Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts (subject). R. L. Norton, Design of Machinery, 6th ed. (mechanisms, cams, gear trains); C. E. Wilson & J. P. Sadler, Kinematics and Dynamics of Machinery, 3rd ed.; Uicker, Pennock & Shigley, Theory of Machines and Mechanisms, 5th ed.; S. S. Rao, Mechanical Vibrations, 6th ed. (Part B). Balancing follows Norton Ch. 13; planetary trains Norton §9.7–9.9.