Inverse Kinematics of Anthropomorphic Arms Yielding Eight Coinciding Circles

In this paper it is demonstrated that the solution space of the inverse kinematic problem of an anthropomorphic, redundant 7R chain for a given pose does consist of eight different coinciding circles instead of a single circle that has been reported as of today. By modeling the structure using the convention by Sheth and Uicker, the displacements within the kinematics of the chain are partitioned in time-invariant displacements along rigid links and time-variant displacements along the seven rotative joints. In particular, the subchains of shoulder, elbow, and wrist are preserved. By respecting the 'flips' of these three substructures the eight-fold occupancy of the redundancy circle is obtained. The result corresponds to the eight IK solutions for regional-spherical arms and provides a prerequisite for using all capabilities of respective robots in practical applications.