Please show all the work and calculations.

Cam profile using Analytical method: Translating knife edge follower

a$.$ A translating knife edge follower uses a $3-4-5$ polynomial displacement profile to

perform the first half of the cam motion: rises through $8$ cm in $70^($@$)$ of counterclockwise

cam rotation, and then dwells for $30^($@$)$ and lifts to $13$ cm over $80^($@$).$ The prime circle is to

have a radius of $30$ mm and the follower has an offset of $3$ cm $.$ Define the cam profile

using the trace point location relative to the follower and the trace point location

relative to the rotated cam for cam angles $50^($@$)$ and $90^($@$)$ and $160^($@$).$

b$.$ Plot the points.