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This article presents preliminary stochastic estimates of the multi-variable human ankle mechanical impedance. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Time histories of the torques in Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions and the associated angles of the ankle were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot and when the Anklebot was worn by a human subject. The difference between these impedance functions provided an estimate of the mechanical impedance of the ankle. High coherence was observed over a frequency range up to 30 Hz, indicating that this procedure yielded an accurate measure of ankle mechanical impedance in DP and IE directions.

This article compares stochastic estimates of multi-variable human ankle mechanical impedance when ankle muscles were fully relaxed, actively generating ankle torque or co-contracting antagonistically. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Muscle activation levels were monitored electromyographically and these EMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot alone and when it was worn by a human subject, the difference between these functions providing an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in both DP and IE directions.

This paper reports quantification of multivariable static ankle mechanical impedance when muscles were active. Repetitive measurements using a highly backdrivable therapeutic robot combined with robust function approximation methods enabled reliable characterization of the nonlinear torque-angle relation at the ankle in two coupled degrees of freedom simultaneously, a combination of dorsiflexion-plantarflexion and inversion-eversion, and how it varied with muscle activation. Measurements on 10 young healthy seated subjects quantified the behavior of the human ankle when muscles were active at 10% of maximum voluntary contraction. Stiffness, a linear approximation to static ankle mechanical impedance, was estimated from the continuous vector field. As with previous measurements when muscles were maximally relaxed, we found that ankle stiffness was highly direction-dependent, being weakest in inversion/eversion. Predominantly activating a single muscle or co-contracting antagonistic muscles significantly increased ankle stiffness in all directions but it increased more in the sagittal plane than in the frontal plane, accentuating the relative weakness of the ankle in the inversion-eversion direction. Remarkably, the observed increase was not consistent with simple superposition of muscle-generated stiffness, which may be due to the contribution of unmonitored deep ankle muscles. Implications for the assessment of neuro-mechanical disorders are discussed.

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