NONEQUILIBRIUM IN THE TRANSLATIONAL EQUATIONS OF MOTION

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The basis of many biomechanical analyses has long been inverse dynamics through the use of rigid body mechanics. Equations of translational motion stipulate that the sum of all external forces acting on a system of rigid bodies must equal the sum of each body's mass/acceleration product. The extent to which this relationship is maintained depends upon the validity of the geometric and segment mass distribution model, the assumptions regarding segment stiffness, and the accuracy of the individual segment acceleration estimates. Our immediate objective is to evaluate the error associated with the implementation of translational equations of motion in a fifteen segment rigid body model of the human form during gait. Our goal is to improve the accuracy of our three- dimensional full-body model. We plan to use measured ground reaction forces (GRF) as criteria against which to compare the sum of segmental mass/acceleration products, calculated using various data collection and analysis techniques. The full-body model is comprised of hand, forearm, foot, shank, thigh, pelvis, trunk/abdomen, and head segments, all modeled as regular geometric shapes. Anthropometric measurements are made to individualize segments for each subject. A passive infra-red motion analysis system is used to collect segmental kinematics, with GRF obtained using two strain gauge force plates. Residual errors are calculated at each sampled instant as the total external force on the body minus the sum of all segmental mass/acceleration products, expressed as percentages of body weight. Seventeen trials were collected on 5 normal males. The means RMS residual was 6.1 +/- 4.4% for the vertical axis, 3.1 +/- 1.3% for the anterior/posterior axis, and 3.0 +/- 4.8% for the medial/lateral axis. Masked by the RMS and ensemble averaging process, residuals in the vertical direction reached magnitudes as large as 43% of body weight near foot strike. These data suggest that our geometric model produced acceptable levels of "nonequilibrium," except at foot strike. Additional study will be made of the effect of kinematic data processing on the minimization of residuals.