The Multi-Variable Torque-Displacement Relation at the Ankle

Abstract

In this paper, we report measurements of the multi-variable torque-displacement relation at the ankle. The passive behavior of the ankle in two degrees of freedom (inversion-eversion and dorsiflexion-plantarflexion) was quantified using the Anklebot. The measured torque-displacement relationship was represented as a vector field using thin-plate spline smoothing with generalized cross validation. Analysis of the experimental results showed that, when maximally relaxed, the ankle behaved like a mechanical spring. However, if muscles were active, the torque-displacement relation was not spring-like. Implications for the contribution of neural feedback to ankle impedance are discussed.

Quantitative Characterization of Steady-State Ankle Impedance With Muscle Activation

“…Considering that single degree of freedom (DOF) movements at the ankle are rare under natural physiological conditions, characterization of ankle impedance in multiple DOFs promises deeper understanding of its roles in lower extremity function. In a previous work by the authors [6], the multivariable steady-state torque-angle relation at the ankle was measured with muscles maximally relaxed, showing that (as expected) the ankle behaved like a (nonlinear) spring under those conditions. Although that work provided a baseline for understanding ankle impedance, it is not directly applicable to normal lowerextremity actions since they involve muscle activation, either singly, synergistically or antagonistically (co-contraction).…”

“…Steady-state torque-angle data in IE−DP space were captured using a wearable ankle robot, Anklebot [7], the same device used in previous work [6]. It was mounted at the knee and operated by a simple impedance controller which enabled stable data capture even in high muscle activation conditions.…”

“…Steady-state ankle impedance at the ankle was represented as a vector field (V), and this was approximated based on the methods introduced in our previous work [6]. In brief, the vector field approximation problem was decomposed into two scalar function (∅ 1 , ∅ 2 ) estimation problems ( Fig.1) and each scalar function was identified by adopting the method of Thinplate Spline (TPS) smoothing with Generalized Cross Validation (GCV).…”

“…The approximated vector field was further decomposed into a conservative (zero curl) and a rotational field (zero divergence). The vector field approximation and decomposition methods are detailed in [6]. Fig.1.…”

Ankle mechanics during sidestep cutting implicates need for 2-degrees of freedom powered ankle-foot prostheses

“…Rouse et al developed a platform capable of applying moment perturbations during the foot-flat stance phase in sagittal plane [24][25]. Mechanical ankle impedance in both DP and IE directions in non-load-bearing and stationary conditions was estimated by Rastgaar et al for dynamic mechanical impedance [26][27] and Lee et al for quasistatic mechanical impedance [28][29][30][31]. Ho et al also studied the directional variation of quasistatic ankle mechanical impedance [32][33].…”