Lie Group Based Method for Type Synthesis of Parallel Mechanisms

Abstract

Lower mobility parallel mechanisms can be sorted into nine categories according to their kinds of mobility. Most of the proposed synthesis methods cannot be applied to all nine categories. An exception is the constraint-synthesis method based on screw theory. However, the constraint-synthesis method belongs to the instantaneous motion field because the screw is instantaneous. An indispensable step of that method is to identify if the synthesized mechanism is only instantaneous or not, which sometimes is rather difficult for some complicated architectures. To overcome this problem, this chapter aims to propose a universally effective type synthesis method based on the Lie group theory in the finite motion field.