show all the work and calculations

Cam profile using Analytical method: Translating roller follower

a$.$ Construct the cam profile for the disk cam with a translating roller follower that rises

through $13$ mm with harmonic motion in $90^($@$)$ of clockwise cam rotation, and then dwells

for $50^($@$)$ and returns using cycloidal motion for $130^($@$)$ and dwells for the remainder of the

rotation. The base circle is to have a radius of $40$ mm and the roller has a diameter of $15$

mm with a $5$ mm offset. Find the trace point location relative to the follower and the

trace point location relative to the rotated cam for cam angles $50^($@$)$ and $170^($@$)$

b$.$ Plot the points on a plot to demonstrate where those points would be on the actual

cam.

c$.$ Compare your work with the results from Cam Design.