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More space truss construction has been planned to develop and utilize space resources. These trusses are designed in the way of large-scale, complex, modular, and on-orbit assembly. To meet the upcoming challenge of large-scale space infrastructure construction, it is necessary to study space truss automation design and robotic construction. This paper proposes an ordinal finite screw adjacency matrix model (OFSAMM), focusing on the relationship between assembly motions, to express and compute a space truss structure. In this model, a space truss is abstracted as a set of ordered assembly motions, each of which is recorded as a finite screw as the basic element of the truss and its assembly. The operation of truss transformation is also derived under this model. Therefore, the truss configuration, the assembly sequence, the truss sub-assembly, the truss components, and the on-orbit assembly task can be expressed and calculated in a unified model, which is calculated and stores the truss topology and assembly with the minimum storage cost. At the end of this paper, we introduce how to synthesize and optimize space truss design through two cases. The study will help to improve design efficiency. Furthermore, it provides a theoretical basis for the automatic construction of space truss structures, especially in the next stage.