:
- Beam Engine (Crank and Lever Mechanism): The fixed link is the frame supporting the beam, which oscillates about a pivot.
- Coupling Rod of a Locomotive (Double Crank Mechanism): The two side rods act as cranks, ensuring parallel motion of the wheels.
- Watt's Indicator Mechanism (Double Lever Mechanism): A four-bar chain used to amplify the small motion of a piston into a larger movement of a pencil on a drum.
In the Beam Engine, the frame is fixed. The crank rotates, causing the beam to oscillate about its pivot. The piston rod is attached to the end of the beam via a connecting link, converting the rotary motion of the crank into reciprocating motion of the piston. Imagine a central pivot point with a beam extending on both sides; one end connects to the crank via a rod, and the other end connects to the piston rod.
In a Whitworth quick return mechanism, the distance between the fixed centers is 60 mm and the driving crank length is 80 mm. The length of the slotted lever is 160 mm, and the length of connecting rod is 140 mm. Calculate the ratio of the times of cutting and return strokes.
Answer
In a Whitworth quick return mechanism, the ratio of the time of cutting stroke to the time of return stroke is given by the ratio of the angles subtended by the crank during these strokes at the fixed center.
Let the distance between fixed centers be d = 60 mm and the driving crank length be r = 80 mm. The angle α subtended by the crank during the return stroke is calculated using the geometry of the mechanism:
Calculating the angle:
The angle of the cutting stroke (β) is:
The ratio of the time of cutting stroke to the time of return stroke is:
Thus, the ratio of the time of cutting stroke to the time of return stroke is approximately 3.35:1.
In a mechanism shown in Figure.1, the link AB rotates with a uniform angular velocity of 30 rad/s. The lengths of links (in mm) are : AB = 100 ; BC = 300 ; BD = 150 ; DE = 250 ; EF = 200 ; DG = 165 ; Determine the velocity and acceleration of the point ‘G’.
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Two parallel shafts are to be connected by spur gearing. The approximate distance between the shafts is 600 mm. If one shaft runs at 120 rpm, and the other at 360 rpm, find the exact center distance between the shafts.
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A simple Epicyclic gear train is shown in the figure 2 below. Deduce, from fundamentals, the expression for velocity ratio of the gear train.
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Find the maximum and minimum speeds of a flywheel of mass 3250 kg and radius of gyration 1.8 m, when the fluctuation of energy is 112 kN – m. The mean speed of the engine is 240 rpm.
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Draw and explain the Turning moment - Crank angle (T - θ) diagram for a multi – cylinder engine. And, from this diagram, deduce the concepts of Maximum fluctuation of energy, Coefficient of Fluctuation of Energy, Maximum Fluctuation of Speed, and Coefficient of Fluctuation of Speed.
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A pulley is driven by a flat belt running at 200 m/minute speed. Find the power transmitted by the belt, if the maximum tension in the belt is 1000 N. Assume the coefficient of friction between the belt and pulley surface as 0.3, and the angle of lap is 160°.
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Derive an expression for ratio of tension in open belt drive system.
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Deduce an expression for the friction moment of a collar thrust bearing, and the assumptions made.
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A pivot bearing of a shaft consists of a frustum of a cone. The diameters of the frustum are 200 mm and 400 mm, and its semi-cone angle is 60°. The shaft carries a load of 40 kN and rotates at 240 rpm. The coefficient of friction is 0.02. Assuming the intensity of pressure to be uniform, determine (i) the magnitude of pressure, and (ii) the power lost in friction.
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Explain the terms: Sensitiveness, Isochronism, Stability, and Hunting in connection with governors.
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The arms of a Porter governor are 312.5 mm long and are pivoted on the axis of rotation. Each ball weighs 735 N, and the central load is 450 N. Determine the equilibrium speed corresponding to radii of rotation 200 mm and 250 mm.
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Distinguish between static balancing and dynamic balancing in rotating machines.
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Draw the profile of a cam to operate a roller follower of 15 mm diameter. The line of stroke of the follower passes through the axis of the camshaft. The least radius of the cam is 5 cm, and the lift of follower is to be 4 cm. The outstroke of the follower occurs with SHM during 150° of cam rotation, followed by a dwell period of 30° of cam rotation. The follower then returns to its original position during 120° of cam rotation with uniform velocity, and dwells for the remaining period.
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