On the automatic generation of product assembly sequences

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  • This article was downloaded by: [University of Connecticut]On: 11 October 2014, At: 10:19Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK

    International Journal ofProduction ResearchPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/tprs20

    On the automaticgeneration of productassembly sequencesC. K. Choi , X.F. Zha , T.L. Ng & W.S. LauPublished online: 14 Nov 2010.

    To cite this article: C. K. Choi , X.F. Zha , T.L. Ng & W.S. Lau (1998) On theautomatic generation of product assembly sequences, International Journal ofProduction Research, 36:3, 617-633, DOI: 10.1080/002075498193606

    To link to this article: http://dx.doi.org/10.1080/002075498193606

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    http://www.tandfonline.com/page/terms-and-conditionshttp://www.tandfonline.com/page/terms-and-conditions

  • int. j. prod. res., 1998, vol. 36, no. 3, 617 633

    On the automatic generation of product assembly sequences

    C. K. CHOI *, X. F. ZHA , T. L. NG and W. S. LAU

    Automatic assembly planning is recognized as an important tool for achievingconcurrent product and process development thus reducing manufacturing costs.It plays an important role in designing and planning the assembly systems. Inorder to recommend a good sequence of assembly operations, the process plannerneeds to generate all such feasible sequences. In this paper, the representation ofthe product assembly relationships and the assembly processes is described.Considering the assembly knowledge and the assembly constraints, a methodol-ogy is presented to generate all feasible assembly sequences by determining anddecomposing the levelled feasible subassemblies. A prototype reasoning expertsystem is developed to generate all feasible assembly sequences automatically. Theresearch ndings are exempli ed with a simple assembly to illustrate the method.

    1. Introduction

    The choice of the sequence in which components or subassemblies are puttogether in the mechanical assembly of a product can drastically a ect the e ciencyof the assembly process. For example, one feasible and reasonable sequence mayrequire less xturing, less changing of tools, and include simpler and more reliableoperations than others. Therefore, assembly sequence planning plays an importantrole in designing and planning the product assembly process.

    Traditionally, the product assembly sequence was planned by an experiencedproduction engineer. However, the planning of assembly sequences is sometimes atrivial and error-prone task especially when there exists a large number of potentialassembly sequences in a complex assembly. Therefore, there is a growing need tosystematize and to computerize the generation of assembly sequences. So far, manyresearch activities have focused on various aspects of assembly sequence planningsuch as assembly modelling, assembly sequence representation and assemblysequence generation algorithms.

    In this paper, focuses are put on the approach and the system for automaticgeneration of assembly sequences, which are the key issues of computer aided as-sembly process planning (CAAPP). A new representation of the product assemblyrelationships and a methodology for generating the detailed feasible subassemblysets of assembly plans for a given product will be described. Based on the assemblyknowledge or information and the method of determination and decomposition offeasible subassembly subsets, an automatic knowledge reasoning system has been

    0020 7543/98 $12.00 1998 Taylor & Francis Ltd.

    Revision received November 1996. Department of Manufacturing Engineering, The Hong Kong Polytechnic University,

    Hung Hom, Hong Kong, PR China. School of Mechanical and Production Engineering, Nanyang Technological University,

    Singapore. Sonca Products Ltd., Hong Kong, PR China. Hong Kong Technical College (Chai Wan), Hong Kong, PR China.* To whom correspondence should be addressed.

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  • developed to generate the assembly sequences. The proposed approach is a combi-nation of the assembly approach and the `disassembly approach.

    This paper is structured as follows: 1 and 2 present the brief introduction andliterature review about the assembly sequence generation and planning respectively.Section 3 deals with the modelling of assembly process that contains the representa-tion of assembly relationships (liaison graph, liaison matrix, knowledge assemblyliaison graph), predicate-based representation of assembly constraints, graph-basedrepresentation of the assembly or disassembly sequences. Sections 4 and 5 present anew approach to assembly sequence generation and the knowledge based automaticreasoning system; 6 gives an example to illustrate the proposed approach; 7 sum-marizes and gives some suggestions for the future research work.

    2. Overview of previous work

    2.1. Assembly sequence generationMany researchers have made attempts to generate the assembly sequences of a

    product. Bourjault (1984) proposed a procedure to obtain all the precedence knowl-edge about the liaisons of an assembly by answering a set of structured questionsbased on this proposed liaison model of the assembly. Defazio and Whitney (1987)simpli ed Bourjaults procedure and reduced the number of the asked questions to2n against 2n of Bourjault s. These two methods study the assembly from the point ofview of assembling the product. For the representation of precedence knowledge ofan assembly, there have been several methodologies widely used in the past such asthe set theory, binary matrix, directed graph, establishment condition, precedencerelationships and function diagrams (Thaler 1989a, b, Homen de Mello andSanderson 1990). However, these methods can only represent the partial assemblyprecedence knowledge. To represent the set of assembly sequences completely,Homen De Mello and Sanderson (1990, 1991a, b) proposed an AND/OR graphrepresentation of all the possible con gurations of the assembly and generate theassembly sequences of a product using a disassembly or decomposition method,based on the assumption that the disassembly sequence is the reverse of a feasibleassembly sequence. Although this representation is complete, the resultant AND/ORgraph is huge and the number of nodes grows exponentially as the part number inthe assembly increases (Ben-Arieh and Kramer 1994). Based on a mathematicalmodel of a product obtained through the de nition of three matrices: the interfer-ence matrix, the contact matrix and the connection matrix, Dini and Santochi (1992)proposed a procedure for the detection and selection of the subassemblies and theassembly sequence of a product, which can be applied in a exible assembly system.One of the main limitations of this model is that only partial disassemblies orassemblies are considered. In the component ordering method proposed by Leeand Ko (1987) a simple sequence was generated and interference checking ensuresthat the components to be assembled do not collide during assembly. A di erentmethod proposed by Lin and Chang (1991) uses a three layer strategy and a specialtree structure to represent the assembly and to generate one feasible sequence. Inorder to obtain the detailed assembly plans, Ben-Arieh and Kramer (1994) presenteda methodology and algorithms to consistently generate all feasible assemblysequences with consideration for the various combinations of subassembly opera-tions. The algorithms are implemented using a LISP program. In addition, BenArieh (1994) applied a fuzzy set based method to evaluate the degree of di cultyof each assembly operation and then select the `best sequence of assembly opera-

