Question No$\mathrm{.}14$: A cam operating a knife$-$edged follower has the following data:

$($i$)$ Follower moves outwards through $40$ mm during $60$ of$-$cam rotation. $-$

$($ii$)$ Follower dwells for the next $45.$

$($iii$)$ Follower returns to its original position during next $90.$

$($iv$)$ Follower dwells for the rest of$-$the rotation.

The displacement of the follower is to take place with simple harmonic motion during both the outward and return strokes. The least radius of the cam is $50$ mm $.$ Draw the profile of the cam when the axis of the follower is offset $20$ mm towards right from the cam axis.