The Hamilton wrist: a four-revolute-joint spherical wrist without singularities

The authors present an inverse kinematic algorithm for a four-revolute-joint (4-R) spherical wrist that provides for a complete set of spatial orientations, is nonsingular, and is simple to implement with existing technology. The algorithm is a rate-controlled method that depends on the required Cartesian rate. In the process of presenting the algorithm, the authors have developed the fundamentals of differential motion with n-revolute-joint spherical wrists. The method is outlined and applied to a 4-R regional structure. The goal is to combine the 4-R spherical wrist with the 4-R regional structure to develop an 8-R manipulator that is free of internal singularities