Abstract Today the assembly sequence for the products isoften carried out manually and its definition, typically, isvery expensive, not guaranteeing optimal solutions. Com-ing up with an efficient assembly sequence is the essentialstep to improve process productivity and reduces the time andcosts related to assembly machines and equipment. The issuerelated to the assembly sequence of a product depends on thetotal number of the its components. In particular, the numberof the possible sequences can be obtained through the calcu-lus of the factorial of the number of the product components.This work presents an automatic approach intended to defineassembly sequences, based on the information regard the con-tacts and the interferences existing among the components,which is obtained by the assembly CAD model of the prod-uct. The level of the information required by this approachallows its implementation at early stages of design, as soon asthe layout of the conceptual solution of the product is defined,independently by the method used to model the CAD assem-bly. The procedure proposed is focused to obtain a reducednumber of assembly sequences, guaranteeing that there isat least one feasible assembly sequence among them. Theprocedure is oriented to iteratively identify independent andimportant subassemblies into the CAD assembly, then mergethem to specific assembling nodes and generate sequencesuntil the whole product is analyzed. After a brief review ofcurrent methodologies developed for assembly planning, inthis paper, the automated procedure for assembly sequence
R. Viganò (B)Mechanical Department, Politecnico di Milano,Via G. La Masa,1, 20156 Milan, Italye-mail: [email protected]
G. Osorio GómezDesign Engineering Research Group, Universidad EAFIT,Carrera 49 No 7 Sur-50, Medellín, Colombiae-mail: [email protected]
generation is explained and applied on an example, obtainingfeasible solutions.
The processes of product design and development are lead-ing to the reduction of the development time and of the coststhrough integration of different industrial expertise areas andthe full exploiting of the informatics tools for the aided designand the information management. This trend, devoted to theevaluation of the functions, architecture and high level infor-mation of the product, is today required, as far as possible,already at the early stages of design. The aim is to allow thedesigner to compare different solutions, rather than focusingon a single version of the product, whose later developmentcould implicate undesired modifications during the last stepsof the design process.
One of these evaluations is devoted to the planning ofthe assembling of the product that it normally takes place atthe final stages of the design process, when the specializedtechnical staff, according to experience and specific require-ments of the assembly line, defines the optimal assemblysequence. Define an efficient assembly sequence is essentialto improve the production process and to reduce the timesand the costs related to the assembly phase, including thoseof the machines and of the equipment [1].
Anyway, researches on the assembly field have devel-oped approaches oriented to define all the feasible assemblysequences, generally, making use of CAD software systems,in order to detect geometrical interferences and to analyse
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the possible relative movement among the parts, so as todefine the precedence between them [2]. The implementa-tion of these approaches is expensive, time consuming andit is very difficult to implement into a collaborative workingenvironment at early stages of the design process since theyare based on specific technical know-how. Also, they requirea detailed level of product information and their suitabilityhas not been proved at industrial level.
This work presents, through the analysis of the currenttheories and coherently with the product design process, thedevelopment of an automatic approach intended to defineassembly sequences, based on the information regard the con-tacts and the interferences existing among the components,which is obtained by the assembly CAD model of the prod-uct. The level of the information required by this approachallows its implementation at early stages of design, as soon asthe layout of the conceptual solution of the product is defined,independently by the method used to model the CAD assem-bly. The procedure proposed is focused to obtain a reducednumber of assembly sequences, guaranteeing that there isat least one feasible assembly sequence among them. Theprocedure is oriented to iteratively identify independent andimportant subassemblies into the CAD assembly, then mergethem to specific assembling nodes and generate sequencesuntil the whole product is analysed.
The next section presents some aspects about the theoryand the development of the assembly sequence planning andthe virtual modelling tasks in order to establish the researchbases for the proposed automatic approach, which is pre-sented further along. Finally, a practical case study is care-fully explained in order to permit a better understand of thefunctionality of the approach and to present some importantconsiderations about its application according to the natureof the product. In a like manner, the efficiency of the approachis compared with a well-known theoretical example.
