Modeling of Mechanical Structures in CAAP-Systems

Computer-aided assembly planning of complex systems is an important area of modern information technology. The assembly sequence and decomposition into assembly units largely depend on the mechanical structure of a technical system (machine, mechanical device, etc.). The paper describes a hypergraph model of the mechanical structure of an assembled product. It is shown that assembly operations can be represented as contraction of the edges of the hypergraph, and the assembly plan can be described as a sequence of contractions that transform the hypergraph into a point. An important concept of s-hypergraphs is introduced. The S-subgraphs of the contractible hypergraph serve as mathematical models of fragments of the product that can be assembled independently. These are, first of all, assembly units of various levels of hierarchy. A theorem on necessary conditions for the contractibility of the s-hypergraphs is given. It is shown that the necessary conditions are not sufficient. An example of a noncontractible hypergraph for which the necessary conditions are satisfied is given. Two theorems on sufficient conditions for contractibility are proved. They provide the theoretical basis for developing an effective computational procedure for searching for the s-subgraphs of various cardinalities