Conceptual Configuration Synthesis of Line-Foldable Deployable Space Truss Structures Utilizing Graph Theory and Entropy
Abstract From the perspective of the truss as a whole, this research presents an approach to synthesizing conceptual configurations for deployable space truss structures that are line-foldable with the help of graph theory and entropy. First, according to graph theory, the bijection between a truss and its graph model is established by defining a bijective mapping between set elements. Therefore, operations can be performed based on graph models. Second, the principle of configuration evolution is interpreted by employing Maxwell’s rule, it also discusses the necessary and sufficient condition of configuration evolution. Configurations of evolution belong to three phases: space configuration, transformation configuration, and linear configuration. And it finds that the reasonable transformation configuration plays a key role. Further, maximum clique detection depending on backtracking is used to screen out unreasonable transformation configurations. Third, it introduces entropy, and the phenomenon of entropy change in configuration evolution is revealed and induction weights of rigid links are defined. It calculates the weight value of a transformation configuration by adding up induction weights of rigid links removed, also, weight values are used to classify transformation configurations. Finally, based on the previous analysis, a procedure to synthesize transformation configurations is formed and it is verified by a truss model with 7 nodes. This research lays the foundation for geometric dimension design and engineering applications.