Analysis of kinematically redundant reaching movements using the equilibrium-point hypothesis

BIOMECHANICAL STABILITY ANALYSIS OF THE λ-MODEL CONTROLLING ONE JOINT

Computer modeling and control of the human motor system might be helpful for understanding the mechanism of human motor system and for the diagnosis and treatment of neuromuscular disorders. In this paper, a brief view of the equilibrium point hypothesis for human motor system modeling is given, and the λ-model derived from this hypothesis is studied. The stability of the λ-model based on equilibrium and Jacobian matrix is investigated. The results obtained in this paper suggest that the λ-model is stable and has a unique equilibrium point under certain conditions.

Adjustment of the human arm viscoelastic properties to the direction of reaching

The viscoelastic properties of the human arm were measured by means of short force perturbations during fast reaching movements in two orthogonal directions. A linear spring model with time delay described the neuromuscular system of the human arm. The obtained viscoelastic parameters ensured movement stability in spite of the time delay of 50 ms. The stiffness and viscosity ellipses appeared to be predominantly orthogonal to the movement direction, which reduced the effect of force perturbation in the direction orthogonal to the reaching movement. Thus, it can be argued that the viscoelastic properties of the neuromuscular system of the human arm are adjusted to the direction of movement according to a "path preserving" strategy, which minimizes the deviation of the movement path from a straight line, when exposed to an unexpected external force.

Basic elements of arm postural control analyzed by unloading

To address the question of how arm posture is controlled, we analyzed shoulder-elbow unloading responses in the horizontal plane for different directions of the initial load. The initial load, produced by a double-joint manipulandum, was suddenly diminished to 1of 12 randomly presented levels (60 to -10% of the initial load; in 6 out of 12 cases the final load direction varied by +/-20 degrees ). Subjects were instructed "not to intervene" in response to unloading. Neither the unloading onset nor the final load level was predictable and we assumed that the responses to rapid unloading were involuntary. Unloading elicited a smooth hand movement characterized by a bell-shaped velocity profile. The changes in hand position, joint angles, and joint torques generally increased with greater amounts of unloading. For each direction of the initial load, tonic electromyographic activity of the shoulder and elbow muscles also changed, depending on the amount of unloading. The shoulder and elbow joint torques before and after unloading were a function of the difference between the actual configuration of the arm and its referent configuration (R) described by the angles at which each joint torque was zero. The R configuration changed depending on the direction of the initial load. Our electromyographic data imply that these changes result from a central modification of muscle activation thresholds. The nervous system may thus control the R configuration in a task-specific way by leaving it unchanged to generate involuntary responses to unloading or modifying it to accommodate a new load direction at the same initial position. It is concluded that the R configuration is a major variable in both intentional and involuntary control of posture.

Joint stiffness of the ankle and the knee in running

The spring-mass model is a valid fundament to understand global dynamics of fast legged locomotion under gravity. The underlying concept of elasticity, implying leg stiffness as a crucial parameter, is also found on lower motor control levels, i.e. in muscle-reflex and muscle-tendon systems. Therefore, it seems reasonable that global leg stiffness emerges from local elasticity established by appropriate joint torques. A recently published model of an elastically operating, segmented leg predicts that proper adjustment of joint elasticities to the leg geometry and initial conditions of ground contact provides internal leg stability. Another recent study suggests that in turn the leg segmentation and the initial conditions may be a consequence of metabolic and bone stress constraints. In this study, the theoretical predictions were verified experimentally with respect to initial conditions and elastic joint characteristics in human running. Kinematics and kinetics were measured and the joint torques were estimated by inverse dynamics. Stiffnesses and elastic nonlinearities describing the resulting joint characteristics were extracted from parameter fits. Our results clearly support the theoretical predictions: the knee joint is always stiffer and more extended than the ankle joint. Moreover, the knee torque characteristic on the average shows the higher nonlinearity. According to literature, the leg geometry is a consequence of metabolic and material stress limitations. Adapted to this given geometry, the initial joint angle conditions in fast locomotion are a compromise between metabolic and control effort minimisation. Based on this adaptation, an appropriate joint stiffness ratio between ankle and knee passively safeguards the internal leg stability. The identified joint nonlinearities contribute to the linearisation of the leg spring.