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Kinematic structural synthesis has been relatively successful when applied to the conceptual design of mechanisms. The approach presented in this paper, however, views the design process from an initial standpoint of a truss structure. First, graphs are generated that represent truss structures with a given number of nodes and links. Each graph is then modified by designating certain edges in the graph to represent links in the structure that incorporate additional degrees of freedom. In so doing, the graph of a structure is transformed into one representing a mechanism. A procedure is presented that enables the exhaustive generation of these graphs for deployable structures of any given number of nodes and links. From these graphs, it is then possible to obtain enumerable novel deployable truss structures as well as those that have been reported in the literature.

In the conceptual design of deployable structures, much of published literature on this topic relates mainly to the analyses of the designs that are presented. What is lacking are discussions on how such ingenious designs come about. This article attempts to bring about such a systematic procedure in the conceptual design of deployable structures by way of a mathematical technique known as graph theory. The resulting approach generates all possible conceptual designs based on a given number of links and nodes within a module of a deployable truss structure. The type of joints (revolute, universal, spherical) to be specified at the interconnections of Imks, is approached using kinematic graphs constrained by kinematic deployment characteristics of the deployable structure. Finally the entire set of concepts are sorted automatically using knowledge-based systems based on criteria such as deployability, total weight and folded volume. This systematic approach results in the enumeration of all conceptual designs including those already reported in the literature.

A special type of truss structures, called truss modules, is presented. Graphs of this class of structures form a subset of the graphs that are generated using the approach presented in Part 1. 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. Promising alternatives to existing designs are identified.