Hypergraph model for assembly sequence problem

Abstract

The article deals with the assembly sequence problem of complex technical products. It is shown that geometric coordination of parts in a product is a variable arity relation. In general, this relation cannot be described by graph means. The hypernetwork and hypergraph models are proposed. It is shown that the mathematical description of coherent and sequential assembly operations is a normal contraction of edges of the hypergraph. The notion of an s-hypergraphs is introduced. It is shown that s-hypergraphs correctly describe structures of technical systems. A theorem on necessary conditions for contractibility of s-hypergraphs is proved.