2 Assembly sequence planning
The assembly task of a product has been studied as an inde-pendent factor in the life-cycle of the product, but when thedemands related to the cost, to the time and to the quality havebecome more stringent, and the whole product developmentprocess has presented the necessity to be shortened, the indus-try has tried to combine all the design process tasks into asingle phase. This has led to the born of different approaches,called: Design for Manufacture (DfM), Design for Assembly(DfA), Design for Variety (DfV), Design for Quality (DfQ),Design for Reliability (DfR), Design for Disassembly (DfD),Design for Maintainability (DfMa), and so on [3]. The Designfor Assembly (DfA) is mainly oriented to redesign the prod-uct with the aim to minimization of both the costs and the timeof the assembly tasks, following the guidelines targeted to thereducing the number of components, ensuring the ability to
be assembled together. The DfX methods do not considercombinatorial aspects related to the choice of the assemblysequence, which is, instead, the target of the approach calledAssembly Sequence Planning (ASP) or Assembly SequenceAnalysis (ASA) [4]. This approach is focused on the defini-tion of the feasible assembly sequences for a product witha defined architecture. It depends on the information andknowledge available for the product and its assembly processand it is useful for the study of very complex systems. Such asin the Computer Aided Assembly Planning (CAAP) meth-ods, the information related to the assembly relationshipsand the constraints among the parts (co-planarity, coaxiality,mating, orientation, etc.), defined during the modelling step,can be retrieved from 3D CAD models.
Most of the current developed methodologies for theassembly sequence planning are based on queries involv-ing skilled staff. Doing so, the generation of the assemblingfeasible sequences relies on the identification of technicalrules or relationships of precedence among the parts, whichare defined by the experts, knowing the layout of the prod-uct [5,6]. Some approaches start from a well-defined productarchitecture, like the methods suggested by Bourjault [7] andDe Fazio and Whitney [8], and are applicable without the useof a 3D CAD model. While CAD-based approaches, as thoseproposed by Gottipolu [9] and Lin [10], require a previousknowledge of the assembly sequence and/or proper defini-tion of the assembly constraints. In any case, the productlayout must be known and visible and the experts’ interven-tion is essential from the first steps of implementation of themethods.
Many of these methods may not be practicable at indus-trial level because of the long time needed for the repetitiveinquiries required, as well as of the great number of solutionsgenerated.
3 Virtual modelling considerations
The issue related to the assembly sequence of a prod-uct depends on the total number of the its components.Mathematical considerations ensure that the extraction ofthe product assembly sequences may be obtained througha combinatorial approach. In particular, without any otherinformation, the number of the possible sequences can beobtained through the calculus of the factorial of the num-ber of the product components. Anyway, the authors arguethat further reduction of the number of the possible feasibleassembly sequences can be directly derived by an automaticextraction of information from the CAD model [11].
Due to the nature of CAD systems and of the procedurescurrently used in the creation of the 3D assembly models, it isvery difficult to establish the assembly precedence, betweentwo components, based on either the assembly relationshipsor by the constraints entered by the user. Here it is worth
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Fig. 1 Pulley-support assembly with model tree
observing that, into the modern feature-based CAD systems,the modelling task of an assembly could be conducted indifferent ways. For example, the assembly model could bedone placing the parts according to a specific assemblysequence or, conversely, they could be placed without a pre-defined order. At least in the first case a sequence of the prod-uct assembly is provided, but may not necessarily be the best.
In both cases, the position of the single part becomes com-pletely defined when the part itself is full constrained withrespect to the other related parts in the 3D assembly. It is,also, easy to prove that the type of constraints, offered by the3D CAD systems, leads to a relationships system other thanthose obtained in the real assembly. This brings to the condi-tion that the single part of the assembly is fixed, by the CADpoint of view, before that all the real constraints are imposed.
Hence, the CAD model requires the definition of alower number of assembly relationships respecting to thoserequired by the product in the reality.
This lower number of constraints present in the CADassembly does not allow to define the assembly sequencein automatic manner.
