Mobility of Spatial Parallel Manipulators

This chapter focuses on the mobility analysis of spatial parallel manipulators. It first develops an analytical methodology to investigate the instantaneous degree of freedom (DOF) of the end-effector of a parallel manipulator. And then, the instantaneous controllability of the end-effector is discussed from the viewpoint of the possible actuation schemes which will be especially useful for the designers of the parallel manipulators. Via comparing the differences and essential mobility of a set of underactuated, over actuated and equally actuated manipulators, this chapter demonstrates that the underactuated, over actuated and equally actuated manipulators are all substantially fully actuated mechanisms. This work is significantly important for a designer to contrive his or her manipulators with underactuated or over actuated structures. Based on the analytical model of the DOF of a spatial parallel manipulator, this chapter develops a general process to synthesize the manipulators with the specified mobility. The outstanding characteristics of the synthesis method are that the whole process is also analytical and each step can be programmed at a computer. Because of the restrictions of the traditional general mobility formulas for spatial mechanisms, a lot of mechanisms having special manoeuvrability might not be synthesized. However, any mechanism can be synthesized with this analytical theory of degrees of freedom for spatial mechanisms.