A Geometrical Analysis of Manipulator Dynamics

Abstract

Robot manipulators and mechanical arms have complicated behavior including interactions among multiple joints, nonlinear effects such as Coriolis and centrifugal forces, and varying inertia depending on the arm configuration. In this paper, a new approach to the geometrical representation of manipulator dynamics is presented. The inertia ellipsoid, which is used to represent dynamic characteristics of a single rigid body, is extended to a series of rigid bodies in order to represent the manipulator dynamics. The geometrical representation of the generalized inertia ellipsoid (GIE) represents the characteristics of the manipulator as a whole. One can understand the complicated inertia effect and nonlinearity of multi-degree-of-freedom motion by simply investigating the GIE configuration. In the latter half of the paper, the presented method is applied to aid the design of a mechanical arm, in which dimensions of an arm structure and its mass distribution are optimized through the evaluation and graphical representation of the arm dynamics.