For example, the assembly conditions for the model ofthe pulley-support shown in Fig. 1, defined by the CAD user,permit the creation of the graph reported in Fig. 2, while thereal graph, useful for the assembly sequence definition, isshown in Fig. 3. This is due to the fact that the shaft is com-pletely constrained when it is related to the right bearing bymeans of the “insert” and the “mate” assembly relationships(Fig. 1), and, in this way, the link with the left bearing isnot required for the purpose of the CAD modelling. Sameconsiderations could be made for the link between the wheeland the left bearing.
Fig. 2 Liaison graph for pulley-support assembly derived from CADmodel (incomplete)
Fig. 3 Liaison graph for pulley-support assembly with correct linksamong the parts
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In this way it is very difficult to obtain a reliable liaisongraph, useful for further development of feasible assemblysequences, through the analysis of standard assembly rela-tionships, even though the designer is able to assembly thedifferent parts in a correct order into the CAD model.
Same considerations can be done with regards to the usageof the top-down paradigm during the CAD modelling andassembly. This modelling method uses a reference sketch,also called skeleton, to build the single parts directly in theassembly environment. So, no mating connection can beextracted from the assembly, and no graph, based on assem-bly constrains, can be realised.
Independently of the chosen modelling CAD technique, inorder to capture design intent, different attempts for assem-bly relationships definition at conceptual stage have beenproposed from many researchers. One of these is based onthe definition of the assembly formalisms and/or using anassembly abstract representation where the relative posi-tion of each part is described specifying its relationshipwith the other components [12–14]. Another relies on thesystematic methodology for assembly design proposed byWhitney [15], where a kinematic constraint structure anda systematic scheme, by which the parts are located in thespace in relative mode to each other, are defined. All ofthis followed by the declaration of assembly features thatconnect parts in such a way to create the desired con-straint relationships. However, in both theories, the defini-tion of the relationships between the parts is still a designer’sjob.
Arun and Rao [16], to facilitate assembly analysis andplanning, proposed an API for a CAD software to extractassembly related data (links and relationships between theassembled parts and the involved features), to replace thehuman interpretation of the assembly design. But, anyway,also in this proposed method, the assembly sequence is notautomatically generated.
Wang et al. [17] state that “most of CAD tools currently donot have the capability to directly analyse the feasibility of agiven assembly plan for a product or to generate an optimalor near-optimal assembly plan”, and so, human interventionis required.
Su [18] presented an integrated software prototype systemto find out the geometric assembly precedence relations basedon the assembly CAD model and to automatically infer feasi-ble assembly sequences applying an optimization algorithm;but the interaction human–computer is required to analysethe assembly conditions existing between each pair of com-ponents.
Neelamkavil [19] proposed a matrix-based analysis inorder to identify sub-assemblies and possible sequences froma detailed CAD assembly, but the matrices are compiled man-ually and the sub-assemblies are identified by the user anddo not automatically extracted by the system.
In conclusion, most of previous researches related to com-puter tools require some human interaction and depend onthe modelling technique used to obtain specific informationfor their corroboration, again.
4 Research bases
The authors consider that better results could be obtainedconsidering only the spatial interactions between the partsand neglecting both the relationships and constraints madeby the user during the realization of the 3D CAD model.
So, by means of computer tools directly connected withthe CAD database, it is possible to automatically extractinformation of contact and interference between componentsable to be used for the generation of topological informationmatrices and/or graphs. From this information is possible toidentify independent subassemblies and reduce the problemcomplexity.
In fact, the assembly planning process based onsub-assemblies identification has demonstrated its suitabil-ity to reduce the number of all possible sequences, decreas-ing considerably the problems encountered on the real worldcombinatorial problems [20]. Lee and Shin have presenteda methodology for assembly planning directed to minimizethe assembly cost, based on the extraction of subassembliesby means of the breakdown of a liaison graph according tothe feasibility and difficulty of disassembly. To do this, theparts geometry, their physical properties and the informa-tion concerning the mating characteristics and the assemblytools, are required. Everything in order to decide the feasibil-ity of an assembly operation [21]. The automatic approachpresented here is similar to the Lee’s methodology seeingthat the identification of possible sub-assemblies, with theirown sequences, is realised through the definition of indices,related to the nodes and to the sub-assemblies, derived froma process of analysis about experimental data and their vali-dation.
