The hip completes one gait cycle per stride, parameterised by phase φ ∈ [0, 1) (0 = heel strike, 1 = next heel strike, ≈60% stance / 40% swing). This sim uses a simplified, idealised biological hip-torque curve:
τ_bio(φ) = T_b · sin(2π(φ − 0.08))
positive = extension effort (weight acceptance, early stance), negative = flexion effort (limb advancement, late stance / pre-swing). A powered exoskeleton adds a phase-locked assistive torque shaped as a Gaussian bump centred on a chosen peak timing φ₀ with width σ:
τ_assist(φ) = A · exp( −Δφ² / (2σ²) ), Δφ = wrapped circular distance(φ, φ₀)
τ_net(φ) = τ_bio(φ) + τ_assist(φ)
P_assist(φ) = τ_assist(φ) · ω_hip(φ)
The peak timing and width sliders are the two parameters real human-in-the-loop exoskeleton optimisation studies (e.g. Zhang et al., Science 2017; Mooney & Herr, 2016) tune per-user — assistance timed well to the biological effort curve measurably reduces the metabolic cost of walking (commonly 10–25% in published ankle/hip exosuit trials), while assistance applied out of phase provides little benefit or actively fights the muscles, increasing cost.
This sim estimates that effect with a cosine-similarity alignment score s between τ_assist(φ) and τ_bio(φ) sampled across a full cycle:
s = ⟨τ_assist , τ_bio⟩ / (‖τ_assist‖ ‖τ_bio‖) ∈ [−1, 1]
metabolic change ≈ −s · 22% · min(1, A / T_b)
A well-timed, correctly-directed assist pushes s toward +1 (reduction in estimated cost); a mistimed or oppositely-directed assist pushes s toward −1 (estimated cost increase) — this is a deliberately simplified pedagogical model, not a validated metabolic-cost predictor, but it captures the real, well-documented sensitivity of exosuit benefit to assistance timing.
- Peak assist torque — the amplitude A of the exoskeleton's actuator torque.
- Peak timing — where in the gait cycle φ₀ the assist is centred; the ring plot marks it live.
- Assist window width — how broad (σ) the torque pulse is around φ₀; narrow = a sharp push, wide = a gentle sustained boost.
- Cadence — walking speed, which scales hip angular velocity ω_hip and therefore instantaneous assist power.