    618 C. K. Choi et al.

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  • tions. These methods and algorithms are less interactive and need much more spaceto store the representation of assembly sequences and processing time to process theassembly operations for the complex assemblies. Therefore, it is di cult to generatethe detailed assembly plans automatically and to deal with the coordination andfeasibility of various subassemblies e ciently.

    2.2. Integrated assembly planningApart from the above mentioned, another important development o ers an inte-

    grated approach to assembly planning by linking aspects of product design, designfor assembly (DFA), assembly planning and production layout within a manufactur-ing enterprise in one procedure. All of them require some interactive input, whichcurrently seems to be the only way of generating practical results. However, the aimsof these few systems are quite di erent. One of these systems is the standard as-sembly analysis tool (STAAT). Incorporated into a larger CAD tool, this system cangenerate and evaluate the geometric assembly sequences of complex products from20 to 40 parts and 500 to 1500 faces, and thus provides immediate feedback to a teamof product designers about the complexity of assembling the product being designed.The researchers of STAAT are working now on extending both these results and theunderlying theory to more sophisticated cases (Romney et al. 1995). However, themost comprehensive one is the project of integrated design and assembly planning(IDAP) (Seidel and Bullinger 1991, Seidel and Swift 1989, Richter 1991), which is avery long project with large scale interaction and is still under development. In thissystem, a model of OPNET (operation network) is constructed to re ect the con-straints intrinsic in the product itself. An OPNET model is structured in the form ofa graph that represents the relationships among tasks and subtasks for DFA evalua-tion and assembly process planning. An interactive operation network editor hasbeen developed to integrate the procedures for network generation, modi cation,queries and evaluation under a uniform graphical man-machine interface (Seidel1989, Seidel and Swift 1989).

    3. Assembly process modelling

    3.1. Notations and assumptionsNotations:

    Components of an assembly are represented as p1,p2, . . . ,pn . A subassembly is represented by a list of components such as [p1,p2,p3,p4]. A subassembly operation is represented by a combination of two sub-assemblies such as [p1],[p2,p3,p4]], [[p1,p2],[p3,p4]], etc. The list should beread from left to right, i.e. the subassembly operation direction or sequence isfrom left to right, for example, [p1] [p2,p3,p4]and [p1,p2] [p3,p4]. An assembly sequence is represented implicitly by nested lists of components.For example [[[[p1,p2],[p3]],[p4]],[p5,p6]]represents the following sequence ofassembly operations: p1 p2 p3 p4 p6.

    Assumptions:

    For a disassembleable product, the assembly sequence is the reverse of thediassembly sequence if there is no destructive operation in the disassembly.

    Automatic generation of product assembly sequences 619

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  • Each component is a solid rigid object, that is, there is no changing of shapeduring assembly and disassembly. Components are interconnected wheneverthey have one or more compatible surface in contact.

    Assembly is carried out step by step and components or subassemblies areassembled one at a time. Once an assembly operation is completed the subassembly would remainunchanged at all assembly stages.

    3.2. Representation of assembly relationships3.2.1. L iaison graph and its matrix representation

    The liaison relationships between two components can be implemented by thetotal relative constraints which can be extracted from the CAD drawing and classi- ed as t contact, plane contact and meshing contact. The assembly liaison relation-ships of a product can be described by the liaison graph (LG), which is de ned as

    Lg = G(V,E)where V is the set of vertices and E is the set of connecting arcs. Each vertexrepresents a component being assembled and each arc represents the liaison betweentwo components (De Fazio and Whitney 1987, Lee 1989, Shin and Ho 1994). Theassembly liaison relationships of a product can also be represented by liaison matrixR (Dini and Santochi 1992), which is de ned as:

    R= {rij} (1)where,

    rij =1 with liaison relationship between pi and pj;0 without liaison relationship between pi and pj{

    The row of matrix R represents the liaison relationships between a componentand other components. The column of matrix R represents the components con-nected by liaison relationships. The sub-matrices of R represent the local liaisonrelationships in subassemblies.

    3.2.2. Knowledge assembly liaison group (KALG)The knowledge assembly liaison group (KALG) is an enhancement of the as-

    sembly liaison graph. It includes much more assembly information and constraints.In constructing the KALG, the following rules would be used:

    (1) Each component assembled (and not to be disassembled anymore) is a vertexof KALG.

    (2) Connecting components with the same type and functions should be regardedas one vertex.

    (3) If components pi and pj are adjacent to each other, there exists an arc con-necting pi and pj. If pi is in contact with pj, the arc is expressed by a solid line.If constraints exist between pi and pj, the arc is expressed by a dotted line.

    (4) The direction of an arc connecting two components or vertices (such as piand pj) would be determined according to the following:

    If pi is a connecting component, the directi...

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