Besides, the proposed automatic approach is able toobtain specific information for assembly sequence defini-tion regardless of the adopted modelling technique and ofthe definition of detailed information only available at laterstages of design [11].
In the next paragraphs and after brief considerations uponthe assembly modelling, the automated procedure proposedfor assembly sequence generation is explained and appliedon an example case.
5 Proposed assembly planning approach
The production process of a product is frequently definedduring the detail design stage, when all the technical aspects
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of the product are already known. The product layout, withthe geometrical information useful for the analysis of theassembly sequences, can also be obtained between the con-ceptual design phase and the embodiment design phase. Thislayout contains qualitative information related to the dispo-sition of the components of the product, as such as the topo-logic data, which seldom change when the quantitative data,i.e. dimensions, tolerances, etc., are defined during the detaildesign stage. According to the last statement, it is hence pos-sible to analyse the feasible assembly sequences already fromthe early stages of the design process.
So, it is possible to define a process able to generate a finitenumber of assembly sequences, including at least one feasi-ble solution, starting from the product information generatedat early stages of the design and without human intervention.
This automatic method is intended to identify the sub-assemblies included into the product and arrange them inhierarchical manner till completion of the whole assemblysequence. This goal is obtained considering, for each sub-assembly, a node or a platform element as a base for thegeneration of the internal sequences of the assembly. Whenthe identified subassemblies have been mounted, they areconsidered as a single part into the system under analysisand, in this way the procedure starts again in order to findnew subassemblies, and so on, until the whole product isassembled.
Grouping of different components into subassemblies andthe definition of their assembly sequences are done merelyon the basis of the existent interactions in the CAD model ofthe product. In this method only the contacts and the inter-ferences among the surfaces of the parts of the 3D modelhave been considered. No other criteria such as the facilityto manipulate the parts or their reciprocal orientation intothe product have been considered, since the implication ofsuch architectural and geometrical aspects requires the col-laboration of expert staff for the extraction of the assemblysequences of the product under study.
In brief, this approach is based on subassembly identifica-tion and grading of nodes and subassemblies through differ-ent indices related to contacts between components and theirimportance.
6 Case study
The proposed approach has been tuned through testingwith several different products, considering different model-ling techniques, the component interactions and the designaspects.
In order to better explain the proposed approach, a casestudy related to a clamp is presented. The CAD model ofthe clamp has been downloaded from a web library of hold-ing products and it has been processed in order to dem-
onstrate that the approach is able to extract at least a fea-sible assembly sequence. The check, about the assemblysequences obtained, will be made through the human inter-vention. The model has been downloaded in the native CADfile format to conserve the original modelling technique andthe design intent, also to demonstrate how this approach isindependent of these aspects. Only the name of the differentcomponents has been changed for better understanding. Theproduct model is composed of fifteen (15) components as awhole, as it is shown in Fig. 4.
The proposed approach is developed in the followingsteps:
1. STEP 0 Identification of contacts or interferences amongcomponents from the 3D-CAD assembly model, whereall components are located in a stable position for thefinal assembly state, independently of possible furthermovements and contacts in operation. As stated by DeFazio and Whitney [8] the contact relationship betweencomponents include force fits, threaded fits, adhesion,compression contact, and even contact by virtue of a partresting on another part.With such information it is possible to generate thesquare symmetric binary adjacency matrix for the wholeassembly system (Fig. 5a). As well, the undirected graph(Fig. 5b) showing the interaction between parts.
2. STEP 1 The automatic analysis starts with the identifica-tion and the reduction of the nodes that have connectiondegree value equal to one (dvi = 1, with dvi as thedegree of the node vi ). This because those componentsinteracting with only one of the other components and,when they are identified, their assembly operation is con-sidered as the first of the possible subassemblies for theassembly sequence.In this case, the “knob (K)” and the “stopper (ST)”parts could be assembled to the “lever 2 (L2)” and tothe “screw (SC)” components respectively, producingsubassemblies “L2*” and “SC*”. So, in the first stepwe have two possible subassemblies, considering thatthe component with higher connection degree is thebase of the subassembly, and the assembly graph isreduced to thirteen (13) components, as it is shown inthe Fig. 6.
