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    Robotics and Computer Integrated Manufacturing 19 (2003) 439448

    Algorithmic selection of a disassembly sequence of a componentby a wave propagation method

    Christian Mascle*, Bogdan-Alexandru BalasoiuMechanical Engineering Department,

    !

    Ecole Polytechnique, C.P. 6079, succ. Centre-Ville, Montr!

    eal, Que., Canada H3C 3A7

    Abstract

    The design of a product for its entire life-cycle is becoming more and more important. Nowadays, a product is designed withsignicant considerations for its manufacturability, serviceability, its functionality and even for its disassemblability. This is due

    to the fact that the modern consumers demand products that are not only functional, but also reliable, easy to repair and alsoenvironmentally friendly.

    For maintenance and re-use, the operation sequencing in disassembly process planning needs of reversible operation selecting.We present a new wave propagation disassembly algorithm of the determined component of a product; the given data are the

    immediate predecessors of each component.We show that the solution exists and that she is unique in the following conditions: the binary matrix of the immediate

    predecessors is non-symmetrical and the data does not contain a cycle. A tracked down cycle method in the data is also proposed.r 2003 Elsevier Ltd. All rights reserved.

    Keywords: Wave propagation; Disassembly; Removal inuence; Irreversible operations; Adjacent components; Matrix of the immediatepredecessors

    1. Introduction

    Disassembly is generally achieved by taking indivi-dual components or subassembly apart from a largerproduct. Disassembling a selected component or a set of components has many applications in engineering, suchfor product maintenance, re-using and virtual assem-bling. Process planning is the act of preparing detailedoperation instructions to transform an engineeringdesign to a nal product [2], but now it is also totransform a failed product to an operational product,on an end-of-life product to sorted components or

    materials.In general, disassembly process planning consists of several or all of the following activities: selection of disassembling operations; sequencing of disassemblingoperations; selection of transferring and grasping tools;determining set-up requirements; calculations of cycletimes; tool path planning and generation of robotprograms; etc.

    Among the process planning activities this paperconsiders the operations selections and sequencing at the

    same time. In others words, the problem considered hereis to determine components to disassemble such thatthe resulting solution satises the precedence constraintsamong irreversible or reversible operations.

    2. State of the art

    2.1. Overview

    Even though the area of design for disassemblyresearch is relatively new, a lot of research activitiesare in progress with new ideas and approaches forbuilding products that are easy to dismantle, and formaintenance or recycling purpose. Therefore, in the nextsection, a brief overview of some of the more signicantpublications in the eld of the design for disassembly ispresented.

    2.2. Design for disassembly

    Most previous research articles consider the opera-tion-sequencing problem only for reversible operation indisassembly planning.

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    *Corresponding authorE-mail address : [email protected] (C. Mascle).

    0736-5845/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0736-5845(03)00032-2

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    Lambert [3] used the term selective disassemblywhich is a reversible disassembly more or less destructiveor the partial dismantling of complex products in sub-assembly or components. This process is performingbecause of two elements: the separation of somecomponents and the materials for their utilisation, fromwhat we do not desire to use. The internationaleconomical tendencies to put more and more the accenton the recycling of the products and the re-use of thematerials and components in the largest proportionpossible.

    Boothroyd [4,12] is the creator of the procedure-baseddesign for assembly and disassembly. He shows thataddressing disassemblability and recyclability at thedesign stage will provide greater nancial benets at theend of product life.

    Ishii [5] introduces a life-cycle design methodologycalled clumping. Clumping refers to a collection of components and/or sub-assemblies that share a physicalrelationship and some common characteristic basedupon user intent. Ishii maintains that clumping can beused to achieve increased product retirement values suchas reuse, recycling, and disposal by treating similar sub-assemblies of a design as one unit and calculating thecost of removing or accessing this unit or clump fromthe rest of the assembly.

    Woo did extensive research in disassembly sequencegeneration [6] and classication of assemblies usingtheir geometric complexity [7]. He uses strictly trans-lation motion of a robot. By traversing a so-calleddisassembly tree generated by mapping the boundaryrepresentation to a tree structure he generates aminimal sequence of disassembly and/or assembly.Based on this idea, Woo also developed analgorithm for disassembling multiple and parallelassemblies [8].

