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 Mechanisms.- Type Synthesis of a Special Family of Remote Center-of-Motion Parallel Manipulators with Fixed Linear Actuators for Minimally Invasive Surgery.- Type synthesis of Non-overconstrainted 3-DOF Translational parallel mechanisms with Less Structural Shakiness.- Type synthesis of Pan-Tilt Wrists with Uncoupled Actuation.
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