3. STEP 2 Next, a new developed algorithm to iden-tify the induced cycles or possible subassemblies isapplied. In graph theory, an induced cycle has nochords or straddling links. A chord or a straddlinglink is an edge joining two vertices of a cycle butis not itself an edge of the cycle. The algorithmapplied in this step is based on a combined algorithmof Breadth-Depth First Search [22] and explores firstall possible fundamental cycles travelling over an ini-tial node and then removes that node from the given
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Fig. 4 CAD model and components of a standard horizontal handle hold-down clamp
(a) (b)
Fig. 5 a Adjacency matrix and b undirected graph
network to avoid enumeration of repeated cycles. Everynode is then progressively explored until no furthernodes remain in the network. In addition, the algo-rithm checks for all expanded nodes to find a node con-nected to the prior node, because this node should beon a straddling link of the cycle, if so, this node isremoved from the path list of nodes for definition ofthe cycle.
The nodes of the undirected graph are evaluated andclassified with a centrality index; ICT(i), related tothe degree of the node, its relative participation aboutall the set of induced cycles of the graph, the meandegree of its neighbours and its weighted clusteringcoefficient. The centrality condition identifies which arethe important nodes that must be assembled first thantheir corresponding neighbours, that is, the platform
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Fig. 6 Undirected graph after step 1. Reduction to nodes “SC*” and“L2*”
component of the subassembly sequence. If more thanone node is identified as a platform, all the possiblesequences that depend from these nodes will be gen-erated.The induced cycles or the independent sub-assem-blies are also evaluated and classified with an impor-tance index; ICI(i), useful to identify both their levelof interaction and the importance of their constituentnodes.If two or more induced cycles present the same impor-tance index they are reduced simultaneously in the samestep of the approach. If they have different nodes thereare possible assembly sequences as cycles are, but if theyshare nodes, the order of reduction of the cycles is accord-ing to the higher value of centrality index of the basenodes.In this way, both the centrality index for each nodeand the importance index for each cycle are cal-culated, to identify the base node of the assemblysequence and the first cycle to be reduced, respec-tively.With the undirected graph presented in Fig. 6, sixinduced cycles have been identified and, accordingto the importance index, ICI, the next subassemblyis composed by the “base (B)”, the “lever 1 (L1)”,the subassembly “L2*” and the “link (L)” where thebase node for the assembly sequence is the com-ponent “lever 1 (L1)” having the higher centralityindex value, ICT. The values of such indexes arepresented in the Table 1. For this subassembly, the
sequences start from the base node and, respectingthe liaisons reduction, 2(k−2) sequences are generated,where k is the length of the concerned cycle, that is,four sequences because the cycle is formed by fournodes.Having identified the subassembly to be mounted,the approach generates possible assembly sequencesfor that subgroup and reduces all components to thebase node without generation of loops or doublededges.So, the induced cycle “B-L1-L-L2*” is reduced to itsbase node into the subassembly “L1*” as it is presentedin the undirected graph of the Fig. 7.
4. STEP 3 At this point, the step to reduce nodes withdegree value equal to one and the following step toidentify induced cycles are iteratively applied untilone cycle remains at the end. Then, each node ofthe cycle is considered as a possible base compo-nent and the sequences are generated for each compo-nent.In this case, the components “shaft 1 (S1)”, “shaft 2(S2)”, “shaft 3 (S3)” and “shaft 4 (S4)” could be assem-bled to the new subassembly “L1*”. So, the assem-bly graph is reduced to six nodes as it is shown inFig. 8.
5. STEP 4 In this case, no more reductions are requiredand with the final cycle composed by six nodes, 6 × 2 ×
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Fig. 7 Undirected graph after step 2. Reduction of cycles to node“L1*”
Fig. 8 Undirected graph after step 3
(k − 2) = 6 × 2 × (6 − 2) = 6 × 16 = 96, ninetysix assembly sequences are obtained. That is, sixteen(16) assembly sequences starting from each node of thecycle.So, the automated approach has arrived to the finalassembly state, finding subassemblies at each step of theprocedure.The summary Table 2 presents all the sequences obtainedfor each subassembly identified in each step of theapproach. This final result can be translated to any typeof assembly representation presented in theory, such aseither AND/OR graphs [6], directed graphs or graphicalrepresentation schemes.The steps of the approach are considered like prece-dence in the assembly sequence and starting from thelast sequences obtained at the last step, replacing thesubassemblies of the previous steps, we finally have ninethousand two hundred sixteen (96 × 24 × 4 × 1 × 1 =
9216) possible assembly sequences for the whole prod-uct. Some obtained assembly sequences are shown inTable 3.
