IntJAdvManufTechnol(1999)15:1711811999Springer-VerlagLondonLimitedDevelopmentofAutomatedFixturePlanningSystemsW.Ma,J.LiandY.RongDepartmentofMechanicalEngineering,WorcesterPolytechnicInstitute,Worcester,MA,USAFixturingisanimportantmanufacturingactivity.Thecomputer-aidedfixturedesigntechniqueisbeingrapidlydevelopedtoreducetheleadtimeinvolvedinmanufacturingplanning.Anautomatedfixtureconfigurationdesignsystemhasbeendevelopedtoselectautomaticallymodularfixturecomponentsandplacetheminpositionwithsatisfactoryassemblyrelation-ships.Inthispaper,anautomatedfixturingplanningsystemispresentedinwhichfixturingsurfacesandpointsareauto-maticallydeterminedbasedonworkpiecegeometryandoper-ationalinformation.Fixturingsurfaceaccessibility,featureaccuracy,andfixturingstabilityarethemainconcernsinthefixtureplanning.Thesystemdevelopment,thefixtureplanningdecisionprocedure,andanimplementationexamplearepresentedinthepaper.Keywords:Accuracy；Clamping；Fixtureplanning；Locating1.IntroductionFixturingisanimportantmanufacturingactivityinthepro-ductioncycle.Acomputer-aided(orautomated)fixturedesign(CAFD)techniquehasbeendevelopedaspartofCAD/CAMintegration1.ThedevelopmentofCAFDcontributestothereductionofmanufacturingleadtime,theoptimisationofmanu-facturingoperations,andtheverificationofmanufacturingpro-cessdesigns2.CAFDplaysanimportantroleinflexiblemanufacturingsystems(FMS)andcomputer-integratedmanu-facturingsystems(CIMS)3.Figure1outlinestheactivitiesforfixturedesigninmanufac-turingsystemswhichincludethreemajoraspects:set-upplan-ning,fixtureplanning,andfixtureconfigurationdesign4.Theobjectiveofset-upplanningistodeterminethenumberofset-ups,thepositionandorientationoftheworkpieceineachset-up,andalsothemachiningsurfacesineachset-up.Fixtureplanningdeterminesthelocatingandclampingpointsonwork-piecesurfaces.Thetaskoffixtureconfigurationdesignistoselectfixturecomponentsandplacethemintoafinalconfigur-Correspondenceandoffprintrequeststo:DrKevinRong,DepartmentofMechanicalEngineering,WorcesterPolytechnicInstitute,Worcester,MA01609-2280,USA.E-mail:rongKFig.1.Fixturedesigninmanufacturingsystems.ationtofulfilthefunctionsoflocatingandclampingtheworkpiece.Anautomatedmodularfixtureconfigurationdesignsystemhasbeendevelopedinwhich,whenfixturingsurfacesandpointsareselectedontheworkpiecemodel,fixtureunitsareautomaticallygeneratedandplacedintopositionwiththeassistanceoffixturecomponentassemblyrelationships4,5.Thispaperdealswithfixtureplanningwhenthefixturingsurfacesandpositionsontheworkpieceareselectedautomatically.Previouspapersonfixturedesignanalysishavebeenpub-lished,butacomprehensivefixtureplanningsystemwhichcanbeusedtogeneratefixtureplansforindustrialapplicationshasnotbeendeveloped.Previousworkincludes:amethodfortheautomateddeterminationoffixturelocationandclampingderivedfromamathematicalmodel6；analgorithmfortheselectionoflocatingandclampingpositionswhichprovidethemaximummechanicalleverage7；kinematicanalysisbasedfixtureplanning8,9；afixturinggradeanddependencygradebasedfixturabilityanalysis10；automatedselectionofset-ups172W.MaandY.Rongwithconsiderationoftolerancefactorsoforientationerrorsinfixturedesign11