A general Newtonian simulation of an N-segment open chain model

Abstract

This paper presents a set of general Newtonian equations which govern the simulation of movement of a body represented by n open chain links. The input for the simulation consisted of the joint moment of force histories, lengths, masses and moments of inertia, the initial absolute angular displacements and velocities and, for the fixed or constrained axis of the nth segment, the acceleration history. Angular accelerations were then determined by solving n linear equations simultaneously, and angular velocities and displacements determined by integrating forwards. The final output was in the form of a graphical display of the linked figure. Applications of the simulation were demonstrated using three-segment representations of movements of the upper and lower extremities and a five-segment representation of a jump. Good agreement was achieved between the displayed angular displacements for the original and simulated movements. The potential for varying the input data has been examined and the implications of anticipating the effects of changed torques, inertial characteristics including attached prosthetic or sports implements and/or the initial conditions for a movement are discussed.