Areviewandanalysisofcurrentcomputer-aidedfixturedesignapproachesIainBoyle,YimingRong,DavidC.BrownKeywords:Computer-aidedfixturedesignFixturedesignFixtureplanningFixtureverificationSetupplanningUnitdesignABSTRACTAkeycharacteristicofthemodernmarketplaceistheconsumerdemandforvariety.Torespondeffectivelytothisdemand,manufacturersneedtoensurethattheirmanufacturingpracticesaresufficientlyflexibletoallowthemtoachieverapidproductdevelopment.Fixturing,whichinvolvesusingfixturestosecureworkpiecesduringmachiningsothattheycanbetransformedintopartsthatmeetrequireddesignspecifications,isasignificantcontributingfactortowardsachievingmanufacturingflexibility.Toenableflexiblefixturing,considerablelevelsofresearchefforthavebeendevotedtosupportingtheprocessoffixturedesignthroughthedevelopmentofcomputer-aidedfixturedesign(CAFD)toolsandapproaches.Thispapercontainsareviewoftheseresearchefforts.Overseventy-fiveCAFDtoolsandapproachesarereviewedintermsofthefixturedesignphasestheysupportandtheunderlyingtechnologyuponwhichtheyarebased.Theprimaryconclusionofthereviewisthatwhilesignificantadvanceshavebeenmadeinsupportingfixturedesign,thereareprimarilytworesearchissuesthatrequirefurthereffort.ThefirstoftheseisthatcurrentCAFDresearchissegmentedinnatureandthereremainsaneedtoprovidemorecohesivefixturedesignsupport.Secondly,agreaterfocusisrequiredonsupportingthedetaileddesignofafixture’sphysicalstructure.2010ElsevierLtd.Allrightsreserved.Contents1.Introduction………………………22.Fixturedesign…………………….23.CurrentCAFDapproaches……………………….43.1Setupplanning…………….43.1.1Approachestosetupplanning……………………...3.2Fixtureplanning…………..43.2.1Approachestodefiningthefixturingrequirement……………3.2.2Approachestonon-optimizedlayoutplanning…….3.2.3Approachestolayoutplanningoptimization………3.3Unitdesign………………...73.3.1Approachestoconceptualunitdesign……………3.3.2Approachestodetailedunitdesign………………...3.4Verification………………..83.4.1Approachestoconstrainingrequirementsverification…………….83.4.2Approachestotolerancerequirementsverification………………..3.4.3Approachestocollisiondetectionrequirementsverification………3.4.4Approachestousabilityandaffordabilityrequirementsverification………………3.5Representationoffixturinginformation…………………..94.AnanalysisofCAFDresearch…………………...94.1ThesegmentednatureofCAFDresearch………………...94.2Effectivelysupportingunitdesign………104.3Comprehensivelyformulatingthe?xturingrequirement………………..104.4ValidatingCAFDresearchoutputs……………………....105.Conclusion…………………...…10References…………………………101.IntroductionAkeyconcernformanufacturingcompaniesisdevelopingtheabilitytodesignandproduceavarietyofhighqualityproductswithinshorttimeframes.Quickreleaseofanewproductintothemarketplace,aheadofanycompetitors,isacrucialfactorinbeingabletosecureahigherpercentageofthemarketplaceandincreasedprofitmargin.Asaresultoftheconsumerdesireforvariety,batchproductionofproductsisnowmorethenormthanmassproduction,whichhasresultedintheneedformanufacturerstodevelopflexiblemanufacturingpracticestoachievearapidturnaroundinproductdevelopment.Anumberoffactorscontributetoanorganization’sabilitytoachieveflexiblemanufacturing,oneofwhichistheuseoffixturesduringproductioninwhichworkpiecesgothroughanumberofmachiningoperationstoproduceindividualpartswhicharesubsequentlyassembledintoproducts.Fixturesareusedtorapidly,accurately,andsecurelypositionworkpiecesduringmachiningsuchthatallmachinedpartsfallwithinthedesignspecificationsforthatpart.Thisaccuracyfacilitatestheinterchangeabilityofpartsthatisprevalentinmuchofmodernmanufacturingwheremanydifferentproductsfeaturecommonparts.Thecostsassociatedwithfixturingcanaccountfor10–20%ofthetotalcostofamanufacturingsystem[1].Thesecostsrelatenotonlytofixturemanufacture,assembly,andoperation,butalsototheirdesign.Hencetherearesignificantbenefitstobereapedbyreducingthedesigncostsassociatedwithfixturingandtwoapproacheshavebeenadoptedinpursuitofthisaim.Onehasconcentratedondevelopingflexiblefixturingsystems,suchastheuseofphase-changingmaterialstoholdworkpiecesinplace[2]andthedevelopmentofcommercialmodularfixturesystems.However,thesignificantlimitationoftheflexiblefixturingmantraisthatitdoesnotaddressthedifficultyofdesigningfixtures.Tocombatthisproblem,asecondresearchapproachhasbeentodevelopcomputer-aidedfixturedesign(CAFD)systemsthatsupportandsimplifythefixturedesignprocessanditisthisresearchthatisreviewedwithinthispaper.Section2describestheprincipalphasesofandthewidevarietyofrequirementsdrivingthefixturedesignprocess.SubsequentlyinSection3anoverviewofresearcheffortsthathavefocuseduponthedevelopmentoftechniquesandtoolsforsupportingtheseindividualphasesofthedesignprocessisprovided.Section4critiquestheseeffortstoidentifycurrentgapsinCAFDresearch,andfinallythepaperconcludesbyofferingsomepotentialdirectionsforfutureCAFDresearch.Beforeproceeding,itisworthnotingthattherehavebeenpreviousreviewsoffixturingresearch,mostrecentlyBiandZhang[1]andPehlivanandSummers[3].BiandZhang,whileprovidingsomedetailsonCAFDresearch,tendtofocusuponthedevelopmentofflexiblefixturingsystems,andPehlivanandSummersfocusuponinformationintegrationwithinfixturedesign.Thevalueofthispaperisthatitprovidesanin-depthreviewandcritiqueofcurrentCAFDtechniquesandtoolsandhowtheyprovidesupportacrosstheentirefixturedesignprocess.2.FixturedesignThissectionoutlinesthemainfeaturesoffixturesandmorepertinentlyofthefixturedesignprocessagainstwhichresearcheffortswillbereviewedandcritiquedinSections3and4,respectively.Physicallyafixtureconsistsofdevicesthatsupportandclampaworkpiece[4,5].Fig.1representsatypicalexampleofafixtureinwhichtheworkpiecerestsonlocatorsthataccuratelylocateit.Clampsholdtheworkpieceagainstthelocatorsduringmachiningthussecuringtheworkpiece’slocation.Thelocatingunitsthemselvesconsistofthelocatorsupportingunitandthelocatorthatcontactstheworkpiece.Theclampingunitsconsistofaclampsupportingunitandaclampthatcontactstheworkpieceandexertsaclampingforcetorestrainit.Typicallythedesignprocessbywhichsuchfixturesarecreatedhasfourphases:setupplanning,fixtureplanning,unitdesign,andverification,asillustratedinFig.2,whichisadaptedfromKangetal.