On hyperbolic normal forms of robot kinematics

We study redundant robot kinematics around singular configurations of corank 1. Sufficient conditions are derived under which the kinematics become equivalent to a hyperbolic normal form. These conditions are specified further to non-redundant kinematics, and illustrated with examples of a double pendulum with links of equal length at the fully folded down configuration as well as of the PUMA manipulator at the wrist singularity. Also, the hyperbolic normal form of the Euler wrist has been re-established. The significance of our normal form result may be appreciated in the context of the singular inverse kinematic problem perceived from the normal form approach perspective. Keywords—robotic manipulator, kinematics, singular configuration, normal form.