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22-Mec-A2 Kinematics and Dynamics of Machines: December 2019

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Mechanism analysis: link types & mobility, transmission angles & Grashof, and number synthesis
  2. Question 2 Mechanical advantage of a mechanical press
  3. Question 3 Velocity, image, Coriolis and sliding acceleration of an inverted crank‑slider
  4. Question 4 Shaking force and balancing of a 3‑cylinder single‑plane engine
  5. Question 5 Radial cam‑follower motion design (rise–dwell–fall)
  6. Question 6 Speed ratio of a compound epicyclic gear train
  7. Question 7 Simple pendulum striking a wall (impact & free vibration)
  8. Question 8 Spring design for a helicopter‑suspended patient bed (bounce & pitch)

Start with Question 1 →

Paper format. National Exams, December 2019 — 16‑Mec‑A2 Kinematics and Dynamics of Machines, 3 hours, open book. Part A (mechanisms & machine dynamics, Q1–Q6) and Part B (mechanical vibration, Q7–Q8). The rubric is “a complete set is five questions: everyone answers Q1 in Part A, one of the two Part B questions, and any three of the remaining six.” Every one of the eight questions is solved here.

Reference texts (subject). R. L. Norton, Design of Machinery, 6th ed. (mobility/number synthesis 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).

Check — incomplete data (please read). Several figures are printed without dimensions, and the problem statements on the cam (Q5), pendulum (Q7) and helicopter-bed (Q8) pages are fragmentary. Accordingly:

  • Questions whose data survive intact — Q4 (3‑cylinder engine), Q5 (cam timing), Q7 (pendulum impact) — are solved to full numeric answers.
  • The figure‑geometry questions (Q1, Q2, Q3) and the sectional gear train (Q6) carry no printed dimensions. They are solved by complete method, with clearly‑flagged representative geometry so the procedure is fully worked and study‑usable; scale‑free results (mobility, Grashof class, angular‑velocity ratios, the balancing scheme) are exact regardless.
  • Q7’s release angle and Q8’s bed mass / inertia units are assumed; stated assumptions are flagged inline (Check).