Series-Elastic Ankle Exoskeleton Energy Return

Exoskeleton Mode

Series-Elastic Ankle

Spring stiffness k 90 N·m/rad

Motor assist gain 40%

Walking cadence 110 steps/min

Gait Cycle

Spring loading (stores energy) Spring releasing (assists push-off) Swing / no engagement

Gait phase

Spring energy now

0.0 J

Patient (biological) ankle work / stride

— J

Metabolic reduction vs. rigid boot

How it works

A series-elastic actuator (SEA) puts a spring in line with the ankle joint. As the body's weight advances over a planted foot (controlled dorsiflexion, roughly 15–45% of the gait cycle), the ankle rotates the spring and it stores elastic energy instead of the calf muscles absorbing it eccentrically:

Spring torque:  τ_s = k·Δθ
Stored energy:  E = ½·k·Δθ²      (Δθ = dorsiflexion angle, radians)

Near push-off (45–62%) the ankle rapidly plantarflexes and the same spring unloads, returning that energy as assistive torque — literally the mechanism the article describes as a "passive" exoskeleton, distinct from an actively powered one. A hybrid unit adds a motor that contributes a further fraction of the required torque on top of the spring:

τ_required(φ)  — biomechanical demand at gait phase φ
τ_assist(φ)    = τ_spring_release(φ) + gain·τ_required(φ)
τ_biological   = max(0, τ_required(φ) − τ_assist(φ))
W_bio          = Σ τ_biological·|Δθ|   over one full stride

The "Patient work / stride" readout integrates τ_biological over one full gait cycle — the model's proxy for the calf muscles' own metabolic effort. Raising k stores/returns more energy during the amber "loading" arc and cyan "releasing" arc on the phase ring; raising the motor gain shaves torque off the whole cycle, not just the elastic window. Switching to "Rigid" sets both to zero — a stiff, unassisted boot — so the reduction percentage always compares against that unassisted baseline.

This is a simplified educational model (idealised joint trajectory, no muscle-tendon dynamics) built to make the store-and-release principle of passive/hybrid exoskeletons visible and adjustable, not a clinical prediction tool.

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