Generalized Singularity Analysis

In this chapter, we consider kinematic singularity in a mechanism as a deviance or abnormality in its instantaneous kinematics. A configuration is said to be regular if in it there is a proper relationship between the input, output, and passive velocities of the mechanism. Namely, both the forward and the inverse instantaneous kinematics problems must be well-posed, allowing full control of the system. Otherwise, we have a degenerate or “singular” case. The obvious division of velocity parameters into input, output, and other (passive) speeds gives rise to a natural classification of the possible degeneracies. The taxonomy is described by six overlapping singularity types partitioning the singularity set into as many as 15 classes. The various possibilities are examined and interpreted with the help of simple examples. Special attention is given to a few cases which best illustrate the inadequacy of using an exclusively input–output relationship as a formulation of the kinematic constraints. The fact that standard serial manipulators have no passive (unactuated) joints, and therefore have a well-defined output map, suggests a false generalization, which has led analysts and designers of more complex robots into error in the past and may do so again unless the lack of generality is well understood.