With this approach, it is possible to find at least one feasi-ble assembly sequence if the product model is correctly con-structed and conceived, since all the solutions are equivalentfrom a topological point of view. So, the user could evaluateand filter some potential solutions using technical parametersof the current assembly line, identifying preferred precedencerelations or through implementation of virtual tools intendedto visual evaluation, according to his/her experience. At thispoint would be interrogated in order to identify the feasiblesolutions.
Anyway, the number of queries can be reduced if the userevaluates the feasibility of the sequences for each subassem-bly obtained at each step of the procedure rather than theircombination. In this way, the final number of possible assem-bly sequences corresponds to the multiplication among fea-sible assembly sequences for subassemblies obtained at eachstep of the process. This query-answer process must be exe-cuted observing the order of the steps, since an unfeasiblesubassembly is identified; the mechanical system should bereviewed.
The querying analysis for the clamp is presented in theTable 4 where (1 + 1 + 4 + 24 + 96 = 126) one hundredtwenty six precedence questions should be answered. Here,in the three first steps of the procedures all the sequences arefeasible and in the final step there are thirty two (32) feasiblesolutions from the ninety six (96) sequences automaticallyobtained.
In this way, after the querying, the first 9216 assemblysequences are reduced to (1 × 1 × 4 × 24 × 32 = 3,072)three thousand seventy two feasible assembly sequences, asit is presented in the Table 5.
Here, taking advantage of this representative example, it isworth noticing that this automatic approach is independent ofthe analysis of the virtual model and no considerations abouteither the modelling technique or the nature of the parts arerequired for the implementation of the approach. In this way,all the components of the product are considered in the analy-sis even if the number of assembly sequences is considerablysensitive to this. In the clamp example, each shaft is consid-ered individually and, hence, twenty four sequences for theirsub-assembly are generated.
Otherwise, the user could be interested in a previous anal-ysis of the model in order to identify some patterns of specificelements to be neglected in the assembly sequence analysiswith the purpose of reducing the number of solutions. Thisapproach has been identified in some researches in order toimprove the analysis and to reduce the human participation.
In the clamp example, the shafts “S1”, “S2”, “S3” and“S4” could be neglected in the analysis since they are directly
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Table 2 Subassembly sequences for each step of the approach
Step Subassembly components Base node Possible assembly sequences Subassemblyname
Qty Precedence
1 K-L2 L2 1 L2 < K L2*
ST-SC SC 1 SC < ST SC*
L1 < L2* < L < B
2 B-L1-L2-L L1 4 L1 < B < L < L2* L1*
L1 < L2* < B < L
L1 < B < L2* < L
L1* < S1 < S2 < S3 < S4
L1* < S1 < S2 < S4 < S3
S1-L1* L1* < S1 < S3 < S2 < S4
S2-L1* L1* < S1 < S3 < S4 < S2
3 S3-L1* L1* 24 . . .. L1**
S4-L1* L1* < S4 < S2 < S1 < S3
L1* < S4 < S2 < S3 < S1
L1* < S4 < S3 < S1 < S2
L1* < S4 < S3 < S2 < S1
L1** < W2 < N2 < SC* < N1 < W1
L1** < W2 < N2 < SC* < W1 < N1
L1** L1** < W2 < N2 < W1 < N1 < SC*
SC* L1** < W2 < N2 < W1 < SC* < N1 Final assembly
4 L1**-SC*-W1-N1-W2-N2 W1 96 . . ..
N1 N2 < W2 < L1** < SC* < N1 < W1
W2 N2 < W2 < L1** < SC* < W1 < N1
N2 N2 < W2 < L1** < W1 < SC* < N1
N2 < W2 < L1** < W1 < N1 < SC*
Table 3 Obtained assemblysequences for the whole product No. Assembly sequence
1 L1 < L2 < K < L < B < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < N1 < W1
2 L1 < B < L < L2 < K < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < N1 < W1
3 L1 < L2 < K < B < L < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < N1 < W1
4 L1 < B < L2 < K < L < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < N1 < W1
.