    Due to increased environmental awareness and theshortage of natural resources, much research has beenconducted that ties in design for disassembly technologywith design for environment issues. A broader designparadigm than design for disassembly, design forenvironment can be approached from many differentviewpoints. Here, mainly design for recyclability per-spectives of the design for environment are examined.

    Li [9] formulates a comprehensive economic modelfor disassembly analysis. A simulated algorithm isemployed to nd the optimal sequences that yield the

    maximum return value and to determine where thedisassembly operation should stop. He ties this methodas a potential tool for analysing the environmentalfriendliness of selecting product materials, assemblycongurations and fastening methods.

    Kirby and Wadehra (1993) discuss the disassembly ina practical point of view. In their research they denehow such factors, as material selection process, fasteningmethods, etc., may affect recycling machine parts. Theyidentify some of the knowledge-base information thata good disassembly tool could be made to takeadvantage of.

    2.3. Wave propagation approach

    An other interesting approach is presented bySrinivasan, Gadh, Figueroa and Mo. This approachuses an algorithm to determine the disassembly direc-tions of a component of assembly, the directions inwhich each component part of the assembly can beremoved without any obstruction during the disassem-bly process.

    Srinivasan and Gadh [1], [1316] present the inuenceof the geometrical form on the disassembly. They usethe selective disassembly term, which represents only

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    Nomenclature

    The nomenclature used in this article is quietly similar as in [1].ASS the assembly or sub-assembly formed by studied componentsA the matrix of the immediate predecessors; type n n Ai ; j 1 if and only if i is immediately before, it

    must be disassembled j

    B sub-matrix of A; it contains only the linked components, from near or far, to the component C xto disassemble

    C x the component for which we determine the wave propagationC i a component of the A SS sub-assemblyD i disassembility of a component C i MA C i the adjacent components with which C i is in contactnS total number of the components in the disassembly sequenceOS optimal sequenceRI C j C i removal inuence ( i a j )t timet i i th wave front of a t waveW components of front waves on the whole length of the waves

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    the disassembly of a sub-assembly or a component,which will be repaired or replaced. So they present theairplane defection case and they explain that in the caseof maintenance of an airplane sub-assembly, it issufcient to disassemble only the defective sub-assemblyaccording to the less expensive disassembly sequence in

    time and money.So, the idea is to determine the best disassemblysequence for a sub-assembly. The authors set out theaccessibility constraints, to dene which componentdepends one on another, which will be after disas-sembled and nish by selecting the best disassemblysequence.

    The component disassembly in an assembly is denedas being a selective disassembly. This aspect is importantfor the maintenance, recycling and re-use applications.The idea is to determine in this way the minimumnumber of components that must be disassembled. Theauthors use the expression of wave propagation,which is a step-by-step disassembly method. Thismethod allows to determine the distance of the allcomponents relative to the impact which representsthe respective component and so the minimal number of the components which must be disassembled to extract therespective component. In order to do that, we have todetermine the optimal number of the components thatmust be disassembled; we must assure ourselves that thegeometrical accessibility is present in order to assure thedisassembly. More precisely, we talk about the spaceand the available faces for the useful insertion, of thedevice or of the robot arm, which help to realise the

    disassembly.Srinivasan and Gadh [10] present the sorting im-

    portance of one or several selected components from thesub-assembly. This method is appropriate to assure aneasy maintenance, to effect the recycling, as well as forthe assembly of one or several components.

    The selective disassembly as proposed, has threesteps:

    (1) The identication of the selected components whichwill be disassembled with the help of a program orthe designer.

    (2) The determination of a better assembly sequence of the selected components, for an easy realisation,with a minimum number of components. So, afterthe study of these aspects, an optimal re-identica-tion of the components which will be disassembledmust be done.

    (3) A precise high-performance disassembly, whichrespects the order of the disassembly.

