Normal forms of non-redundant singular robot kinematics: Three DOF worked examples

Abstract

A collection of mathematical models (normal forms) of 3 degree of freedom (DOF) corank 1 singular manipulator kinematics is derived using a general theory presented in Tchoń and Muszyński.1 All 3-DOF kinematic structures, from PPP up to RRR, are investigated. Singular configurations are distinguished by their corank. For each kinematics geometric conditions making the kinematics spatial and defining the corank of the appropriate Jacobian matrix are established. Several instructive examples of kinematic singularities are examined in detail and given a readable geometric interpretation. © 1996 John Wiley & Sons, Inc.