DC Gearmotor Joint Actuator: Back-EMF & Torque-Speed (2D)

The 2D companion to the 3D joint actuator, built around the same real motor equations but staged as a live torque-speed diagram: armature current is set by the difference between applied voltage and speed-dependent back-EMF, output torque is geared up by a reduction ratio (with a real efficiency loss), and a user-set load torque pulls the operating point down the motor's characteristic line. Watch the dot slide toward the intersection of the motor line and the load line as the joint spins up, and read off the current, back-EMF, torque and instantaneous efficiency exactly as they are computed frame by frame.