Introduction.- Fundamentals of group theory.- Rotation and displacements of rigid body.- Lie group based method for type synthesis of parallel mechanisms.- Type Synthesis of 5-DOF 3R2T Parallel Mechanisms.- Type Synthesis of 4-DOF 2R2T Parallel Mechanisms.- Type Synthesis of 4-DOF Parallel Mechanisms with Bifurcation of Schoenflies Motion.- Type Synthesis of 3-DOF RPR-equivalent Parallel Mechanisms.- Type Synthesis of 3-DOF PU-equivalent Parallel...