.
....
9,213 N2 < W2 < L1 < L2 < K < L < B < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
9,214 N2 < W2 < L1 < B < L < L2 < K < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
9,215 N2 < W2 < L1 < L2 < K < B < L < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
9,216 N2 < W2 < L1 < B < L2 < K < L < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
related to the joining process of the components “L1”, “L2”,“L” and “B” or they could be summarized into a unique com-ponent “shaft”. In the first case, not considering the shafts,the automated solutions could be reduced to (1×1×4×96 =384) three hundred eighty four solutions and with the feasi-bility analysis, there are (1×1×4×32 = 128) one hundredtwenty eight feasible solutions.
De Fazio and Whitney [8], in their example for the assem-bly sequence analysis of a transmission for trucks, do notconsider fasteners in the analysis since they assume thatwhen two parts secured by threaded fasteners are mated,they are placed and secured. In this way, these componentsare transparent to the approach when not represented bynodes. The authors have analysed this specific bibliographic
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Table 4 Feasibility analysis for each sequence of the identified sub-assemblies
Step Subassemblycomponents
Base node Possible assembly sequences Subassembly name Feasibility
Table 5 Feasible assemblysequences obtained after thefeasibility querying
No. Assembly sequence
1 L1 < L2 < K < L < B < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < W1 < N1
2 L1 < B < L < L2 < K < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < W1 < N1
3 L1 < L2 < K < B < L < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < W1 < N1
4 L1 < B < L2 < K < L < S1 < S2 < S3 < S4 < W2 < N2 < SC < ST < W1 < N1
.
.
....
3,069 N2 < W2 < L1 < L2 < K < L < B < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
3,070 N2 < W2 < L1 < B < L < L2 < K < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
3,071 N2 < W2 < L1 < L2 < K < B < L < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
3,072 N2 < W2 < L1 < B < L2 < K < L < S4 < S3 < S2 < S1 < W1 < N1 < SC < ST
example achieving 96 different feasible and unfeasibleassembly sequences in contrast with the 440 possible assem-bly sequences obtained with the De Fazio and Whitney’smethod [23].
So, this proposed automatic approach allows automat-ically obtaining a lower number of possible assemblysequences respecting to theoretical approaches based on que-rying and answering techniques. Besides, the information
required for its implementation could be retrieved in earlystages of design with rough conceptual virtual models.
7 Conclusions
The proposed method is able to obtain automatically at leastone feasible assembly sequence of the product, starting from
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the topological information and the interaction among itsparts, enclosed in the CAD model. This approach allows spe-cialized or non-specialized personnel to obtain initial feasibleassembly sequences already during the early phases of theproduct design and development process.
Owing to the nature of information required (contactor interference) no dimensional or material information isrequired to be included into the assembly model, makingthis approach very suitable for assembly sequence genera-tion starting from 3D layouts of solution principles identi-fied at the conceptual and embodiment stages of design. It isworth noticing the impact of the CAD model configurationand the functional nature of the parts concerning the num-ber of assembly sequences obtained with this approach, inthis way, could be interesting to check the “wellness” of theCAD model before its use in order to avoid a great numberof solutions.
Otherwise, if not a single feasible solution is obtained;this situation indicates that such mechanical system designshould be controlled in order to identify instability or overconstrained conditions.
The sub-assembly identification approach is adequate toindustrial configurations where multiple assembly worksta-tions are introduced in order to speed the product processup, since the assembly plan offers parallelism and flexibilityin assembly when independent subassemblies are identified.According to this, it would be interesting to observe the tablewith the assembly sequences for identified sub-assembliespointing to the definition and positioning of workstations inthe assembly line.
It is expected that such proposed methodology opens apossibility for better integration of assembly planning top-ics into the early stages of design in order to reduce prod-uct development time and cost and to increase the productquality.
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