基于聯(lián)動(dòng)機(jī)制理論自動(dòng)化組合夾具規(guī)劃 畢業(yè)設(shè)計(jì)論文外文文獻(xiàn)翻譯

Automatedmodularfixtureplanningbasedonlinkagemechanismtheory1.IntroductionModularfixtureisakindofverypromisingflexiblefixturedevicesinmanufacturing.Itisalsousedinassemblyandverificationprocesses.Theuseofmodularfixtureseemstobeatrendinthemanufacturingfieldasitcanmeetthedesireforgreaterflexibility(i.e.itisabletodealwiththeworkpieceswithirregularshapesbycombiningmodularfixtureelements).Byusingmodularfixtures,theflexibilityandrapidresponsecapabilityofmanufacturingsystemscanbeimproved.However,modularfixtureplanningisaverydifficultproblem,especiallyforthemodularfixturewiththedowel-pinsystemasthelocatorsofsuchmodularfixturescanonlybeinsertedintothefixeddoweledholes.Thatiswhymodularfixtureplanningisstillperformedbyfixturedesignersinindustriesuptonow,relyingondesigner′sexperiencesandtrialanderrormethod.Themainproblemwithmanualplanningofmodularfixturesliesinthatitisalmostimpossibleforadesignertoenumerateallthealternativefixtureplans,whichmakesitextremelyhardtofindouttheoptimalfixtureplan.Obviouslyithinderstheuseofmodularfixtureswithdowel-pinsysteminindustries.Onewaytosolvetheaboveproblemsistousecomputertoassistdesignersinperformingmodularfixtureplanning.Inrecentyears,theresearchonautomatedmodularfixtureplanninghasbeenpaidmoreandmoreattention,andseveralapproacheshavebeenproposedinthisarea.AsadaandBy[1]describedthebasicconceptofanadaptablefixturingsystemanditshardwareimplementation.Theanalytictoolofthefixturewasdeveloped,includingthatofaccessibilityanddetachability.Thekeycomponentsofthissystemarefixturebasetablewithmagneticchuckingcapability.Suchasystemisadaptableforflexibleassemblyandtheproductwithsmallbatchsize.BrostandGoldberg[2]andBrostandPeters[3]presenteda“complete”algorithmforsynthesizingmodularfixturesforapolygonalworkpiece.Thebasicassumptionsoftheirmethodarethataworkpiececanberepresentedwithsimplepolygons;locatorscanberepresentedbyacirclewhoseradiusislessthanhalfofthegridspacing;thefixturingconfigurationsareinfiniteandallcontactsarefrictionless.Theoutputofthealgorithmincludesthepositionsofthreelocatorsandtheclamppoint,aswellasthelineardisplacementandrotationalangleoftheworkpiecerelativetothebaseplate.Theirmethodforfindingoutthethreelocatorsofagivenworkpieceisbasedontheenumerativealgorithm.Zhuangetal.[4]exploredtheexistenceofmodularfixturesolutionsforagivenfixtureconfigurationmodelandaworkpiece,andpresentedaclassofpolygonswhichcannotbefixedbymodularfixtureswithdowel-pinsystem.WallackandCanny[5]developedanautomateddesignalgorithmforafixturingtoolkitcalledthefixturevise,whichinvolvestwofixtureplatesmountedonjawsofaviseandmodularfixtureelements.Theyalsoproposedanoutput-sensitivealgorithm.Thealgorithmfirstenumeratesallthequartetsofthejaw-specifiededgesegmentscapableofprovidingforceclosure,thenforeachedgequartetenumeratesallthequartetsoffixturepositions,verifiesforceclosure,andgeneratesalltheconfigurationsofamodularfixturingtoolkitcapableofimmobilizingagivenprismaticobject.PenevandRequicha[6]studiedthefixturefoolproofingforpolygonalworkpiecesandpresentedanalgorithmforcalculatingthepositionsoffoolproofingpinsthatmaketheincorrectloadingposeimpossible.Overmarsetal.