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Draw profile of cam to raise the valve with S.H.M. through 5cm..........

Question: 

Draw profile of cam to raise the valve with S.H.M. through 5cm in 120° of revolution, keep it fully raised through 30° and lower it with equal uniform acceleration and retardation through 90° of rotation. The valve remain closed during the rest of rotation. The diameter of the roller is 2 cm and the minimum radius of the cam is 5cm. The axis of the valve rod is offset 2cm from the axis of the shaft. Assume the cam rotating in clockwise direction.

Answer: