Stability Analysis of a Robotic Mechanism Using Computer Albegra

Abstract

This paper concerns the stability analysis of a two degree of freedom lumped mass model of a robotic mechanism. The equations of motion as well as the Hamiltonian for the system are derived using the symbolic manipulation system MACSYMA. The second order, nonlinear, coupled, ordinary differential equations which govern the system are linearized about a particular operating point. We emphasize the advantage of using MACSYMA to derive this linear system. The regions of flutter and divergence instabilities in a two dimensional parameter space are determined from a quartic characteristic equation. A MACSYMA program is used to perform a root locus study of this equation. A discussion of the application of the results to the control of a mechanical robot is presented.