,andfinallyageometricanalysisbased2Dfixtureplanningsystem12.Inourpreviousresearch,fixturingfeatures13,fixturingaccuracy14,15,geometricconstraints16,andfixturingsurfaceaccessibility17havebeenstudied.Aframeworkhasbeendevelopedforset-upplanningandfixturedesign18.Inthispaper,anautomatedfixtureplanningsystem,Fix-Planning,ispresentedwherefixturingsurfacesandpointsaredeterminedwhentheworkpiecemodelandset-upplanninginformationisinputtothesystem.2.BasicRequirementsofFixturePlanningInengineeringpractice,fixtureplanningisgovernedbyanumberoffactors,includingworkpiecegeometricinformationandtolerance；set-upplanninginformationsuchasmachiningfeatures,themachinetoolandcuttingtoolstobeusedineachset-up；initialandresultingformsoftheworkpieceineachset-up；andavailablefixturecomponents.Toensurethatthefixturecanholdtheworkpieceinanacceptablepositionsothatthemanufacturingprocesscanbecarriedoutaccordingtothedesignspecifications,thefollowingconditionsshouldbesatisfiedforafeasiblefixtureplan.1.Thedegreesoffreedom(DOF)oftheworkpiecearetotallyconstrainedwhentheworkpieceislocated.2.Machiningaccuracyspecificationscanbeensuredinthecurrentset-up.3.Fixturedesignisstabletoresistanyeffectsofexternalforceandtorque.4.Fixturingsurfacesandpointscanbeaccessedeasilybyavailablefixturecomponents.5.Thereisnointerferencebetweentheworkpieceandthefixture,andbetweenthecuttertoolandthefixture.Inthisinvestigation,wefocusonthefirstfourrequirements.Fixtureplanningiscarriedoutbasedonthefollowingconsider-ations:1.Althoughtheworkpiecegeometrycanbecomplexinindus-trialproduction,inmostfixturedesigns,planarandcylindri-calsurfaces(internalandexternal)areusedasthelocatingandclampingsurfacesbecauseoftheeaseofaccessandmeasurementofthesefeatureswhentheworkpieceisfixed.Inthisinvestigation,planarandcylindricalsurfacesareusedinfixtureplanning.2.ManyCNCmachines,especiallymachiningcentres,canbeusedtoperformvariousoperationswithinoneset-up.Inmostcases,thecutting-toolaxisofthemachinetoolisfixed.Whenconsideringfixturingstability,thelocatingsur-facesarepreferablythosewithnormaldirectionsoppositeto,orperpendicularto,thecutting-toolaxis.Forclampingfeatures,thenormaldirectionsshouldbeinlinewith,orperpendicularto,thecutting-toolaxis,because,infixturedesign,clampingforcesshouldbeagainstlocators.3.Forthesurfacestobemachined,thereshouldexistdatumsurfaceswhichserveaspositionandorientationreferencesfromwhichotherdimensionsandtolerancesaremeasured.Infixtureplanning,surfaceswithhighaccuracygradesshouldbeselectedpreferentiallyaslocatingsurfacessothattheinheritedmachiningerrorisminimisedandtherequiredtolerancesofthemachiningfeaturesareeasilyattained.4.Infixtureplanning,morethanoneworkpiecesurfacemustbeselectedforthelocatingandclampingsurfacesforrestrictingtheDOFoftheworkpieceinaset-up.Therefore,besidestheconditionsforindividualsurfaces,thecombi-nationstatusoftheavailablelocatingsurfacesisalsoimportantfortheaccuratelocationoftheworkpiece.5.Sincethelocatorsandclampsareincontactwiththeworkpiece,thedistributionoffixturingpointsplaysacriticalroleinensuringfixturingstability.6.Forafeasiblefixturedesign,thefixturingsurfacesmustbeaccessibletothefixturecomponents.Theusable(effective)areaofthefixturingsurfaceshouldbelargeenoughtoaccommodatethefunctionalsurfacesofthelocatorsandclamps.Besidesconsideringafixturingsurface,theaccessi-bilityofpotentialfixturingpointsonthesurfaceisalsoimportantforthedeterminationofthefinalfixturingpointdistribution.3.FixturingSurfacesTheconceptoffeatureshasbeenwidelyusedindesignandmanufacturing.Aworkpiecetobemachinedcanbeviewedasacombinationoffeaturessuchasplanes,steps,pockets,slots,andholes.Inaparticularoperationset-up,featuresusedforfixturingtheworkpiececanbedefinedasfixturingfeaturesorfixturingsurfaces.Inpractice,mostfixturingfeaturesareplanarandcylindricalsurfaces.Accordingtothefixturingfunctions,thefixturingsurfacescanbeclassifiedintolocating,clamping,andsupportingfeatures.Unlikedesignandmanufacturingfea-tures,fixturingsurfacesareorientation-dependent.Theydonotplaythesamerolethroughoutthemanufacturingprocesses.Asetofsurfacesmayserveasfixturingsurfacesinaset-up,butmaynotbeusedforfixturingorhavedifferentfixturingfunctionsinanotherset-up.Theconceptoffixturingfeaturesallowsthefixturingrequire-mentstobeassociatedwiththeworkpiecegeometry.Featureinformationinafeature-basedworkpiecemodelcanalsobeuseddirectlyforfixturedesignpurposes.Formanufacturingfeatures,theinformationnecessaryfordescribingafixturingfeaturecontainsgeometricandnon-geometricaspects.Theformerincludesfeaturetype,shapeanddimensionalparameters,andpositionandorientationoftheworkpiece.Thelatterincludesthesurfacefinish,accuracylevelandrelationshipswithmachiningfeatures,andsurfaceaccessibility.3.1DiscretisationofFixturingSurfacesInmostfixturedesigns,thefixturingfeatures,especiallythelocatingsurfaces,areplanarandcylindricalsurfaces.Inordertoevaluatefixturingsurfaceaccessibilityanddeterminelocating/clampingpointsonfixturingsurfaces,acandidatefix-turingsurfaceissampledintogrid-arrayeddiscretepointswithDevelopmentofAutomatedFixturePlanningSystems173equalintervalT.IfTissmallenough,thediscretesamplepointswillbealmostcontinuous.Inordertomakethesamplingalgorithmgeneric,anouter-boundingrectangleonthesurfaceisusedasthesamplingregion.Sinceinmostcases,theprimarylocatingsurfaceisperpendiculartotheotherlocatingsurfaces,especiallyinmodu-larfixturedesigns,thefixturingsurfacesareconsideredasbottom-locating,top-clamping,side-locating,andside-clampingsurfaces.Forabottom-locating/top-clampingsurfacewithanormalZ(or2Z)direction,twoedgesoftheouter-boundingrectanglemustbeparalleltotheX-axisandtwootheredgesparalleltotheY-axis.Foraside-locating/clampingsurface,theremustbetwoedgesparalleltotheZ-axis,whiletheothertwoedgesmustbeperpendiculartothefirsttwoedges.Figure2showsanexampleofsampledcandidatefixturingsurfaceswiththeouter-boundingrectangle.WiththeassumptionthattheZ-axisisnormaltothesurfaceinthesurfacelocalcoordi-natesystem,thepointswithintheouter-boundingrectanglecanberepresentedas:x=Xmin+Tu,u=1,2,%,Nuy=Ymin+Tv,v=1,2,%,Nv(1)whereNuandNvarethenumbersofpointsintheX-andY-directions,respectively,whichare:Nu=int(Xmax2Xmin)/TandNv=intYmax2Ymin)/T.3.2FixturingSurfaceAccessibilityFixturingsurfaceaccessibilityisameasureofwhetheracandi-datefixturingsurfaceisaccessibletoaregularfixturecompo-nent.Threemajorfactorsmustbetakenintoaccount:1.Thegeometryofthefixturingsurfacewhichinvolvestheeffectiveareaandshapeofthesurface.2.Possibleobstructionoftheworkpiecegeometryalongthenormaldirectionand/oraroundthegeometricregionofthefixturingsurface.3.Thesizeandshapeofthefunctionalfixturecomponents.Inpracticalsituations,itispossiblethataplanarsurfaceoftheworkpiecehasacomplexshapeandhasafull/partialobstructionalongitsnormaldirectionand/orarounditsgeo-Fig.2.Samplingofacandidatefixturingsurfacewithanouter-bound-ingrectangle.metricregion.Itisthusrequiredthattheaccessibilitymodelshouldcomprehensivelyreflectthesefactssothatareasonablycomparableaccessibilityvaluecanbeappliedforeverycandi-datefixturingsurface.Thesurfaceaccessibilityisdefinedasastatisticalvaluebasedonthepointaccessibility(PA)ofeveryvalidsamplepointonthesurface,wherePAconsistsoftwoparts:thepointselfindividualaccessibility(SIA)andthepointneighbourrelatedaccessibility(NRA).TheSIAcorrespondsmainlytotheisolatedaccessibilityofthefixturingpoint,whereastheNRAreflectstheextendedaccessibilityofthefixturingpoint.TheSIAofasamplepointisdefinedonthebasisofthreeattributetags.Thetags1isusedtoindicatewhetherthesquaretestgridwithitscentreatthecurrentsamplepointisinside,on,oroutsidetheouter-loopofthefixturingsurface.Threediscretevaluesareassignedtorepresentitsstatus,i.e.0,1,and2,respectively.Ifthereexistsobstructiveworkpiecegeometryinthesurfacenormaldirectionorsurroundingthesamplepoint,thisaffectsthesurfaceaccessibilityatthesamplepoint.Forexample,asshowninFig.3(a),onacandidatebottom-locatingsurfaceofaworkpiece,samplepointp1isnotaccessiblebecauseoftheobstructivegeometryoftheworkpiecealongthebottom-locat-ingdirection,andp2isnotaccessibleeitherbecauseoftheobstructionssurroundingit.Toevaluateautomaticallywhetheranobstructionexistsinthesurfacenormaldirection,avirtualvolumeisgeneratedbyextrudingthesquaretestgridtoasolidentityinthesurfacenormaldirection.Byemployingatechniquefordetectingtheinterferencebetweentwosolidentities,theobstructioncanbeidentified,asshowninFig.3(b).TheextrudingmethodisalittledifferentforthesquareFig.3.Obstructioncheckingatvirtualsamplepointsonabottom-locatingsurface.(Kpimeanstheextrusioniscarriedoutatpointpialongitsaccessibledirection.)174W.MaandY.Rongtestgridontheside-locating/clampingsurface,wherethesquaretestgridisfirststretchedalongthebottom-locatingdirection,andthenthestretchedgridisextrudedalongtheside-locating/clampingdirectionasillustratedinFig.4.Theattributetags2isusedforrecordingtheresultofobstructioncheckingatasamplepoint.Whensuchanobstructionisdetected,s2=1,otherwise,s2=0.Ifthetestgridatthesamplepointisfoundtobenotobstructed,itsindividualaccessibilityislargelydependentonthecontactareabetweenthetestsurfaceandthefixturecomponents,whichisrepresentedbytheattributetags3.Thedefinitionofs3iss3=Area1T2,s3P0,1(2)whereAreaIisthecontactareaandTistheedgelengthofthetestgrid.Onthebasisofabovethreeattributetags,theSIAofasamplepointpu,vcanbegivenbyanumericalvalueaccordingtothefollowingrules:ifs1=OutsideOuterLoop,SIA=21(inaccessible)；ifs1OutsideOuterLoopANDs2