    Sometimes, the disassembly is realised with difcultiesand with important costs. If the disassembly formaintenance is done, sometimes, it is preferable toreplace the component, which are in contact, even if they

    are still in a good condition. The selective disassembly isvery important in the de-manufacturing case, espe-cially for the maintenance and recycling realisation. Sosince the preliminary phases of a product, we also studythe selective disassembly an aspect for the maintenanceand recycling.

    The authors [10] propose to determine the optimalnumber of components that must be disassembled,having the assurance of meeting the necessary geome-trical accessibility in order to assure the dismantling.

    We present the results obtained by Srinivasan andGadhs methods in 1998, applied to the assembly ASS in Fig. 1a .

    For t 0 ; t 0 C X C 3 ; we have MA 3 f C 1 ; C 2 ; C 4g; so for t 1 ; f C 1 ; C 2 ; C 4gA t 1 : So, we canchoose the wave t 1 ; the direction C 3 - C 4 orC 3 - f C 1 ; C 2g. Fairly, we have on t 2 ; the componentsC 11 and C 6 (because C 2 - C 11 and C 4 - C 6 - f C 7 ; C 8g).We choose the disassembly sequence W 1 f C 11 ; C 1 ; C 2 ; C 3g where nS 4 ; as an alternative toW 2 fC 7 ; C 8; C 6 ; C 4 ; C 3g where nS 5 : So, the opti-mal sequence OS f C 11 ; C 1 ; C 2 ; C 3g. Fig. 1b illustratesthis solution.

    2.4. Summary

    Design for disassembly methods may come togetherto form interactive design tools and they will help todesign the most disassembly friendly products [11]. Thedesign for disassembly research needs to focus on the

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    Fig. 1. The results with Srinivasans and Gadhs method.

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    near future and they will be one of the keys of technology.

    All of these researchers focus on generating eithermotion or disassembly sequences, for removing compo-nents of an assembly. Also, most of them are based onsome sort of a geometric constraint or another. These

    methods assume that the components are readilyremovable. In real life scenarios, this is not always thecase. This article introduces a new algorithm, whichhelps us to determine the most suitable sequence of disassembly for whatever product it may be.

    3. Solution approach and solution algorithms

    3.1. Application context of the algorithm proposed

    3.1.1. Non-symmetric assumptionWe impose the following constraint: if the component

    i is an immediate predecessor of the j component, andinversely. Then, we must choose only one of thepossibilities. This restriction can be avoid by applyingthe same algorithm several times or by choosing therelation of the immediate predecessors depending on therequired time for the disassembly.

    3.1.2. Disassembly of only one componentThe goal of the algorithm is to give only the waves of

    the disassembly absolutely necessary to extract a xcomponent of an assembly. In consequence, several com-ponents, non-absolutely necessary to extract this com-ponent will not be disassembled; the algorithm can beapplied after that to disassemble another componentamong the remained components. So, this is a selectivedisassembly algorithm. This case is met in practice forthe recuperation of a x component (in recycling forexample); we do not need to disassemble the wholeassembly of components.

    3.1.3. Assembly versus disassemblyThe same algorithm can be used to assemble a tted

    component by waves. The waves are considered ininverse order. It is about assembly a tted componentwith all components which are linked with it (near orfar). For the non-symmetric constraint, the remarks,done for the disassembly, remain valid.

    3.2. Notations and denitions

    3.2.1. DisassembilityPrecise propriety for the binary variable which

    indicates if the C j components is removable or not (soif WP is determinate or not).

    If D Cj true ) the WP is determinate ;If D Cj false ) we have to determinate the WP :

    3.2.2. Adjacent links multitudeTwo components C i and C j i a j are in contact, if

    they have one or several faces totally or partially incontact. Each existing link between components reducesthe number of freedom degrees. We denite MA C i asbeing the multitude of adjacent links ( MA ) of the C j components which are in contact with C i :

    3.2.3. Disassembly directionEach disassembly direction is denoted as d i ; j and

    represents the chosen disassembly direction of the C i component which is to be disassembled relatively to C j :

    3.2.4. The removal inuence

    The removal inuence RI j i it is a binary variable whichindicates if we can move away C i in the absence of

    several components C j A MA Ci ; i a j :

    If RI Cj Ci true ) it is necessary to disassemble C j ;

    If RI Cj Ci false ) it is necessary to disassemble C j :

    If we can disassemble a component by moving anothercomponent, we say that it is a removal inuence on thedisassembly.

