Journal of Intelligent Manufacturing, 15, 543±559, 2004 # 2004 Kluwer Academic Publishers. Manufactured in The Netherlands. An approach to determine geometric feasibility to assembly states by intersection matrices in assembly sequence planning CEM S _ INANOG Æ LU 1 and H. RIZA BO È RKLU È 2 1 Erciyes University Department ofMechanical Engineering, CAD/CAM Research Laboratory, 38039 Kayseri, Turkey 2 University of Gazi, Technical Education Faculty Department of Machine Education, 06500, Ankara, Turkey Received February 2003 and accepted December 2003 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 de®ned 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 ®ve-part shaft bearing system; 373 assembly sequences for a seven-part clutch system and assembly states have been investigated. Keywords: Assembly sequence planning, intersection matrices, graph based approach 1. Introduction The competition between manufacturing ®rms makes it necessary that ®rms must supply high-quality goods in a short time and the goods must be cheaper, in order to survive in the international market. Intensive research in this ®eld aims at augmenting methods and tools for product development and manufac- turing. By the use of new and ef®cient methods, it is possible to shorten the time from design to manu- facturing and reduce human errors. Therefore, full automation of the manufacturing processes can be accomplished. An assembly can be de®ned as the overall function of individual parts after joining with each others, each of which has an independent function. It is possible to divide an assembly into various subassemblies depending on its complexity level (Pahl and Beitz, 1988). Although intensive research efforts are in progress in the ®eld of assembly sequence planning,