INFLUENCE OF EXTERNAL FORCES ON THE CONTROL AND PERFORMANCE OF A MINIMUM TIME SHOULDER FLEXION TASK

Abstract

INTRODUCTION AND METHODS We have been using planar mathematical models to simulate the task of a rapid bilateral arm raise and to obtain minimum movement time solutions. Here we report the effect of gravity (G), ground reaction force (GRF) and center of pressure (COP) location on the solutions of a three segment model. We modeled the arms as a rigid segment, the head, torso, upper and lower legs as a second rigid segment, and the feet as a third rigid segment. The shoulder and ankle joints were modeled as revolute pin joints. A nonlinear rotational spring and damper restrained the movement of the ankle joint within physiological limits. Joint muscle torques were generated through two idealistic torque generators. Torque history values (for each joint) were controlled by eight evenly spaced nodes, while intermediate values were obtained by linear interpolation. The foot to ground interaction was modeled with the use of two 2-D springs (nonlinear vertically, linear horizontally) and dampers. One set was attached at the toes and one at the heel. Thus, the feet were free to move off and slide along the ground depending on the dynamics of the simulation. The initial position was quiet erect stance with the arms and feet perpendicular to it. A variable step integrator was used for the forward simulations. The parameterized torque histories were optimized using a nonlinear optimization algorithm. We compared solutions with G, without G (free floating or attached to the ground), and with the COP location at the initial and final state proscribed to be either below the ankle joint or at the middle of the feet. This adjustment of the COP was accomplished by defining the initial and final orientation of the body segment. The arms and feet initial and final orientation, as well as the anthropometric parameters and strength limits of the model were held constant for all solutions. RESULTS AND CONCLUSIONS The overall performance and &ody kinematics were very similar and well within human subject experimental results, but the 1G condition revealed higher maximum arm angular velocity (8radsec) than the OG conditions (7 radsec). Although the 1G solution used maximum ankle torque, the heel moved up minimally (< 6 mm) only early in the stopping phase. On the other hand, although the OG free floating solution used minimal ankle torque values, there was maximum dorsiflexion followed by maximum plantarflexion. The 1G condition revealed significant plantar- and shoulder-flexion torques at the end of the movement that the OG attached to the floor model did not have. Finally, the two COP conditions produced opposite ankle torque coordination, a variability also observed during human subject experiments.