An approach to determine geometric feasibility to assembly states by intersection matrices in assembly sequence planning

In this article, an approach is described for the development of a process for the determination of geometric feasibility whose binary vector representation corresponds to assembly states. An assembly consisting of four parts is considered as an example. First, contact matrices generate the assembly's connection graph. The developing connection graph was used to model the example assembly. In the assembly's connection graph, each node corresponds to a part in the assembly, and edges in the graph of connections correspond to connecting every pair of nodes. Moreover, in the connection graph, each connection corresponds to an element in the binary vector representation. In the development of the approach, intersection matrices are used to represent interference among assembling parts during the assembly operation. Intersection matrices are defined to along the Cartesian coordinate system's six main directions. The elements of intersection matrices are constituted to Boolean values. Each element of binary vector representations includes a connection between a pair of parts. First, ordered pairs of parts are established. Then, Cartesian products, which are produced from these established ordered pairs of parts, are applied to Boolean operators. Finally, geometric feasibility of these binary vector representations is determined. In this work, some assembly systems are sampled and examined. Among these examples, six assembly sequences for a four-part packing system; two assembly sequences for a five-part shaft bearing system; 373 assembly sequences for a seven-part clutch system and assembly states have been investigated.