Industrial Robotics — Kinematics, Jacobians & Motion Planning

Engineering

Advanced 120 minutes 2 lessons

PhD-level treatment of industrial robot mechanics: Denavit–Hartenberg parameterisation, forward and inverse kinematics for serial manipulators, the velocity Jacobian, singularity analysis, workspace computation, and trapezoidal/S-curve trajectory generation for smooth, jerk-limited motion.

Learning Objectives

Assign Denavit–Hartenberg parameters to a serial manipulator and derive the forward kinematic map T_{0n}
Compute the geometric Jacobian and use it to map joint velocities to end-effector Cartesian velocities
Identify and classify singularities using the determinant and SVD of the Jacobian matrix
Solve the inverse kinematics problem analytically for 2R and 3R planar robots and numerically for 6-DOF arms
Design trapezoidal and quintic-polynomial joint trajectories that satisfy velocity, acceleration and jerk constraints