Stability and Bifurcations of an Underactuated Robot Manipulator

Abstract

The stability and bifurcations of a two-degree-of-freedom (2-DOF) under-actuated robot manipulator with linear viscous damping and constant torque are studied. It is shown that, under some conditions on the parameters, the Jacobian matrix has a double zero eigenvalue and a pair of pure imaginary eigenvalues. Around such parameters, the system has a bifurcation zoo: since codimension one (Hopf and fold), three (cusp and degenerate zero-Hopf), and higher (degenerated double zeroHopf and Hopf-Hopf). The center manifold theorem and normal form theory are used, and some numerical experiments are presented to illustrate the results.