    Given C 1 ; C 2 ; y ; C n the set of components of a sub-assembly and C x the component to extract ( 1p xp n) .We note A the binary matrix denite by Ai ; j 1 only

    if C j is an immediate predecessor of C i : The relationAi ; j 1 can be represented by C i - C j : We say that thematrix A is non-symmetric if Ai ; j A j ; i o 2; 8i and j :We name chain leaving from C i 1 , arriving in C i qan assembly f C i 1 ; C i 2 ; ::: C i q g of components asC i 1 - C i 2 - ? - C i q :

    We name empty line any line i having the conditionAi ; k 0 ; for any values of k 1 ; 2; y n (meaning if P nk 1 Ai ; k 0).

    A chain fC i 1 ; C i 2 ; ::: C i q g is cyclic if C i q - C i 1 : We alsosay that, in this case, the matrix itself has a cycle.

    The algorithm constructs the waves from a matrix B obtained from A in this manner: B i ; j 1 only if Ai ; j 1 and if it exists a chain leaving from C x andarriving in C i (C x being a component to disassemble).

    Otherwise said, B i ; j 1 only if C i - C j is a link of achain leaving from C x and arriving in C j (C x being thecomponent to extract).

    3.3. The algorithm basis

    The algorithm determines automatically the totalnumber of components nS for the target componentC x in the manner that it satises the functionalobjective.

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    The main attributes of the wave propagation WP method to determine the optimal sequence of disas-sembly are:

    (1) Find the minimum components to disassemble;(2) Determine the components C j A ASS to disassemble

    the C x element, chosen with a minimal number of components and movements;

    (3) Determine the number of component of A SS whichwill be analysed with WP method for the elementC x disassembly. The number varies between 1 andn ; depending on the C x position in ASS : If C x is at ageometrical extremity side of the sub-assembly, thenumber of analysed components is small.

    The nodes of the graph of the sub-assembly ASS ;correspond at the C i components which form thesub-assembly.

    Step 1 (to obtain the matrix B ): The construction of matrix B from A (by putting at 0 some values 1 of A)has been realised with the help of a non-exhaustivealgorithm of the branch and bound type. Anillustration of a matrix B obtained from a matrix A(n 11) is shown in Fig. 2b .

    Step 2 (wave construction ).

    Lemma 1. If B does not have cycle , then it has at leastone empty line i such P nk 1 B k ; i X 1 (meaning that C i does not have predecessor but C i is connected to C x by achain ).

    Remark. The propriety Pnk 1 B k ; i X 1 is veried whenC i is connected to C x :

    An existing cycle is detected when it is impossible tond an empty line i such P nk 1 B k ; i X 1 after n tries ormore. In effect, if all components have a predecessor,this last one will be, in its turn, a predecessor. Weconclude that we nally obtain a cycle, because thecomponents number is nished.

    Wave No. 1 construction : The assembly of the lines of B verifying the condition of Lemma 1 represents the rstwave (meaning the assembly of components to disas-semble at rst if we want to extract C x : Indeed, thesecomponents do not have immediate predecessor andthey must be disassembled before extracting C x ; so there

    is a chain connecting C x to these components (by thedenition of B ).

    Lemma 2 (construction of the following wave). If B isnon-symmetric and if the component set fC i 1 ; C i 2 ; : : : C i q grepresents a wave , so, by putting again at 0 all theelements B (k,i ) where i i 1 ; i 2 ; y i q and by eliminatingthe lines i 1 ; i 2 ; y i q , we obtain a matrix B 0 verifyingLemma 1.

    Justication. As the component set fC 1 ; C 2 ; y C qg is awave, by putting again to 0 the elements B k ; i wherei i 1 ; y i q and k 1 ; 2; y n ; we remove the last link of the chain leaving from C x ; arriving in C 1 ; C 2 , and C q ;and so B 0 veries the conditions of Lemma 1.

