Planar 3R Manipulator — Jacobian IK (2D)

This 2D companion drives the same damped-least-squares Jacobian inverse-kinematics solver as the 3D 6-DOF manipulator, scaled down to a 3-revolute-joint planar arm so the math reads directly off the canvas: drag the magenta target to set where the tip should reach and the amber marker to set the angle it should point at, and watch the joints solve toward both every frame. A live readout panel shows the end-effector position and orientation, the distance still remaining to the target, and det(J) — the manipulability measure that collapses toward zero and triggers the on-screen singularity warning whenever the arm nears full extension.