Techreport,
Generic Singularities of Robot Manipulators
Technical Report, TR88-943. Cornell University, Computer Science Department, (November 1988)
Abstract
The singularities of the differential kinematic map, i.e., of the
manipulator Jacobian, are considered. We first examine the notion
of a ``generic'' kinematic map, whose singularities form smooth manifolds
of prescribed dimension in the joint space of the manipulator. For
3-joint robots, an equivalent condition for genericity using determinants
is derived. The condition lends itself to symbolic computation and
is sufficient for the study of decoupled manipulators, i.e., manipulators
which can be separated into a 3-joint translating part and a 3-joint
orienting part. The results are illustrated by analyzing the singularities
of two classes of 3-joint positioning robots.
