Design a cam for operating the exhaust valve of an oil engine. It is required to give equal uniform acceleration and retardation during opening and closing of the valve each of which corresponds to 60^{\circ} of cam rotation. The valve must remain in the fully open position for 20^{\circ} of cam rotation.
The lift of the valve is 37.5 mm and the least radius of the cam is 40 mm. The follower is provided with a roller of radius 20 mm and its line of stroke passes through the axis of the cam.
Question : Design a cam for operating the exhaust valve of an oil engin...
Construction
First of all, the displacement diagram, as shown in Fig. 20.27, is drawn as discussed in the following steps :
1. Draw a horizontal line ASTP such that AS represents the angular displacement of the cam during opening (i.e. out stroke ) of the valve (equal to 60^{\circ}), to some suitable scale. The line ST represents the dwell period of 20^{\circ} i.e. the period during which the valve remains fully open and TP represents the angular displacement during closing (i.e. return stroke) of the valve which is equal to 60^{\circ}.
2. Divide AS and TP into any number of equal even parts (say six).
3. Draw vertical lines through points 0, 1, 2, 3 etc. and equal to lift of the valve i.e. 37.5 mm.
4. Divide the vertical lines 3f and 3′ ′ f into six equal parts as shown by the points a, b, c . .. and a′, b′, c′ . . . in Fig. 20.27.
5. Since the valve moves with equal uniform acceleration and retardation, therefore the displacement diagram for opening and closing of a valve consists of double parabola.
6. Complete the displacement diagram as shown in Fig. 20.27.
Now the profile of the cam, with a roller follower when its line of stroke passes through the axis of cam, is drawn as shown in Fig. 20.28
