Systematic nonlinear relations between displacement amplitude and joint mechanics at the human wrist

Abstract

This study quantified the systematic effects on wrist joint mechanics of changes in amplitude of displacement ranging from within the region of short range stiffness (0.2% of resting muscle length) up to 3% of resting muscle length. The joint mechanics were modelled using a second order system from which estimates of joint stiffness, viscosity, inertia, natural resonant frequency and damping ratio were obtained. With increasing amplitude of displacement, the stiffness decreased by 31%, the viscosity decreased by 73%, the damping ratio decreased by 71% and the resonant frequency decreased from 10.5 Hz to 7.3 Hz. The patterns of change in joint mechanics with displacement amplitude were nonlinear but systematic and were well described by power relationships with high R 2 values. These relationships provide normative data for the adult population and may be used in the modelling of human movement, in the study of neurological disorders and in robotics where human movement is simulated. The observed patterns of high initial stiffness and viscosity, decreasing progressively as displacement amplitude increases, may provide a good compromise between postural stability and liveliness of voluntary movement.

The passive stiffness of the wrist and forearm

“…The measurements presented in this report fall in the middle of the range of measurements from prior studies. Prior measurements of wrist stiffness during contraction of flexors and/or extensors (Halaki et al 2006;Milner and Cloutier 1993;Sinkjaer and Hayashi 1989) generally give higher values, because muscle stiffness increases with muscle contraction, but these measurements of active stiffness are not comparable to the measurements of passive stiffness presented in this article. The only prior measurement of passive stiffness in RUD (1.45 Nm/rad) (Rijnveld and Krebs 2007) is very close to the measurements in our study.…”

“…Several studies have measured wrist stiffness in flexion and/or extension (Axelson and Hagbarth 2001;Cornu et al 2003;De Serres and Milner 1991;Gielen and Houk 1984;Halaki et al 2006;Lakie et al 1984;Lehman and Calhoun 1990;Leger and Milner 2000;Milner and Cloutier 1993;Sinkjaer and Hayashi 1989) or radial-ulnar deviation (Rijnveld and Krebs 2007). Although these 1-degree of freedom (DOF) measurements inform us of the dynamics the neuromuscular system must overcome to rotate in pure flexion-extension (FE) or pure radial-ulnar deviation (RUD), the wrist rarely rotates in pure FE or RUD.…”

Mechanical Impedance and Its Relations to Motor Control, Limb Dynamics, and Motion Biomechanics

“…A common method to resolve mechanical impedance from oscillatory motion was implemented in the wrist joint [80] and ankle joint [65]. In this latter case, the foot was driven relative to the shank and the torque was delivered by means of a band-limited oscillatory Gaussian signal.…”

“…Such systems were implemented for the ankle joint in plantar and dorsi flexion motion [65, 66], the wrist joint [80], and the trunk using the load sudden-release method [102]. Active extension exertions were also used in the trunk to estimate the active impedance component values using second-order trunk dynamics following preload that caused small amplitude trunk movements [103].…”

A comparison of resonance tuning with positive versus negative sensory feedback

“…1a. This simplistic model has previously been used to describe a variety of biological movements and has been shown to sufficiently represent the dynamics of a one-degree-of-freedom system (Winters and Stark 1987;Holt et al 1990;Long and Nipper 1996;Halaki et al 2006). As such, the motion of the mechanical subsystem is governed by…”