Harmonic Drive vs Spur Gear: Backlash in a Surgical Robot Joint (2D)

Teleoperated surgical robots translate a surgeon's hand motion at the console into instrument motion inside the patient through a chain of precision actuators, and the gear stage inside each joint decides whether that translation is crisp or sloppy. This simulator renders one such joint two ways at once: as a real strain-wave (harmonic-drive) gear set — an elliptical wave generator flexing a thin flexspline into full mesh with a rigid circular spline — and as a conventional spur-gear stage with an explicit tooth-clearance dead zone, both driven from the same input speed every frame. Drive the input speed and apply a reversing load torque with static friction to see the output torque model τ = kθ·θ_err − b·ω + f_s·sign(ω) play out live: the harmonic drive holds transmission error to a fraction of a degree through a load reversal, while the spur gear free-wheels through its backlash gap every time, visible directly on the dual-trace oscilloscope and the arcminute readouts for both transmissions side by side.