AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting
of the American Society of Biomechanics
Clemson University, South Carolina
September 24-27, 1997
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| AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting |
The haptic perceptual system is the system by which one knows the body, and objects adjacent to or attached to the body, by means of the body. Its sensory basis is provided by mechanoreceptors and its loss severely limits a person to a few purposeful movements that can only be conducted with considerable concentration and intel-lec-tual effort (e.g., sneezing when standing, and note taking while sitting, result in a complete loss of balance). The intimate connection between this perceptual system and movement coordination defines the level of muscular-articular links or synergies, a functional level of the nervous system responsible for stable and reproducible spatio-temporal relations among body segments. Thorough information about muscle and joint states places this level in a unique position. Only it is able to control the large-scale movement patterns (e.g., running). Higher functional levels must rely on the level of muscular-articular linksÕ ability when many muscles are involved. A person with peripheral neuropathy (loss of haptic perception) tends to limit visual control to one mus-cle at a time; when many are involved simultaneously, they are simply co-contracted, not orches-trated. The production of coordination patterns is no longer available to patients with peripheral neuropathy. Standing, walking, reaching and the manipulation of objects are challenging if not impossible tasks and the ability of these pa-tients to perceive by eye proves to be a poor substitute for their inability to perceive by muscle. The purpose of this keynote lecture is to summarize investigations into the rhythmic coordinations of contralateral limbs and the nonvisible perception of the properties of handheld wielded objects, two major achievements of the level of muscular-articular links. Understanding the bases for these achievements requires both classical dynamics and contemporary nonlinear, qualitative dynamics.
Among the subsystems of haptic perception, that which is almost exclusively anchored in the mass action of the muscle and tendon mechanoreceptorsÑreferred to as effortful or dynamic touchÑis of largest significance to the level of muscu-lar-articular links. In manual activity, this subsystem is functioning whenever one takes hold of something firmly and moves it (e.g., when one lifts a cup, turns a door handle, carries a briefcase, stacks a plate, hefts a ball, wields a stick, and so on) or uses one object to probe another, more distal object. Many spatial and other perceptual capabilities of effortful touch arise from the sensitivity of the bodyÕs tissues to the inertia tensor and attitude spinor, quantities of rotational dynamics about a fixed point that do not vary with variation in the rotational forces (torques) and motions. Specifically, research on the wielding of occluded handheld objects has shown that perceived length, width, and shape, and perceived heaviness, are functions of the magnitudes (eigenvalues) of the eigenvectors of the inertia tensor. Further, the research has shown that the perception of object-to-hand relations and hand-to-object relations, are functions of the directions of the tensorÕs eigenvectors and, additionally, of the objectÕs attitude spinor when attention must be directed to one of two oppositely directed object segments. These lessons learned from wielding attachments to the body (handheld objects) apply to the body. The nested body segments can be interpreted as a nest-ing of inertia tensors. If the normal relation between an armÕs spatial axes and the armÕs inertial eigenvectors is broken by means of an attached splint, the positioning of the occluded arm is systematically altered relative to vi-sual targets. People point with the armÕs eigenvectors rather than the armÕs longitudinal axis. When the position of one forearm is matched nonvisually with that of the other, under conditions in which splints have rotated the eigenvectors relative to the limb segmentÕs spatial axes, the matching is in terms of the respective forearm eigenvectors rather than elbow angles.
Oscillations of two or more body segments at the same frequency is a common feature of the movement patterns of most animals. Despite its elementary nature, each instance of 1:1 frequency locking involves a large number of components at very many levels. Despite the internal complexity of two limbs sharing a temporally repeating pattern, at their own level they seem to follow a relatively uncomplicated coordination law. Theory and experiments show that the collective dynamics can be modeled by a first order motion equation in relative phase. The equation successfully predicts interlimb coordination equilibria and their bifurcations as a function of movement speed and differences between limbs in natural frequency. The bodyÕs functional asymmetry shows up as a modification of the fundamental coupling function and attentional effects in bimanual coordination are revealed as parameterizations of the modified coupling function. For any rhythmic bimanual coordination, the collective vari-able at the pattern level is formed from the cooperative activity of a number of subsystems each expressible as a first-order, autonomous, ordinary differential equation identifying an active degree of freedom (DF). A reproducible, stable coordination pattern implies an attractorÑa geometric object to which the (longer term) motions composing the pattern are con-fined. Because all variables are generically connected in a nonlinear process, measure-ment of a single scalar, such as the amplitude of one hand, can suffice to reconstruct the vector space of the attractor and to determine the number of active DFs governing motion on the attractor. Application of the phase-space reconstruction method reveals that the dynamics of single-joint rhythmic behavior contain more than the two active DFs expected from limit cycle dynamics. Observed positive Lyapunov exponents and fractal attractor dimensions suggests that the gross variability of rhythmic movement stems largely from low-dimensional chaotic motion on strange attractors.
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