Construct the displacement diagram and the cam profile for a plate cam with an oscillating radial flat-face follower that rises through 30◦ with cycloidal motion in 150◦ of counterclockwise cam rotation, then dwells for 30◦, returns with cycloidal motion in 120◦, and dwells for 60◦. Determine the necessary length for the follower face, allowing 5 mm clearance at the free end. The prime-circle radius is 30 mm and the follower pivot is 120 mm to the right.