Math Modeling of Sequential Coherent and Linear Assembly Plans in CAD Systems

The paper considers computer aided assembly planning of complex technical systems. Splitting into assembly units is an important design decision that affects technical characteristics of a product and the economic performance of the production. The rational decomposition depends on the geometry of a product, the structure of mechanical links, the system of design dimensional chains and many other design and technological factors. This is a complex engineering problem, which is difficult to solve without the use of modern computer aided design systems. The fundamental properties of assembly operations and processes are considered in the article. A hypergraph model is proposed that correctly describes the geometric coordination of parts in a product obtained by means of mechanical contacts. A mathematical description of the assembly process is given. An important special case of the assembly process is considered, when a product is mounted without preliminary decomposition into assembly units. A mathematical model of linear assembly is proposed. The theorem on necessary and sufficient conditions for linear contractibility of hypergraphs is proved.