Structural synthesis of two-layer and two-loop spatial mechanisms with coupling chains

Structural synthesis is one of the most important tasks in the creative design of mechanisms. In the past decades, spatial parallel mechanisms have been extensively synthesized. However, structural synthesis of more complex spatial mechanisms with coupling chains is seldom addressed. This paper aims to propose a general method for synthesizing a class of important spatial mechanisms with coupling chains, called two-layer and two-loop (TLTL) mechanisms, which are the basic units for constructing multi-layer and multi-loop mechanisms with more complex couplings. First, the motion screw equation of TLTL mechanisms is derived, with which mobility or degree-of-freedom (DOF) of the class of mechanisms can be analyzed and rigid substructures can be detected. Then, a general method for structural synthesis of TLTL mechanisms is proposed on the basis of the principle of mobility analysis. Finally, TLTL mechanisms with fourteen kinds of degrees of freedom are synthesized, illustrating the effectiveness of the method.