[7]introducedapoint/edgefixtureparadigmwhereinobjectsareimmobilizingbyacombinationofoneedgeandtwopointcontacts.Wagneretal.[8]studiedthemethodoffixturing3Dfacetedpartswithsevenmodularstruts.Wuetal.[9,10]presentedasystematicmethodforanalyzingthegeometry,accuracy,clampingandaccessibilityofamodularfixture.Intheirmethod,threelocator-workpiececontactsituationsaredeterminedaccordingtothetypesoflocatingfacesandthetypesofcontactingfacesoflocators,andtheassemblyrelationshipsbetweenlocatorsandtheworkpiecearedescribedbythreetrianglefunctionequations.Bysolvingthethreeequations,thepositionoftheworkpiecerelatedtothefixtureandthepositionsofthreelocatorsareobtained.Basedonthedegree-of-freedomanalysisof2-Dobjects,astep-by-stepalgorithmisdevelopedtofindoutthepossibleclamppositionsbyenumeratingallthepossibleclampingedges.Theirmethodisfeasibleandsystematic,butitiscomplicatedanditscomputationefficiencyneedstobefurtherimproved.Theinvestigationonoptimizationalgorithmsoffixturedesignisalsorelatedtothiswork.Inthisaspect,KingandHutter[11]presentedamethodforoptimalfixturelayoutdesign,whichusestherigidbodymodelofafixture–workpiecesystembutaccountsforthecontactstiffness.DeMeter[12,13]usedarigidbodyfixture–workpiecemodelandthemin–maxloadcriteriontoachievethesynthesisoftheoptimalfixturelayoutandminimumclampactuationintensity,andpresentedafiniteelement-basedmethodofsupportinglayoutoptimization.However,thesenonlinearprogrammingmethodscanneitherachieve“global”or“near-global”optimumsolutionsnordeterminethelocatorsandclamppositionsexplicitly.Inaddition,themodelsusedareverysensitivetotheinitialfeasiblefixturelayout.Duringthelastdecade,afewresearchersutilizedgeneticalgorithmtosolvethisproblem.WuandChan[14]usedthegeneticalgorithmtodeterminethemoststaticallystablefixturelayout.IshikawaandAoyama[15]adoptedthegeneticalgorithmtodeterminetheoptimalclampingconditionforanelasticworkpiece.KrishnakumarandMelkote[16]presentedamethodofachievingfixturelayoutoptimizationusinggeneticalgorithm,inwhichafinite-elementapproachisemployedtoevaluatethegeneratedfixturelayouts.WangandPelinescu[17]developedanalgorithmoffixturelayoutoptimizationbasedonaccuratelocalization,minimallocatorcontactforceandbalancedlocatorcontactforce.Mervynetal.[18]presentedanapproachtoautomatedsynthesisofmodularfixturedesignsusinganevolutionarysearchalgorithm.Ingeneral,thecurrentachievementsoncomputer-aidedmodularfixturedesignstillhaveacertaindistancefromwhatindustriesexpect.Themainlimitationsofthecurrentworksinclude:(1)becausetheassemblyrelationshipsbetweenlocatorsandtheworkpiecearenotdescribedinananalyticway,thecurrentmethodsofdetermininglocationplansareenumerativeinnatureandthusverytimeconsuming;(2)thecurrentapproachestodeterminationofthesideclampingpositionsarerelativelycomplex;(3)theexistingqualitymetricsaboutfixturedesigndonotconsiderthegeometrystructureoftheworkpieceandtheassemblyrelationshipbetweentheworkpieceandlocatorswhichalsoaffectthequalityoflocationplans.Inthispaper,wepresentanewapproachtoautomatedplanningofmodularfixtureswithdowel-pin.Theapproachidentifiesallthealternativelocationplansofaworkpiececomprisingbothplanarandcylindricalfacesinageneralandefficientwaybyusingfour-barmechanismtheory,andperformsaccessibilityandfixturabilityanalysisandgeneratesfeasibleclamppositionsofafixtureplaninaneffectivemannerbasedonseveralnewconcepts.Intheapproach,theassemblyrelationshipbetweenlocators,sideclampingpointsandworkpiecearedescribedinananalyticway.Theapproachisintendedtobemoregeneralandmorerobust.2.Identificationoflocatingplancandidates2.1.ProblemstatementandmethoddescriptionInthispaper,weassumethattheprimarylocatingfacesetoftheworkpiecehasbeendetermined,whichcouldbeasingleplanarfaceorconsistsoftwoorthreeparallelplanarfaceswithdifferentheights,andassumethatthesecondaryandtertiarylocatingfacesareperpendiculartotheprimarylocatingface(s),butunlikethosein3–2–1locatingscheme,theyneednotbeperpendiculareachother.Consideringthatinmostfixturedesigns,onlyplanarandcylindricalfacesareselectedaslocatingfaces,especiallyformodularfixtureapplications[10],theworkpieceinthisworkislimitedtothepartwhosesideclampingfacesconsistofplanarandcylindricalfaces.Withoutlossofgenerality,wefurtherassumethatthetopfaceofthemodularfixture’sbaseplateisthesupportfaceoftheworkpieceanditiscoplanarwiththeprimarylocatingfaceoftheworkpiece.Thenitindicatesthatafteraworkpieceisputonthebaseplateofamodularfixture,itsthreeDOFsareconstrained.Inordertomaketheworkpiececompletelyfixed,theremainderthreeDOFsoftheworkpieceneedtobeconstrainedaswell.Foramodularfixturewithdowel-pin,threeroundlocatorswitheachoneinsertedintoadoweledholeandcontactedwithasidefaceoftheworkpieceareusedtocompletelylocatetheworkpiece.Thethreelocatorsthatcancompletelylocatetheworkpiecearecalledalocationplanoftheworkpiece.Obviously,noteverythreelocatorsinsertedintothearbitrarythreedoweledholescanformalocationplanoftheworkpiece.Therefore,howonecanidentifyallthealternativelocationplansbecomestheissuethatneedstobesolvedfirst.Basedontheassumptionthatthesecondaryandtertiarylocatingfacesoftheworkpieceareperpendiculartoitsprimarylocatingface(s),theproblemofidentifyinglocationplansofaworkpiececanbeconvertedtoa2Dproblem.Fig.1isusedtoillustratethis,whichshowsthebaseplate’stopfaceofamodularfixturewithdowel-pin,theprojectionoftheworkpieceonthebaseplate’stopface,andalocationplancandidate.Inthefigure,“o”standsforthelocatingholeusedtofixtheroundlocators,“x”referstothetappedholeusedtoconnectfixtureelements,andthedashedlinesrefertotheoffsetoftheworkpiece’sprofileonthebaseplate.Here,theoffsetdistanceisequaltotheradiusofthelocator.WiththehelpofFig.1,wecanclearlydescribetheproblemofidentifyingalocationplancandidateasfollows:toidentifyalocationplancandidateistofindoutthreedoweledholesonthebaseplatethatsatisfyfollowingtwoconditions:first,theworkpiececanbeputonthebaseplatewiththeoffsetoftheworkpiece’sprofileprojectedonthebaseplatebeingthroughallthethreedoweledholes’centers(notethattheworkpiece’sprofileherejustconsistsoftheprojectionsoftheplanarandcylindricalfacesoftheworkpiecethatareperpendiculartotheprimarylocatingface);second,whenthreeroundlocatorsareinsertedintothethreedoweledholesandaclampforceisimposedontheworkpiecefromaproperposition,theworkpiecewillbecompletelyfixed.Asanexample,inFig.1threeroundlocatorsa,bandc,whichareinsertedintothreedoweledholes,formalocationplancandidateoftheworkpiece.Accordingtothedegree-of-freedomanalysis,a2Dobjectcanbelocatedintwoways:(a)twoboundaryedgesofthe2Dobjectarerestrictedbythreefixedpoints,withoneedgerestrictedbytwofixedpoints,andtheotherrestrictedbythethirdfixedpoint;(b)threeboundaryedgesofthe2Dobjectarerestrictedbythreefixedpoints,witheachedgerestrictedbyonefixedpoint.Inviewthattheway(a)isanextensionofthetraditional3–2–1locationrule[20]andthelocationplansrespondingtosuchlocationwayareeasytobedetermined,onlythesecondlocationwayisconsideredinthispaper.Ourapproachtoidentifyingalocationplanconsistsoftwosteps:first,determinethefirsttwodoweledholeswhosecentersareontheoffsetoftheworkpiece’sprofile;second,identifythethirddoweledholewhosecentersareontheoffsetoftheworkpiece’slocatedprofile.Toeffectivelyidentifythethirddoweledhole,thefour-barmechanismandlinkagecurveareemployedinourapproach,whichisillustratedbyFig.2.InFig.2,Mstandsforafixedplane,aandbaretwocurvesontheplaneM,thetriangleM1standsfora2DregiononM,andA,BaretwofixedpointsofM1.SupposeM1movesintheMinthewaykeepingAandBtomovealongthecurveaandb,respectively,thenthelocusofanarbitraryfixedpointCinM1formsaslidecurve.Particularly,whenaandbareeitherlinearorcircular,themotionofM1relativetoMisalinkageplanemotion,andthusthecorrespondinglocusofthepointCinM1isalinkagecurve.Sinceaandbarethelocioftwohingepointsofthelinkageplaneaccordingtothefour-barlinkagemechanismtheory[21],hereafter,a,barecalledhingepointloci,andA,Barecalledhingepoint.Inordertodeterminethethirddoweledholeofalocationplancandidateusinglinkagemechanismtheory,weconstructafour-barmechanismandalinkagecurveasfollows:takingtheprimarylocatingfaceoftheworkpieceasM,thebaseplateasM1,thecentersofthefirsttwodoweledholesonthebaseplateastwohingepointsAandB,andtwooffsetedgesthatthefirsttwodoweledholes’centersare,respectively,onastwohingepointlociaandb.Sincealltheedgesoftheworkpiececonsideredinthisworkareeitherlinearorcircular,therelativemotionofthebaseplatetotheworkpieceisexactlyalinkageplanemotionaccordingtothemechanismtheory,andthelocusofthecenterofanyotherdoweledholeexceptthefirsttwodoweledholesisalinkagecurve.Herethelinkagecurveisasingleparametriccurveandthecurveparameterisalsoapositionparameteroflinkagemechanism.Therefore,ifthelinkagecurveintersectswithanyotheroffsetedgeoftheworkpiece’sprofileexceptaandb,thecorrespondingdoweledholeoflinkagecurveisthethirddoweledholethatcanformapotentiallocationplanwiththefirsttwodoweledholes[21].Therelativepositionoftheworkpiecewiththebaseplateoffixturecanbedeterminedbycalculatingtheparametricvalueofintersectionpoint,andtherelativepositionsoffirsttwolocatorstotheworkpiececanalsobedetermined.Itshouldbepointedoutthatbecausefour-barmechanismandlinkagecurvecaneffectivelyrepresenttheassemblyrelationshipbetweenlocatorsandtheworkpiece,itismorestraightforwardandefficienttodeterminethepositionofthethirdlocatorusingthelinkagemechanismtheorythanusingotheranalysismethodssuchasthescrewtheoryandforceclosureanalysisalthoughthelatterisveryusefulforanalyzingtheclosureofthesidelocatingandsideclampingoftheworkpieceaftertheyaredetermined.2．2AlgorithmfordetermininglocationplancandidatesThealgorithmfordetermininglocationplancandidatesisdividedintothefollowingtwoparts:(1)Determinationofthefirsttwodoweledholes:inordertodeterminealllocationplancandidates,thefirsttwodoweledholesofallthelocationplancandidatesaredeterminedfirst.Wedivideallthefirsttwodoweledholesintotwocases:oneisthatthetwocentersofthetwodoweledholesareonthesameoffsetedgeoftheworkpiece’sprofile;theotheristhattheyareonthedifferentoffsetedges.Inthiswork,wedetermineallthefirsttwodoweledholesusinganapproachsimilartothatofBrostandGoldberg[3],bywhichthetwocasesofthefirsttwodoweledholesarehandledindifferentways,asshowninFig.3.Duetothespacelimitation,thespecificalgorithmisnotdescribedhere.(2)Determinationofthethirddoweledhole:giventhefirsttwodoweledholeswhosecentersP1andP2aresupposedtobeontwodifferentoffsetedgesE1andE2oftheworkpiece’sprofile,asshowninFig.4,wefindoutthesetofthethirddoweledholethatcanformalocationplancandidatewiththefirsttwodoweledholesusinglinkagemechanismtheory.Thealgorithmconsistsofthefollowingthreesteps:(a)Determinethetypeofthesimulatedlinkagemechanismanditsmotionparameterrange.ThesimulatedlinkagemechanismtakesP1P2asitslinkage,E1andE2asitstwohingepointloci.AccordingtothetypesofE1andE2,thetypeofthelinkagemechanismcanbeeasilydeterminedasfollows:IfbothE1andE2arecircularedges,thecorrespondinglinkagemechanismisahingedfour-barmechanism;IfbothE1andE2arelinearedges,thecorrespondingsimulatedmechanismisadouble-slidermechanism;ifonehingepointlocusislinearandtheotheriscircular,thecorrespondingmechanismisacrank-slidermechanism.Becauseeveryedgepaircandefineasimulatedlinkagemechanism,themaximumnumberofthesimulatedlinkagesforapolygonwithnlocatingedgesis.Afterthetypeofasimulatedlinkagemechanismisdetermined,thevalidmotionparameterrangeofthesimulatedlinkagemechanismiscalculatedaccordingly,whichisaffectedbyseveralfactorssuchasthepositionsofthestartandendpointsofhingepointloci,andtheconfigurationofthesimulatedlinkagemechanism[19].