Kinematic synthesis of deployable-foldable truss structures using graph theory

A graph theoretic approach is applied to the conceptual design of deployable truss structures. The characteristics that relate to the inter-connectivity of the elements of a deployable truss structure can be captured in a schematic representation, called a graph. A procedure is presented that enables the exhaustive generation of these graphs for structures of any given number of nodes and links and which are foldable onto a plane or onto a line.; A special type of truss structures, called truss modules, is presented. Graphs of this class of structures form a subset of the graphs of truss structures. Two procedures are presented that are applied to recognize these graphs among graphs of truss structures. The procedures also generate information on the relative lengths of the links in a truss module by examining the graph it represents. This enables the generation of numerous novel (deployable) truss modules as well as those that have been reported in the literature.; A procedure is presented for the generation of all possible folded configurations of deployable truss structures. By applying this procedure to deployable truss modules, truss modules are identified that exhibit special geometrical properties which allow the module to fold using fewer joints than dictated in the initial phase of the conceptual design process. Using an alternate definition of graphs, procedures are presented for the specification of the joint types and joint inter-connectivity that accommodates the folding and/or deployment of a deployable truss structure. These procedures are applied to generate all possible joint assignments for deployable truss modules.; Procedures for the conceptual design of deployable truss structures result in the generation of innumerable design concepts. An expert system is developed to aid the designer of deployable truss structures in the evaluation of such designs. Incorporated in this expert system are selection criteria that are developed to assist a designer in selecting the best candidates for any given application. Employing this approach, many promising novel designs, as well as those that have been reported in the literature, are identified.