A novel family of umbrella-shaped deployable mechanisms constructed by multi-layer and multi-loop spatial linkage units

This paper aims to construct a novel family of umbrella-shaped deployable mechanisms based on new multi-layer and multi-loop spatial deployable linkage units. Firstly, a general method is proposed for analyzing the degree-of-freedom (DOF) of the deployable units by identifying independent geometrical constraint equations of them. Then, multi-layer and multi-loop deployable units are synthesized systematically based on structural modules and DOF constraint conditions. Finally, three mobile assembly modes of the new deployable units are established, and many novel umbrella-shaped mechanisms are obtained by assembling the deployable units. This paper greatly extends our previous work on the deployable mechanism design based on two-layer and two-loop deployable units in breadth and in depth, and presents new design methods as well as many novel umbrella-shaped deployable mechanisms with potential applications in space exploration and civil engineering.