Series-Chain Planar Manipulators: Inertial Singularities

Abstract

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation of their dynamic equations. An important step in the simulation is the inversion of a matrix, often known as the inertia matrix of the system. In the configurations, where the inertia matrix is singular, the simulation is prone to large numerical errors. Commonly, it is believed that this inertia matrix is always positive definite (or, nonsingular) no matter what geometric and inertial attributes are assigned to the links. In this paper, we show that the inertia matrix of a multi-degree-of-freedom mechanical system modeled with point masses can be singular at special configurations of the links. We present a way to systematically enumerate some of these configurations where the inertia matrix for planar series-chain manipulators built with revolute and prismatic joints are singular.