The Singularities of Redundant Robot Arms

Abstract

A robot arm is redundant if it has extra degrees offreedom. In such cases the kinematic function is a mapping from a higher-dimensional joint space to a lower-dimensional work space. The manipulator may have singular configurations, which are singularities of the kinematic function. At or near the singularities, the robot may be difficult to control. The redundancy may help to avoid some singularities, but other singularities may be unavoidable. To help in the robot design and in order to devise a controlling strategy that would avoid singularities, it is important to know analytically which singularities are avoidable. This paper gives some tools for classifying singularities. The singularities of 3-joint manipu lators operating in 2-dimensional work spaces are classified, and an analysis is performed for case studies, with various manipulator designs.