Problem 3 (20 points) Cam Motion: Analytically construct a displacement follower program for a CYCLOIDAL rise of 8 inch over 90 degrees with a dwell for 90 degrees and then a 4 inch PARABOLIC (symmetric) return over 90 degrees and a 45 degree dwell followed by a 4 in HARMONIC return over the last 45 degrees. Use the figure to sketch the profile and guide your solutions. 8 inch 0 90 96 180 270 360