[6].Duringsetupplanningworkpieceandmachininginformationisanalyzedtodeterminethenumberofsetupsrequiredtoperformallnecessarymachiningoperationsandtheappropriatelocatingdatumsforeachsetup.Asetuprepresentsthecombinationofprocessesthatcanbeperformedonaworkpiecewithouthavingtoalterthepositionororientationoftheworkpiecemanually.Togenerateafixtureforeachsetupthefixtureplanning,unitdesign,andverificationphasesareexecuted.Duringfixtureplanning,thefixturingrequirementsforasetuparegeneratedandthelayoutplan,whichrepresentsthefirststeptowardsasolutiontotheserequirementsisgenerated.Thislayoutplandetailstheworkpiecesurfaceswithwhichthefixture’slocatingandclampingunitswillestablishcontact,togetherwiththesurfacepositionsofthelocatingandclampingpoints.Thenumberandpositionoflocatingpointsmustbesuchthataworkpiece’ssixdegreesoffreedom(Fig.3)areadequatelyconstrainedduringmachining[7]andthereareavarietyofconceptuallocatingpointlayoutsthatcanfacilitatethis,suchasthe3-2-1locatingprinciple[4].Inthethirdphase,suitableunitdesigns(i.e.,thelocatingandclampingunits)aregeneratedandthefixtureissubsequentlytestedduringtheverificationphasetoensurethatitsatisfiesthefixturingrequirementsdrivingthedesignprocess.Itisworthnotingthatverificationofsetupsandfixtureplanscantakeplaceastheyaregeneratedandpriortounitdesign.Fixturingrequirements,whichalthoughnotshowninKangetal.[6]aretypicallygeneratedduringthefixtureplanningphase,canbegroupedintosixclasses(Table1).The‘‘physical’’requirementsclassisthemostbasicandrelatestoensuringthefixturecanphysicallysupporttheworkpiece.The‘‘tolerance’’requirementsrelatetoensuringthatthelocatingtolerancesaresufficienttolocatetheworkpieceaccuratelyandsimilarlythe‘‘constraining’’requirementsfocusonmaintainingthisaccuracyastheworkpieceandfixturearesubjectedtomachiningforces.The‘‘a(chǎn)ffordability’’requirementsrelatetoensuringthefixturerepresentsvalue,forexampleintermsofmaterial,operating,andassembly/disassemblycosts.The‘‘collisiondetection’’requirementsfocusuponensuringthatthefixturedoesnotcollidewiththemachiningpath,theworkpiece,orindeeditself.The‘‘usability’’requirementsrelatetofixtureergonomicsandincludeforexampleneedsrelatedtoensuringthatafixturefeatureserror-proofingtopreventincorrectinsertionofaworkpiece,andchipshedding,wherethefixtureassistsintheremovalofmachinedchipsfromtheworkpiece.Aswithmanydesignsituations,theconflictingnatureoftheserequirementsisproblematic.Forexampleaheavyfixturecanbeadvantageousintermsofstabilitybutcanadverselyaffectcost(duetoincreasedmaterialcosts)andusability(becausetheincreasedweightmayhindermanualhandling).SuchconflictsaddtothecomplexityoffixturedesignandcontributetotheneedfortheCAFDresearchreviewedinSection3.Table1Fixturingrequirements.GenericrequirementAbstractsub-requirementexamplesPhysical●Thefixturemustbephysicallycapableofaccommodatingtheworkpiecegeometryandweight.●Thefixturemustallowaccesstotheworkpiecefeaturestobemachined.Tolerance●Thefixturelocatingtolerancesshouldbesufficienttosatisfypartdesigntolerances.Constraining●Thefixtureshallensureworkpiecestability(i.e.,ensurethatworkpieceforceandmomentequilibriumaremaintained).●Thefixtureshallensurethatthefixture/workpiecestiffnessissufficienttopreventdeformationfromoccurringthatcouldresultindesigntolerancesnotbeingachieved.Affordability●Thefixturecostshallnotexceeddesiredlevels.●Thefixtureassembly/disassemblytimesshallnotexceeddesiredlevels.●Thefixtureoperationtimeshallnotexceeddesiredlevels.CollisionPrevention●Thefixtureshallnotcausetoolpath–fixturecollisionstooccur.●Thefixtureshallcauseworkpiece–fixturecollisionstooccur(otherthanatthedesignatedlocatingandclampingpositions).