Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts (subject). R. L. Norton, Design of Machinery, 6th ed. (number synthesis & mobility Ch. 2, position/velocity Ch. 4–6, cam design Ch. 8, epicyclic trains §9.6–9.9, balancing Ch. 13); J. J. Uicker, G. R. Pennock & J. E. Shigley, Theory of Machines and Mechanisms, 5th ed.; C. E. Wilson & J. P. Sadler, Kinematics and Dynamics of Machinery, 3rd ed.; S. S. Rao, Mechanical Vibrations, 6th ed. (Part B: single-DOF transient Ch. 2–4, multi-DOF Ch. 5–6). Open-book exam; everyone answers Q1, then any three of Part A (Q2–Q5) and one of Part B (Q6–Q7). Every question is solved here.