Question Paper: Theory of Machines - 1 Question Paper - December 2016 - Mechanical Engineering (Semester 4) - Mumbai University (MU)
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Theory of Machines - 1 - December 2016

MU Mechanical Engineering (Semester 4)

Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any four questionQ.1(a,b,c,d,e)

1(a) What is Kutzback's criterion for degree of freedom of plane mechanism? In what way it differd from Grubler's criterion? 5 marks

1(b) Draw a neat sketch of Hart's machanism and prove that it produces an exact straight line motion. 5 marks

1(c) Define the following terms as applied to cam with a neat sketch,
i) Base circle ii) Pitch circle iii) Prime circle
5 marks

1(d) Differentiate between involute and cycloidal gear tooth profile. 5 marks

2(a) The driving crank AB of the quick return mechanism as shown in figure revolves at a uniform speed of 200 rpm. Find the velocity and acceleration of the toolbox R, in the position shown, when the crank makes an angle of 60° with the vertical line of centres. PA. What is the acceleration of sliding of the block at B alongt the slotted lever PQ?
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5 marks

2(b) Draw the polar diagram depicting the sailent features of driving and driven shaft speed in a Hooke's joint. 5 marks

3(a) The lengths of various links of a mechanism, as shown in the figure are:
OA=0.3, AB=1m, CD=0.8m, AC=CB. Determine for the given configuration, the velocity of the slider D if the crank OA rotates at 60 rpm in the clockwise direction. Also find the angular velocityof the link CD. Use instantaneous centre method.
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5 marks

3(b) A sphere of radius 0.2 m starts rolling without slip up an inclined plane, inclined at an angle 30° with the horizontal. If the initial angular velocity of the sphere is 10 rad/s, determine how far the sphere will travel before it reverses its motion. 5 marks

4(a) 2.5kW of power is transmitted by an open belt drive. The linear velocity of the belt is 2.5 m/s. The angle of lap on the smaller pulley is 165°. The coefficient of friction is 0.3. Determine the effect on power transmission in the following cases:
i) initial tension in the belt is increased by 8%
ii) angle of lap is increased by 8% by the use of an idler pulley, for the same speed and the tension on the tight side.
5 marks

4(b) Two involute gears of 20°pressure angle are in mesh. The number of teeth on pinion is 20 the gear ration is 2. If the pitch expressed in module is 5 mm and the pitch line speed is 1.2 m/s,assuming addendum as standard and equal to one module, find:
i) the angle turned through by pinion when one pair of teeth is in mesh
ii) the maximum velocity of sliding.
5 marks

5(a) A cam rotating clockwise at a uniform speed of 100 rpm is required to give motion to knife edge follower as below:
i) Follower to move outwards through 25 mm during 120° of cam rotation.
ii) Follower to dwell for the next 60° of cam rotation.
iii) Follower to return to its starting position during next 90° of cam rotation
iv) Follower to dwell for the rest of the cam rotation. The minimum radius of the cam is 50 mm and the line of stroke of th e follower passes through the axis of the cam shaft. If the displacement of the follower take place with uniform acceleration and retardation on both the outward and return strokes, find and draw the maximum velocity and acceleration during outward and return stoke.
5 marks

5(b) Derive the equation for the length of chain with the help of a neat sketch. 5 marks

6(a) Pressure angle in cams and methods to control it. 5 marks

6(b) Grasshopper's mechanism. 5 marks

6(c) Oldham's coupling. 5 marks

6(d) Whitworth quick return motion mechanism. 5 marks

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