a$)$ Draw the profile of a disc cam with roller follower to give rise of $63$ mm during $\frac{3}{8}$ revolution of cam and dwell in the lifted position for $\frac{1}{8}$ revolution and a sudden drop of the follower through $33mm$ and followed by a dwell of $\frac{1}{8}$ revolution and further fall to the lowest position during $\frac{1}{4}$ revolution and remain at rest for the rest of the revolution of the cam. The rise of the follower takes place through cycloidal motion and fall will take place through SHM$.$ Least radius of the cam is $40mm$ and the roller diameter is $20mm.$ The line of stroke of the follower is in line with the axis of the cam. Assume the cam shaft to rotate clockwise uniformly.