Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts (subject). R. L. Norton, Design of Machinery, 6th ed. (mobility Ch. 2, cams Ch. 8, epicyclic/compound trains §9.6–9.9, balancing Ch. 13); Uicker, Pennock & 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, Ch. 3 base excitation, Ch. 6 multi-DOF torsional).