Robotics
Robotics questions cover coordinate frames, forward and inverse kinematics, Jacobians, singularities, actuators, sensors, dynamics and path planning. The exam tests geometric reasoning and the ability to distinguish a robot configuration from its workspace.
Core rules
- A planar 2R arm with links L1, L2 and joint angles q1, q2 has x=L1cos q1+L2cos(q1+q2), y=L1sin q1+L2sin(q1+q2).
- The Jacobian maps joint rates to end-effector velocity: v=J(q)q̇. A singularity occurs when det(J)=0; for the planar 2R arm, det(J)=L1L2 sin q2, so q2=0 or π is singular.
- Homogeneous transforms compose frame changes; rotation and translation order matters. DH parameters follow a fixed convention.
- Degrees of freedom count independent motion; a 6-DOF arm can generally position and orient in 3D, but reach limits still apply.
- Inverse kinematics may have multiple solutions; choose by joint limits, collision and dexterity.
Worked example
L1=0.4 m, L2=0.3 m, q1=30°, q2=60°. x=0.4cos30°+0.3cos90°=0.346+0=0.346 m. y=0.4sin30°+0.3sin90°=0.200+0.300=0.500 m. The Jacobian determinant is 0.4×0.3×sin60°=0.104 m², so the arm is not at a singularity here.
Traps
- Using degrees in a formula that expects radians.
- Adding link lengths without transforming through the second joint angle.
- Treating a Jacobian transpose as an inverse in all configurations.
- Confusing workspace with dexterous workspace.
- Ignoring joint limits when selecting an inverse-kinematics solution.