Conceptual configuration synthesis and topology structure analysis of double-layer hoop deployable antenna unit

A method involving conceptual configuration synthesis and topology structure analysis is developed based on graph theory to obtain a series of double-layer hoop deployable antenna units (DHDAUs) that can be folded into straight lines. First, a procedure for synthesizing the conceptual configurations of DHDAUs is obtained by combining graph properties, weighted adjacency matrixes, and several principles. Second, a fundamental topological graph is presented to describe joint connections in a DHDAU on the basis of the adjacency matrix. The fundamental topological graph is reduced to a two-color topological graph by applying various simplified rules and topology properties. Third, a procedure for the identification of kinematic joints is established to fold DHDAUs into lines. Finally, three types of DHDAUs are obtained through this synthesis approach. The models, which were produced via 3D printing, can be deployed flexibly, thus proving the correctness of the theoretical analysis. These methods can provide guidance for the design of large aerospace deployable mechanisms.