Bifurcations and isolated singularities in the inverse kinematics of linkages and manipulators

A general technique for differential analysis, previously developed for regular configurations and so-called ordinary singularities, has been extended to encompass other types of singularities classified as bifurcations and isolated singularities. This technique provides exact inverse rate solutions (i.e. joint velocities, accelerations, etc. for a given end-effector velocity, acceleration, etc.) as well as differential displacement models that are useful in the numerical inversion of end-effector trajectories at singularities. Examples show applications to RCRCR linkages and the PUMA manipulator