Conceptual configuration synthesis of line-foldable type quadrangular prismatic deployable unit based on graph theory

This study proposes a conceptual configuration synthesis method based on graph theory to obtain a series of quadrangular prismatic deployable units (QPDUs) which can be folded into a straight line. Firstly, according to graph theory, graphs of statically determinate QPDUs are synthesized. Secondly, in order to establish the conceptual configuration of QPDUs, weighted graph, weighted adjacency matrix and some rules are analyzed. Combined with graph properties, a procedure for synthesizing conceptual configuration of QPDUs is obtained. Finally, all 78 kinds of QPDUs are discovered by using synthesis approach mentioned above. These QPDUs are then used to build large deployable space mechanisms, such as mast, planar and hoop mechanisms, in different construction methods. This study expands the deployable unit configuration library, and the method can provide experience for the theoretical research in aerospace deployable mechanisms.