22-Mec-B12 Robotics
Worked solutions to 4 past sittings (2016–2019), 28 questions. Pick a sitting, or start from a topic below.
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- DH table (3 sittings): December 2019 Q6 · May 2016 Q3 · Undated paper Q6
- Frame diagram (3 sittings): December 2018 Q3 · May 2016 Q2 · Undated paper Q2
- Axis assignment (2 sittings): May 2016 Q3 · Undated paper Q6
- Composition of transformations (2 sittings): May 2016 Q2 · Undated paper Q2
- Dexterous workspace (2 sittings): May 2016 Q6 · Undated paper Q7
- Forward kinematics (2 sittings): May 2016 Q3 · Undated paper Q6
- Jacobian (2 sittings): May 2016 Q6 · Undated paper Q7
- Reachable workspace (2 sittings): May 2016 Q6 · Undated paper Q7
- Static joint torques (2 sittings): December 2018 Q6 · May 2016 Q7
- Transforming a position (2 sittings): May 2016 Q1 · Undated paper Q1
- Velocity between frames (2 sittings): May 2016 Q1 · Undated paper Q1
Questions by sitting
December 2019
- Question 1: Mapping a point and a free vector between frames
- Question 2: Frame graph and a compound transform
- Question 3: Cubic joint trajectory for a rest-to-rest move
- Question 4: Inverse position kinematics of a 4R manipulator
- Question 5: Angular and linear acceleration of a single link
- Question 6: Link frames, DH table and link transforms for a 3-DOF arm
- Question 7: Jacobian of a planar 3R arm by velocity propagation
December 2018
- Question 1: Meaning of the columns of a rotation matrix, and testing a candidate matrix
- Question 2: Mapping a position vector and a velocity vector between frames
- Question 3: Frame diagram and the transform relating two frames through a graph
- Question 4: Frame assignment, DH parameters and forward kinematics of the RPR arm
- Question 5: Orientations unattainable by a 3R mechanism with non-orthogonal twists
- Question 6: Static joint torques and singular configurations of a two-link planar manipulator
- Question 7: Two-segment cubic spline through a via point with continuous acceleration
May 2016
- Question 1: Transforming a position and a velocity between frames
- Question 2: Frame diagram and composition of transformations
- Question 3: Axis assignment, DH table and forward kinematics
- Question 4: Inverse position kinematics — all closed-form solutions
- Question 5: Inverse orientation for a spherical wrist — Z–Y–Z Euler angles
- Question 6: Jacobian, reachable workspace and dexterous workspace
- Question 7: Static joint torques and singular configurations of a two-link arm
Undated paper
- Question 1: Transforming a position and a velocity between frames
- Question 2: Frame diagram and composition of transformations
- Question 3: Two-segment cubic spline with continuous acceleration
- Question 4: All joint-3 angles reaching a given position
- Question 5: Equations of motion of the PR manipulator
- Question 6: Axis assignment, DH table and forward kinematics
- Question 7: Jacobian, reachable workspace and dexterous workspace