A general method for kinematics analysis of two-layer and two-loop deployable linkages with coupling chains

Abstract Two-layer and two-loop deployable linkages with coupling chains are new deployable units developed in the past two years for constructing umbrella-shaped deployable mechanisms. However, a method for kinematics analysis of the class of linkages has not been established, which leads to the problem that further performance analysis and dimensional design of them have not been performed. In this paper, first, the remaining new two-layer and two-loop deployable linkage units are systematically synthesized. Moreover, a general method is developed for kinematic analysis of all kinds of those units based on their structural characteristics and motion characteristics. In addition, the complexity of kinematics analysis of those linkage units is evaluated. Such a method lays a key foundation for dynamics analysis, dimensional design and structure optimization of two-layer and two-loop deployable linkage units and umbrella-shaped deployable mechanisms based on those units.