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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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Characterization of multi-variable ankle mechanical impedance is crucial to understanding how the ankle supports lower-extremity function during interaction with the environment. This paper reports quantification of steady-state ankle impedance when muscles were active. Vector field approximation of repetitive measurements of the torque-angle relation in two degrees of freedom (inversion/eversion and dorsiflexion/plantarflexion) enabled assessment of spring-like and non-spring-like components. Experimental results of eight human subjects showed direction-dependent ankle impedance with greater magnitude than when muscles were relaxed. In addition, vector field analysis demonstrated a non-spring-like behavior when muscles were active, although this phenomenon was subtle in the unimpaired young subjects we studied.

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.

Haptic virtual texture can enhance people's experience in interacting with virtual objects by providing surface information. We present a study to analyze how people distinguish between 2D and 3D square-wave gratings using a point-source haptic interface. Our analyses were based on objective vibration and force measurements and psychophysical experiments with human subjects. The results indicated that people were unable to detect the difference between the two textures when they moved their hands across textures with either the amplitude or period smaller than 1.52 mm (0.06 inch) for a texture stiffness of 2 N/mm. This result implies that a simple 2-degree-of-freedom haptic interface may be sufficient to convey the same 3-dimensional tactile feeling for certain textures if the textures are small enough.