22-Mec-B12 Robotics, December 2019: worked solutions

Paper format. National Exams, December 2019 — 16-Mec-B12 Robot Mechanics. Three hours; CLOSED BOOK with one 8.5″×11″ two-sided formula sheet and an approved Casio or Sharp calculator. Five questions constitute a complete paper: Section 1 holds five questions of which the candidate answers any three, and Section 2 holds two questions which are both compulsory. Each question is worth 20 marks. All seven questions are solved here.

Reference texts.

J. J. Craig, Introduction to Robotics: Mechanics and Control, 4th ed., Pearson, 2018 — the notation of this paper (leading super/subscripts, modified Denavit–Hartenberg parameters, velocity propagation) follows Craig chapter for chapter.
M. W. Spong, S. Hutchinson and M. Vidyasagar, Robot Modeling and Control, 2nd ed., Wiley, 2020 — alternative (standard DH) treatment of the same kinematics and Jacobians.
S. B. Niku, Introduction to Robotics: Analysis, Control, Applications, 3rd ed., Wiley, 2020 — worked numerical examples of frame algebra and trajectory planning.
R. M. Murray, Z. Li and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press — rigid-body kinematics background.

Note. Where the printed paper rounds a value (for example the target height 1.707), the solution says so explicitly.

22-Mec-B12 Robotics: December 2019