A new methodology is presented to generate all of the assembly sequences for a production system configured as a N-station assembly line with kn (n  = 1, 2,…, N) parts or subassemblies to be assembled at stations 1, 2,…, N, respectively. This expands current approaches in sequence generation applicable for binary assembly process to a k-ary assembly process by including: (i) nonbinary state between two parts, i.e., multiple joints between two parts or subassemblies, is taken into consideration, and (ii) simultaneous assembly of Y (Y3) parts or subassemblies. The methodology is based upon proposed k-piece graph and k-piece mixed graph approaches for the assemblies without and with assembly precedence relationship, respectively. Compared with the currently used liaisons graph (or datum flow chain) representation which shows part-to-part assembly relations, the k-piece graph (or k-piece mixed graph) shows all of the feasible subassemblies and their constituent parts and joints (pairs of mating features). Based upon the k-piece graph or k-piece mixed-graph approach, all of the feasible subassemblies for a predetermined assembly line configuration are identified, and all of the sequences for a k-ary assembly process are generated. Case studies are presented to illustrate the advantages of the presented methodology over the state-of-the-art research in assembly sequence generation.

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