    Result. We can construct the following wave as beingthe rst wave of the new matrix B 0:

    Note. The algorithm allows to nd an unique solutionwhen B is non-symmetric (cf. Lemma 2). Lemmas 1 and 2assure the existence and the unique solution.

    3.4. The case of non-symmetric matrix

    If we have simultaneous C i - C j and C j - C i ; in fact,this is a particular case of cycle. In this case, theprogram should be executed twice (once with Ai ; j 1and A j ; i 0 and then with Ai ; j 0 and A j ; i 1 :

    The choice between these two solutions implies totake in consideration others criteria (for example:minimising the asked disassembly time). This problem

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    Fig. 2. The matrix of the immediate predecessors.

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    is resolved by choosing the symmetric elements as analternative to the rst diagonal in the way that theaddition of the corresponding asked time be minimal(this can be done by applying algorithms of linearprogramming, for example). After that, we apply thealgorithm already presented.

    3.5. Disassembly cases of different components in thesame product

    The disassembly cases of several components succes-sively chosen can be done also by successive applicationsof the same algorithm.

    4. Numerical results obtained with the algorithm

    The algorithm has been implemented as a functionalcomputer program called WaveDisassembly , using the

    programme language Visual Basic, Version 6. The usermust choose the number of components and completethe matrix of immediate predecessors for each compo-nent. He will be guided at each step of the data input.The interface is presented in Fig. 2 . The solution ( Fig. 3 )appears as a list (a wave per line).

    We tried the algorithm with the data given by theexample used by Srinivasan and Gadh [10], and weobtained the same results; to compare these results, seeFigs. 1b, 2 and 3 .

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    Fig. 4. Exploded view drawing for the power brake.

    Fig. 3. The disassembly waves.

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    In Fig. 2a we have all the predecessors of thecomponent C x ; and in Fig. 2b , we have the matrix B ;which contains only the necessary predecessors of thecomponent C x :

    A more complex example with 30 components ispresented in Figs. 46 . The Power Brake parts are

    presented in Fig. 4 and they are listed in approximatelydisassembly order in the part list of Table 1 .

    Most sub-assemblies can have several disassemblysequences. With the help of this algorithm, we willdetermine several disassembly sequences. After that, wechoose the most suitable. A simulation of the all foundsequences can be done and the algorithm will chooseautomatically the sequences with the minimal number of disassembly components.

    In Fig. 7 , we present a pump with sprocket wheels,which have the function of bringing the oil underpressure by the de-pressure created between the teeth of the sprockets. In Table 2 , we present the parts list forthe pump with sprockets wheels. So, we propose todisassemble the ruling axle 11.

    We will determine all possible disassembly sequencespossible with the algorithm presented in that article. Inthis way, we will construct the matrix of the immediatepredecessors in Fig. 8 . After that, the program deter-mines automatically the disassembly sequences shown inFig. 9 , respectively, for each matrix of the predecessor.

    For the chosen example, we nd two disassemblysequences. The rst one has the component numberto disassemble nS 9 ; and the second one has nS 6 :

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    Fig. 5. The matrix of the immediate predecessors for the power brake.

    nS = 14

    Wave No. 1 : 3Wave No. 2 : 4Wave No. 3 : 5Wave No. 4 : 6 7 10Wave No. 5 : 9Wave No. 6 : 8Wave No. 7 : 11Wave No. 8 : 12 16Wave No. 9 : 13

    Wave No. 10 : 14Wave No. 11 : 17

    Fig. 6. The disassembly waves for power brake.

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    Finally, the program does an optimisation, choosingautomatically the disassembly sequence with n S minimal(nS 6 ; in this case).

    When several disassembly sequences exist and wewant quickly to determine the optimal sequence with theminimal number of components to disassemble, thisalgorithm is greatly advantageous.

    5. Conclusion

    This paper considered the operation sequencingproblem in disassembly process planning, which is animportant problem for maintenance, recycling and re-using. We propose a new method of the wave propaga-tion for a disassembly analysis. The advantage of ourmethod is that it has, at the fairly wave of thecomponent to disassemble, a maximal possible numberof components, contrary on the other algorithm, whichhas at the nearest wave of the component to be

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    Table 1Parts list for the power brake

    Fig. and index no. Nomenclature Units per assy.

