NivaarExam PrepOfficial exam papers ↗

22-Mec-B12 Robotics: Undated paper

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

  1. Question 1 Transforming a position and a velocity between frames (20 marks)
  2. Question 2 Frame diagram and composition of transformations (20 marks)
  3. Question 3 Two-segment cubic spline with continuous acceleration (20 marks)
  4. Question 4 All joint-3 angles reaching a given position (20 marks)
  5. Question 5 Equations of motion of the PR manipulator (20 marks)
  6. Question 6 Axis assignment, DH table and forward kinematics (20 marks)
  7. Question 7 Jacobian, reachable workspace and dexterous workspace (20 marks)

Start with Question 1 →

Paper format. National Exams — 16-Mec-B12 Robot Mechanics, 3 hours, CLOSED BOOK, one 8.5″×11″ aid sheet (both sides) and an approved calculator permitted. The paper runs in two sections: Section 1 holds five questions of which the candidate answers only three, and Section 2 holds two questions which are both compulsory. Each question is of equal value (20 marks), and marks for each part are shown in parentheses. All seven questions are worked here.

Reference texts. J. J. Craig, Introduction to Robotics: Mechanics and Control, 4th ed. (this paper's leading-super/subscript notation, its modified DH convention and its via-point spline formulae follow this text directly); M. W. Spong, S. Hutchinson and M. Vidyasagar, Robot Modeling and Control, 2nd ed.; S. B. Niku, Introduction to Robotics: Analysis, Control, Applications, 3rd ed.; K. M. Lynch and F. C. Park, Modern Robotics, 1st ed.

Notation (from the exam's own nomenclature page). A leading superscript names the frame a quantity is referenced to, so $^{A}V$ is the vector $V$ expressed in frame $\{A\}$. A leading subscript together with a leading superscript names a transformation: $^{B}_{A}T$ describes frame $\{A\}$ relative to frame $\{B\}$, and therefore maps coordinates the other way, $^{B}P={}^{B}_{A}T\,{}^{A}P$. Keeping that direction straight is the single most common source of lost marks on this paper, so every question below states explicitly which way the given transform points.

The printed footer reads 16-Mec-B12/May 2019.
Check: sign convention for the revolute joint of Figure 3. Figure 3 shows the direction of positive motion with a curved arrow but does not label a sense on the base triad. Throughout Questions 6 and 7 the base frame is taken as $x_{0}$ along the horizontal arm, $z_{0}$ vertically up and $y_{0}$ completing the right-handed set, with positive $q_{2}$ following the right-hand rule about $+x_{0}$. Every result below is stated in that frame; a candidate who assigns the opposite sense obtains the same magnitudes with $q_{2}\rightarrow-q_{2}$.