Exoskeleton Hip Torque: Inverse-Dynamics Model (2D)

This 2D companion swaps the scripted-kinematics view of exoskeleton assistance for an inverse-dynamics one: rather than assuming a biological torque curve, it prescribes the hip's actual swing trajectory θ(φ) and solves Newton's second law for rotation backward — I·θ″ + b·θ′ + mgL·sin(θ) — to find the torque that trajectory truly demands at every phase of the stride. A phase-locked, Gaussian-shaped exoskeleton assist torque is then subtracted from that requirement to reveal exactly how much is left for the muscles. A stick-figure swing leg animates the prescribed trajectory beside a live strip chart of required, assist and muscle torque across the gait cycle, while a mechanical-effort integral (∫|τ_muscle·θ′|dφ) reports how assist timing changes the muscles' real workload — well-timed assistance measurably lowers it, mistimed assistance raises it, exactly as published human-in-the-loop exosuit optimisation results report.