22-Mec-B12 Robotics: December 2018

Paper format. National Exams, December 2018 — 16-Mec-B12 Robotics. Closed book, three hours, one 8.5″×11″ two-sided formula sheet and an approved Casio or Sharp calculator permitted. Seven questions, each of equal value (20 marks); the rubric states that five questions constitute a complete paper and that only the first five in the answer book are marked. As a study resource all seven are solved here. Marks shown in parentheses are the printed sub-part values.

Notation. The paper's own nomenclature is used throughout: $\hat{X}_A,\hat{Y}_A,\hat{Z}_A$ are the unit vectors of frame $\{A\}$; a leading superscript as in ${}^{A}V$ names the frame the vector is referenced to; and ${}^{B}_{A}T$ is the transform of frame $\{A\}$ expressed relative to $\{B\}$. This is Craig's convention, so Craig's modified (distal) Denavit–Hartenberg parameters are used for the link tables.

Reference texts.

• Craig, J. J., Introduction to Robotics: Mechanics and Control, 4th ed., Pearson, 2018 — the notation, the Z–Y–Z Euler convention and the two-segment cubic spline of Question 7 all follow this text (Ch. 2, 3, 5 and 7).
• Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control, 2nd ed., Wiley, 2020 — alternative treatment of DH assignment and Jacobian singularities (Ch. 3, 4).
• Niku, S. B., Introduction to Robotics: Analysis, Control, Applications, 3rd ed., Wiley, 2020 — worked frame-graph and trajectory examples.
• Siciliano, B., Sciavicco, L., Villani, L. and Oriolo, G., Robotics: Modelling, Planning and Control, Springer, 2009 — differential kinematics and statics duality (Ch. 3).