Dynamics of in-plane motion of a robot arm

Abstract

A robot arm is modeled as an elastic rod fixed at one and free at the other end. It is assumed that the rod is loaded by a compressive follower type force (Beck's rod). In-plane motions of such rod are analyzed. Equations of motions are derived for the case when the deformations are not small and material of the rod behaves according to the classical Bernoulli-Euler rod theory. Also we assume that the compressive force has periodic component, so that parametric instability is possible. Stability boundary is obtained numerically.