●Thefixtureshallnotcausefixture–fixturecollisionstooccur(otherthanatthedesignatedfixturecomponentconnectionpoints).Usability●Thefixtureweightshallnotexceeddesiredlevels.●Thefixtureshallnotcausesurfacedamageattheworkpiece/fixtureinterface.●Thefixtureshallprovidetoolguidancetodesignatedworkpiecefeatures.●Thefixtureshallensureerror-proofing(i.e.,thefixtureshouldpreventincorrectinsertionoftheworkpieceintothefixture).●Thefixtureshallfacilitatechipshedding(i.e.,thefixtureshouldprovideameansforallowingmachinedchipstoflowawayfromtheworkpieceandfixture).3.CurrentCAFDapproachesThissectiondescribescurrentCAFDresearchefforts,focusingonthemannerinwhichtheysupportthefourphasesoffixturedesign.Table2providesasummaryofresearcheffortsbaseduponthedesignphasestheysupport,thefixturerequirementstheyseektoaddress(boldtexthighlightsthattherequirementisaddressedtoasignificantdegreeofdepth,whilstnormaltextthatthedegreeofdepthislesserinnature),andtheunderlyingtechnologyuponwhichtheyareprimarilybased.Sections3.1–3.4describesdifferentapproachesforsupportingsetupplanning,fixtureplanning,unitdesign,andverification,respectively.Inaddition,Section3.5discussesCAFDresearcheffortswithregardtorepresentingfixturinginformation.3.1.SetupplanningSetupplanninginvolvestheidentificationofmachiningsetups,whereanindividualsetupdefinesthefeaturesthatcanbemachinedonaworkpiecewithouthavingtoalterthepositionororientationoftheworkpiecemanually.Thereafter,theremainingphasesofthedesignprocessfocusondevelopingindividualfixturesforeachsetupthatsecuretheworkpiece.Fromafixturingviewpoint,thekeyoutputsfromthesetupplanningstagearetheidentificationofeachrequiredsetupandthelocatingdatums(i.e.,theprimarysurfacesthatwillbeusedtolocatetheworkpieceinthefixture).Thekeytaskwithinsetupplanningisthegroupingorclusteringoffeaturesthatcanbemachinedwithinasinglesetup.Machiningfeaturescanbedefinedasthevolumesweptbyacuttingtool,andtypicalexamplesincludeholes,slots,surfaces,andpockets[8].Clusteringofthesefeaturesintoindividualsetupsisdependentuponanumberoffactors(includingthetolerancedependenciesbetweenfeatures,thecapabilityofthemachinetoolsthatwillbeusedtocreatethefeatures,thedirectionofthecuttingtoolapproach,andthefeaturemachiningprecedenceorder),andanumberoftechniqueshavebeendevelopedtosupportsetupplanning.Graphtheoryandheuristicreasoningarethemostcommontechniquesusedtosupportsetupplanning,althoughmatrixbasedtechniquesandneuralnetworkshavealsobeenemployed.3.1.1.ApproachestosetupplanningTheuseofgraphtheorytodetermineandrepresentsetupshasbeenaparticularlypopularapproach[9–11].Graphsconsistoftwosetsofelements:vertices,whichrepresentworkpiecefeatures,andedges,whichrepresenttherelationshipsthatexistbetweenfeaturesanddrivesetupidentification.Theirnaturecanvary,forexampleinSarmaandWright[9]considerationoffeaturemachiningprecedencerelationshipsisprominent,whereasHuangandZhang[10]focusuponthetolerancerelationshipsthatexistbetweenfeatures.Giventhattheseedgescanbeweightedinaccordancewiththetolerancemagnitudes,thisgraphapproachcanalsofacilitatetheidentificationofsetupsthatcanminimizetolerancestackuperrorsbetweensetupsthroughthegroupingoftighttolerances.However,thiscanproveproblematicgiventhedifficultyofcomparingthemagnitudeofdifferenttolerancetypestoeachotherthusHuang[12]includestheuseoftolerancefactors[13]asameansoffacilitatingsuchcomparisons,whicharerefinedandextendedbyHuangandLiu[14]tocaterforagreatervarietyoftolerancetypesandthecaseofmultipletolerancerequirementsbeingassociatedwiththesamesetoffeatures.Whilesomemethodsuseundirectedgraphstoassistsetupidentification[11],Yaoetal.