DC Gearmotor Joint Actuator: Back-EMF & Torque-Speed

Robot joints are usually taught as pure kinematics — a hinge with an angle. This simulator instead models the actuator underneath: a permanent-magnet DC gearmotor whose armature current is set by the difference between applied voltage and its own speed-dependent back-EMF, whose torque is geared down (or rather, geared up) by a reduction ratio, and whose output has to lift a payload against gravity. Switch between open-loop PWM duty and a closed-loop proportional position controller, tune gear ratio and payload mass, and watch current spike under load and settle as the joint reaches equilibrium — exactly the trade-off an engineer sizing a real actuator has to navigate.