Singularities of Nonredundant Robot Kinematics

Abstract

This article is concerned with an investigation of kinematic singularities of nonredundant robot manipulators, conducted toward describing the kinematics by simple mathematical mod els called normal forms. The adopted approach comes from the singularity theory of maps. The analysis is concentrated on kinematic singularities of codimension 1. The kinematics at singular configurations are characterized by a number called the differential degree. It is proved that, if this degree is finite, then the kinematics can be transformed to normal forms called pre-Morin or Morin forms. If the differential degree becomes infinite, the kinematics can be given either the prehyperbolic or the hyperbolic normal form. Special attention has been paid to the kinematics of the Unimation PUMA manipulator. A sin gularity analysis of the PUMA kinematics has shown that in a neighborhood of the shoulder and elbow singular configura tions, the kinematics assume a simple quadratic (Morin) form, whereas at the wrist singularity, the kinematics are represented by the hyperbolic normal form.