Synthesizing Design Solutions for Assembling Complex Items on the Basis of Hypergraph Cutting

The study deals with the problem of computer aided assembly planning for complex items. The main trends in this area of information technology are briefly reviewed and as a result, a hypergraph model for the mechanical structure of the item is proposed. The study shows that the model correctly describes coordination of product parts through assembly bases. Within the research we introduce the concepts of s-hypergraph and s-hypergraph cutting and show that cutting works as a correct mathematical description for assembly and disassembly operations and test configurations of the item that allow for and require checking for geometric solvability. We introduce a combinatorial space of all s-hypergraph cuts and show that it is a universal generating medium for synthesising assembly sequences and diagrams of decomposition into units. Hence, a property called geometric inheritance during assembly is formalised. Moreover, we state the problem of analysing geometric obstructions during complex item assembly as a two-player (decision maker against nature) non-zero-sum game of colouring vertices of an ordered set using two colours. Rational colouring strategies will minimise the number of direct geometrical checks. Finally, we prove a theorem on the structure of ordered sets generated from s-hypergraph cutting and a theorem on characterisation of correct ordered set colouring options

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