Kinematics of a Hybrid Series-Parallel Manipulation System

In this paper we first derive the coordinate transformations associated with a three-degree-of-freedom in-parallel-actuated micro-manipulator. Then we combine these results with the transformations associated with an in-series three-axis wrist on which the in-parallel micro-manipulator is mounted. The results are the basic transformation equations between joint-space position variables and end-effector ( or task space) position variables for a hybrid series/parallel six-degree-of-freedom manipulator system. This structural combination results in a manipulator which exhibits desirable fine and gross motion characteristics as both a stand-alone device or as a sub-system of a more complex system with redundant degrees of freedom. The forward and inverse position kinematics and rate and force decomposition for this hybrid six-degree-of-freedom linkage are presented.