Configuration synthesis of generalized deployable units via group theory

Abstract. The generalized deployable mechanism is composed of generalized links and generalized kinematic pairs. The generalized links include the flexible members, springs, and cables etc. The generalized kinematic pairs include the preloaded kinematic pairs and flexible hinges etc. The generalized deployable mechanism consists of generalized deployable units. Based on group theory, this paper presents a brief and effective configuration synthesis method for generalized deployable units which is composed of generalized links and generalized kinematic pairs expressed by group. The permutation group is used to obtain all the permutation types of generalized kinematic pairs and generalized links. The configuration matrix of generalized deployable unit is established through combining permutation group, and the topological configurations of generalized deployable units are created. The combining rules of groups are developed. The method of isomorphism detection is used to ensure the uniqueness of configurations. The configurations of generalized deployable units including four and six generalized links are generated respectively.