Jacobian Derivation & Kinematic Analysis
Full symbolic and numerical Jacobian derivation for a serial manipulator — singularity identification, manipulability ellipsoids, and workspace mapping in MATLAB.
This project performs a complete Jacobian analysis for a serial robot manipulator. The geometric Jacobian was derived analytically from the DH parameter table and implemented in MATLAB for numerical evaluation at arbitrary joint configurations.
Singular configurations — where the Jacobian loses full rank and the manipulator cannot move in one or more task-space directions — were identified analytically and visualized. Yoshikawa's manipulability measure was computed across the joint space and plotted as ellipsoids showing the preferred motion directions at each configuration. The reachable workspace was mapped by Monte Carlo sampling of joint angles.