A Geometric Theory for Synthesis and Analysis of Sub-6 DoF Parallel Manipulators

This paper presents a rigorous and precise geometric theory for the analysis and synthesis of sub-6 DoF parallel manipulators. We give a rigorous definition for the parallel manipulator synthesis problem, and introduce a general method for specifying the corresponding subchains which will result in the desired parallel manipulator. Following this, a procedure for solving the parallel manipulator synthesis problem is proposed when the set of desired end-effector motions is in the form of Lie subgroup or a regular submanifold of SE(3). Numerous examples are used to illustrate the generality and effectiveness of the proposed synthesis method.