[15],ZhangandLin[16],andZhangetal.[17]usedirectedgraphsthatfacilitatethedeterminationandexplicitrepresentationofwhichfeaturesshouldbeusedaslocatingdatums(Fig.4)inadditiontosetupidentificationandsequencing.Also,Yaoetal.refinetheidentifiedsetupsthroughconsiderationofavailablemachinetoolcapabilityinatwostagesetupplanningprocess.Experientialknowledge,intheformofheuristicreasoning,hasalsobeenusedtoassistsetupplanning.Itspopularitystemsfromthefactthatfixturedesigneffectivenesshasbeenconsideredtobedependentupontheexperienceofthefixturedesigner[18].Tosupportsetupplanning,suchknowledgehastypicallybeenheldintheformofempiricallyderivedheuristicrules,althoughobjectorientedapproacheshaveonoccasionbeenadopted[19].ForexampleGologlu[20]usesheuristicrulestogetherwithgeometricreasoningtosupportfeatureclustering,featuremachiningprecedence,andlocatingdatumselection.Withinsuchheuristicapproaches,thefocustendstofalluponrulesconcerningthephysicalnatureoffeaturesandmachiningprocessesusedtocreatethem[21,22].Althoughsometechniquesdoincludefeaturetoleranceconsiderations[23],theirdepthofanalysiscanbelessthanthatfoundwithinthegraphbasedtechniques[24].Similarly,kinematicapproaches[25]havebeenusedtofacilitateadeeperanalysisoftheimpactoftoolapproachdirectionsuponfeatureclusteringthanistypicallyachievedusingrule-basedapproaches.However,itisworthnotingthatgraphbasedapproachesareoftenaugmentedwithexperientialrule-basestoincreasetheiroveralleffectiveness[16].Matrixbasedapproacheshavealsobeenusedtosupportsetupplanning,inwhichamatrixdefiningfeatureclustersisgeneratedandsubsequentlyrefined.Ongetal.[26]determineafeatureprecedencematrixoutliningtheorderinwhichfeaturescanbemachined,whichisthenoptimizedagainstanumberofcostindicators(suchasmachinetoolcost,changeovertime,etc.)inahybridgeneticalgorithm-simulatedannealingapproachthroughconsiderationofdynamicallychangingmachinetoolcapabilities.HebbalandMehta[27]generateaninitialfeaturegroupingmatrixbaseduponthemachinetoolapproachdirectionforeachfeaturewhichissubsequentlyrefinedthroughtheapplicationofalgorithmsthatconsiderlocatingfacesandfeaturetolerances.Alternatively,theuseofneuralnetworkstosupportsetupplanninghasalsobeeninvestigated.Neuralnetworksareinterconnectednetworksofsimpleelements,wheretheinterconnectionsare‘‘learned’’fromasetofexampledata.Onceeducated,thesenetworkscangeneratesolutionsfornewproblemsfedintothenetwork.MingandMak[28]useaneuralnetworkapproachinwhichfeatureprecedence,toolapproachdirection,andtolerancerelationshipsarefedintoaKohonenself-organizingneuralnetworktogroupoperationsforindividualfeaturesintosetups.3.2.FixtureplanningFixtureplanninginvolvesthecomprehensivedefinitionofafixturingrequirementintermsofthephysical,tolerance,constraining,affordability,collisionprevention,andusabilityrequirementslistedinTable1,andthecreationofafixturelayoutplan.Thelayoutplanrepresentsthefirstpartofthefixturesolutiontotheserequirements,andspecifiesthepositionofthelocatingandclampingpointsontheworkpiece.Manylayoutplanningapproachesfeatureverification,particularlywithregardtotheconstrainingrequirements.Typicallythisverificationformspartofafeedbackloopthatseekstooptimizethelayoutplanwithrespecttotheserequirements.Techniquesusedtosupportfixtureplanningarenowdiscussedwithrespecttofixturerequirementdefinition,layoutplanning,andlayoutoptimization.Fig.4.Aworkpiece(a)anditsdirectedgraphsshowingthelocatingdatums(b)(adaptedfromZhangetal.