    1 Housing 12 Stud 14 103 Nut 104 Washer 105 Cover 16 Gasket 17 Washer 28 Seat 29 Spring 2

    10 Ball 14 dia. 211 Spring 2

    12 Pin 213 Spacer 1 12 dia. 214 PackingNeoprene 215 Nut 1 1/8 216 Pin 3/8 00 dia. 217 Piston 218 PackingNeoprene 819 Spacer 1 1/8 220 Nut 7/8 00 14 NF 221 Cap nut 222 Washer 223 Nut 1032 NF 224 Screw 132 NF 225 Link 226 Shaft 5/8 00 Nickel Steel 227 Shaft 9/11 00 dia. Nickel Steel 228 LeverAssembly 129 Nut 5/16 230 Screw 3/8 dia. 5/16 2

    Fig. 7. The pump with sprocket wheels.

    Table 2Parts list for the pump with sprocket wheels

    Fig. and index no. Nomenclature Units per assy.

    1 Housing 12 Conducted axle 13 Screw 84 Washer 85 Cover 16 O ring 27 Security ring 18 Simmering 19 Seal 1

    10 Body x1 of the ruling axle 1

    11 Ruling axle 112 Body x2 of the ruling axle 113 Body x1 of the conducted axle 114 Body x2 of the conducted axle 1

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    disassembled, a maximum number of components.We consider that in the big assembly case,it is preferable to begin to disassemble rst themaximal number of components for practical reasons(example: the disassembly of a component from anairplane).

    The great advantage of the present algorithm, whichwe have created, is evidence in the case that we haveseveral disassembly sequences to execute, and when wewant to determine rapidly the optimal sequence, havinga minimal number of components to disassemble. Formost sub-assemblies, we can envisage several disassem-bly sequences. With this algorithm help, we candetermine several disassembly sequences; after this, wecan choose the most suitable disassembly sequences.Our algorithm allows realising a simulation of all founddisassembly sequences. Following that, it choosesautomatically the sequence, which has the minimalnumber of components to disassemble. We can take theexample with the pump with sprocket wheels. In thebeginning we nd two disassembly sequences, and afteroptimisation we nd the disassembly sequence havingthe nS minimal. We can consider an example with 1000sequences and select one or several having the nSminimal.

    Acknowledgements

    This work was funded by NSERC research grant(RGPIN15027001).

    References

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    Fig. 8. The matrix of the immediate predecessors. (a) Matrix No. 1 and (b) Matrix No. 2.

    nS = 9Wave No. 1 : 3 4 7Wave No. 2 : 8Wave No. 3 : 5Wave No. 4 : 9Wave No. 5 : 10 13Wave No. 6 : 11

    nS = 6Wave No. 1 : 3 4Wave No. 2 : 1Wave No. 3 : 12 14Wave No. 4 : 11

    Disassembly sequence No. 1 Disassembly sequence No. 2(a) (b)

    Fig. 9. The disassembly waves for the pump with sprocket wheels.

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    [13] Srinivasan H, Gadh R. Complexity reduction in geometricselective disassembly, using the wave propagation abstraction.International Conference on Robotics and Automation (ICRA),May 1621, Luevere, Belgium, 1998.

    [14] Srinivasan H, Figueroa R, Gadh R. Selective disassembly forvirtual prototyping as applied to de-manufacturing. RoboticsComput Integrated Manuf 1999;15(3):23145.

    [15] Srinivasan H, Mo J, Fuegeuroa R, Gadh R. Virtual assembly anddisassembly. I-CARVEs A3D Aid CAD Projects, SiliconGraphics World Magazine, June 1999. p. 134.

    [16] Ray KJ, Wadehra I. Desigining Business Machines for Disas-sembly and Recycling. Proceedings 1993 IEEE Int. Symposiumon Electronics & the Environment (1012 May 1993). Arlington.VA. IEEE, 1994:323.

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