Design and Mobility Analysis of Large Deployable Mechanisms Based on Plane-Symmetric Bricard Linkage

In this paper, a class of large deployable mechanisms constructed by plane-symmetric Bricard linkages is presented. The plane-symmetric Bricard linkage is a closed-loop overconstrained spatial mechanism composed of six hinge-jointed bars, which has one plane of symmetry during its deployment process. The kinematic analysis of the linkage is presented from the perspectives of geometric conditions, closure equations, and degree-of-freedom. The results illustrate that the linkage has one degree-of-freedom and can be deployed from the folded configuration to one rectangle plane. Therefore, the plane-symmetric Bricard linkage can be used as a basic deployable unit to construct larger deployable mechanisms. Four plane-symmetric Bricard linkages can be assembled into a quadrangular module by sharing the vertical bars of the adjacent units. The module is a multiloop deployable mechanism and has one degree-of-freedom. The singularity analysis of the module is developed, and two methods to avoid singularity are presented. A large deployable mast, deployable plane truss, and deployable ring are built with several plane-symmetric Bricard linkages. The deployment properties of the large deployable mechanisms are analyzed, and computer-aided design models for typical examples are built to illustrate their feasibility and validate the analysis and design methods.