Theoretic-Lattice Approach to Computer Aided Generation of Assembly Units

The paper discusses product decomposition into assembly units in CAD systems. This is an important design decision on which many economic indicators of manufacturing and technical characteristics of the product depend. The coordination of the parts in the process of assembly of the product is achieved through a set of mechanical connections. In general, the coordination relation is not binary and can not be correctly represented by graphs and networks. An apparatus of s-hypergraphs is proposed. It adequately describes the behavior of products during assembly and disassembly. The vast majority of assembly operations of modern production are coherent and sequential. Mathematical descriptions of such operations and processes are given. It is shown that any fragment of the product, that can be assembled independently, is represented as an s-subgraph. The set of all s-sub-graphs of an s-hypergraph, ordered by inclusion, is a lattice. A formalization of the product decomposition into assembly units is proposed. A theorem is proved that allows us to model this design decision by algebraic means.