[17]).3.2.1.ApproachestodefiningthefixturingrequirementComprehensivefixturerequirementdefinitionhasreceivedlimitedattention,primarilyfocusinguponthedefinitionofindividualrequirementswithinthephysical,tolerance,andconstrainingrequirements.Forexample,Zhangetal.[17]under-taketolerancerequirementdefinitionthroughananalysisofworkpiecefeaturetolerancestodeterminetheallowedtoleranceateachlocatingpointandthedecompositionofthattoleranceintoitssources.Theallowedlocatingpointaccuracyiscomposedofanumberoffactors,suchasthelocatingunittolerance,themachinetooltolerance,theworkpiecedeformationatthelocatingpoint,andsoon.Thesedecomposedtolerancerequirementscansubsequentlydrivefixturedesign:e.g.,thetoleranceofthelocatingunitdevelopedintheunitdesignphasecannotexceedthespecifiedlocatingunittolerance.Inasimilarindividualisticvein,definitionoftheclampingforcerequirementsthatclampingunitsmustachievehasalsoreceivedattention[29,30].Inamoreholisticapproach,Boyleetal.[31]facilitateacomprehensiverequirementspecificationthroughtheuseofskeletonrequirementsetsthatprovideaninitialdecompositionoftherequirementslistedinTable1,andwhicharesubsequentlyrefinedthroughaseriesofanalysesandinteractionwiththefixturedesigner.Hunteretal.[32,33]alsofocusonfunctionalrequirementdrivenfixturedesign,butrestricttheirfocusprimarilytothephysicalandconstrainingrequirements.3.2.2.Approachestonon-optimizedlayoutplanningLayoutplanningisconcernedwiththeidentificationofthelocatingprinciple,whichdefinesthenumberandgeneralarrangementoflocatingandclampingpoints,theworkpiecesurfacestheycontact,andthesurfacecoordinatepositionswherecontactoccurs.Fornon-optimizedlayoutplanning,approachesbaseduponthere-useofexperientialknowledgehavebeenused.Inadditiontorule-basedapproaches[20,34,35]thataresimilarinnaturetothosediscussedinSection3.1,case-basedreasoninghasalsobeenused.CBRisageneralproblemsolvingtechniquethatusesspecificknowledgeofpreviousproblemstosolvenewones.Inapplyingthisapproachtolayoutplanning,alayoutplanforaworkpieceisobtainedbyretrievingtheplanusedforasimilarworkpiecefromacaselibrarycontainingknowledgeofpreviousworkpiecesandtheirlayoutplans[18,36,37].Workpiecesimilarityistypicallycharacterizedthroughindexingworkpiecesaccordingtotheirpartfamilyclassification,tolerances,features,andsoon.LinandHuang[38]adoptasimilarworkpiececlassificationapproach,butretrievelayoutplansusinganeuralnetwork.Furtherworkhassoughttoverifylayoutplansandrepairthemifnecessary.ForexampleRoyandLiao[39]performaworkpiecedeformationanalysisandifdeformationistoogreatemployheuristicrulestorelocateandretestlocatingandclampingpositions.3.2.3.ApproachestolayoutplanningoptimizationLayoutplanoptimizationiscommonwithinCAFDandoccurswithrespecttoworkpiecestabilityanddeformation,whicharebothconstrainingrequirements.Stabilitybasedoptimizationtypicallyfocusesuponensuringalayoutplansatisfiesthekinematicformclosureconstraint(inwhichasetofcontactscompletelyconstraininfinitesimalpartmotion)andaugmentingthiswithoptimizationagainstsomeformofstabilitybasedrequirement,suchasminimizingforcesatthelocatingand/orclampingpoints[40–42].WuandChan[43]focusedonoptimizingstability(measuringstabilityisdiscussedinSection3.4)usingaGeneticAlgorithm(GA),whichisatechniquefrequentlyemployedindeformationbasedoptimization.GAs,whichareanexampleofevolutionaryalgorithms,areoftenusedtosolveoptimizationproblemsanddrawtheirinspirationfrombiologicalevolution.ApplyingGAsinsupportoffixtureplanning,potentiallayoutplansolutionsareencodedasbinarystrings,tested,evaluated,andsubjectedto‘‘biological’’modificationthroughreproduction,mutation,andcrossovertogenerateimprovedsolutionsuntilanoptimalstateisreached.Typicallydeformationtestingisemployedusingafiniteelementanalysisinwhichaworkpieceisdiscretizedtocreateaseriesofnodesthatrepresentpotentiallocatingandclampingcontactpoints,asperformedforexamplebyKashyapandDeVries[44].Setsofcontactpointsareencodedandtested,andtheGAusedtodevelopnewcontactpointsetsuntilanoptimumisreachedthatminimizesworkpiecedeformationcausedbymachiningandclampingforces[45,46].Ratherthanusenodes,someCAFDapproachesusegeometricdata(suchasspatialcoordinates)intheGA,whichcanofferimprovedaccuracyastheyaccountforthephysicaldistancethatexistsbetweennodes[47,48].Pseudogradienttechniques[49]havealsobeenemployedtoachieveoptimization[50,51].Vallapuzhaetal.[52]comparedtheeffectivenessofGAandpseudogradientoptimization,concludingthatGAsprovidedhigherqualityoptimizationsgiventheirabilitytosearchforglobalsolutions,whereaspseudogradienttechniquestendedtoconvergeonlocaloptimums.Ratherthanconcentratingonfixturedesignsforindividualparts,KongandCeglarek[53]defineamethodthatidentifiesthefixtureworkspaceforafamilyofpartsbasedontheindividualconfigurationofthefixturelocatinglayoutforeachpart.ThemethodusesProcrustesanalysistoidentifyapreliminaryworkspacelayoutthatissubjectedtopairwiseoptimizationoffixtureconfigurationsforagivenpartfamilytodeterminethebestsuperpositionoflocatingpointsforafamilyofpartsthatcanbeassembledonasinglereconfigurableassemblyfixture.ThisbuildsuponearlierworkbyLeeetal.[54]throughattemptingtosimplifythecomputationaldemandsoftheoptimizationalgorithm.3.3.UnitdesignUnitdesigninvolvesboththeconceptualanddetaileddefinitionofthelocatingandclampingunitsofafixture,togetherwiththebaseplatetowhichtheyareattached(Fig.5).Theseunitsconsistofalocatororclampthatcontactstheworkpieceandisitselfattachedtoastructuralsupport,whichinturnconnectswiththebaseplate.Thesestructuralsupportsservemultiplefunctions,forexampleprovidingthelocatingandclampingunitswithsufficientrigiditysuchthatthefixturecanwithstandappliedmachiningandclampingforcesandthusresultinthepartfeaturedesigntolerancesbeingobtained,andallowingtheclamporlocatortocontacttheworkpieceattheappropriateposition.Unitdesignhasingeneralreceivedlessattentionthanbothfixtureplanningandverification,butanumberoftechniqueshavebeenappliedtosupportbothconceptualanddetailedunitdesign.3.3.1.ApproachestoconceptualunitdesignConceptualunitdesignhasfocuseduponthedefinitionofthetypesandnumbersofelementsthatanindividualunitshouldco