(b)Establishthesetofpotentialthirddoweledholesforeachoffsetedgeoftheworkpiece’sprofile.Wefindoutthosefromallthedoweledholesonthebaseplatewhosecenters’locihavepossibilitytointersectwiththeoffsetedgeduringthemovingofthesimulatedlinkagemechanism,andtheyformthesetofpotentialthirddoweledholes(calledDHShereafter)oftheoffsetedge.HerenotethatoffsetedgesE1andE2aswellasthoseedgesparallelwithE1orE2areexcludedbecausewhenthethirdlocatorcontactswithsuchedgesitcannotformavalidlocationplanwiththefirsttwodoweledholes.Specifically,theDHSofanoffsetedgeoftheworkpiece’sprofileisdeterminedbyfirstcalculatingthesweepingregionformedbytherelativemotionoftheoffsetedgetothebaseplateduringthemovingofthesimulatedlinkagemechanism,thenfindingoutallthedoweledholesinthesweepingregion.(c)DeterminethevalidthirddoweledholesfromDHS.ForeachpotentialthirddoweledholeintheDHS,wecheckifitisavalidthirddoweledholebycalculatingtheparametricvalueoftheintersectionpointbetweenthelocusofthehole’scenterandthecurrentoffsetedgeoftheworkpiece’sprofile.Consideringthatthelinkagecurveisaparametriccurvewithhighorder,wefirstsearchtheintersectioninparameterspacewithafixedstep,andthencalculatetheparametricvaluebydichotomymethod.LettheparameterrangeofthecurrentoffsetedgeEbe(v1,v2)andthemotionparameterrangeofthesimulatedlinkagemechanism,i.e.thedefinedparameterrangeofthelocusLE,be(u1,u2),ifthereexistsanintersectionpointIbetweenLEandE,anditsparametricvalueonLEandEare,respectively,uandvsatisfyingu1ouou2andv1ovov2,itindicatesthatLEintersectswithEintheirinteriors,andthedoweledholewhosecenter’slocusisLEisdeterminedasthethirddoweledholethatcanformalocationplancandidateoftheworkpiecewiththefirsttwodoweledholes.Forinstance,asshowninFig.4,thedoweledholewhosecenterisP3isdeterminedasthethirddoweledholewhichformsalocationplancandidatewiththefirsttwodoweledholesatP1andP2sinceitslinkagecurveLEintersectswithoffsetedgeE3intheirinteriors.中文翻譯：基于聯(lián)動(dòng)機(jī)制理論自動(dòng)化組合夾具規(guī)劃RobertW.Irving和SandyScott英國(guó)1．簡(jiǎn)介在制造業(yè)中，組合夾具是一種非常有前景的柔性夾具裝置。它還可被用在裝配和檢驗(yàn)過程。在制造業(yè)領(lǐng)域，由于組合夾具能夠滿足制造業(yè)對(duì)更大的靈活性的渴望，組合夾具的使用似乎成為了一個(gè)趨勢(shì)（例如它能夠通過對(duì)組合夾具元素的有機(jī)結(jié)合來處理形狀不規(guī)則的工件）。通過采用組合夾具裝置，制造系統(tǒng)的柔性和快速反應(yīng)能力得到了改善。不過，組合夾具規(guī)劃是一個(gè)十分棘手的問題，尤其是對(duì)這種帶有定位銷的組合夾具系統(tǒng)，因?yàn)檫@種夾具的定位器只能被插入到固定的銷孔中。這就是為什么到現(xiàn)在為止，在現(xiàn)代工業(yè)中組合夾具的規(guī)劃仍然是由夾具設(shè)計(jì)師來施行，主要依賴于設(shè)計(jì)師的經(jīng)驗(yàn)和審視判斷和糾錯(cuò)的方法。這種人工規(guī)劃的組合夾具方案主要問題在于：一個(gè)設(shè)計(jì)師根本不可能列舉所有的夾具備選計(jì)劃方案，這使得我們非常迫切需要找出一個(gè)最佳的夾具規(guī)劃。很明顯，它阻礙了這種帶有定位銷系統(tǒng)的組合夾具在現(xiàn)代工業(yè)當(dāng)中的使用。其中一個(gè)解決上述問題的方法，就是使用電腦協(xié)助設(shè)計(jì)師來實(shí)施組合夾具規(guī)劃。近年來，在組合夾具規(guī)劃的自動(dòng)化研究方面受到了越來越多的關(guān)注，并且在這個(gè)領(lǐng)域內(nèi)已經(jīng)提出了幾種解決方法。Asada和By[1]描述了一個(gè)多適應(yīng)性夾具系統(tǒng)的基本概念，以及其硬件的實(shí)現(xiàn)。在夾具的開發(fā)過程中，包括可實(shí)現(xiàn)性和可分離性的解析工具得到了較快的發(fā)展。這個(gè)系統(tǒng)的關(guān)鍵組成部分是固化在它的磁夾持能力的基本表中。這樣一個(gè)系統(tǒng)是為適應(yīng)柔性裝配和產(chǎn)品小批量生產(chǎn)。Brost和戈德堡[2]與Brost和彼得斯[3]給一個(gè)多邊形工件提交了一份“完整”算法的模塊化合成裝置。他們的研究方法的基本假設(shè)是一個(gè)工件可以用簡(jiǎn)單多邊形表示；定位可以用一個(gè)半徑不到一半網(wǎng)格間距的圓圈來表示；裝夾配置是無限的和并且所有接觸都是無摩擦的。該算法的輸出結(jié)果包括三個(gè)定位點(diǎn)的位置和夾緊點(diǎn)，以及工件相對(duì)底板的直線位置距離和旋轉(zhuǎn)角度。他們計(jì)算出某一個(gè)給定工件的三個(gè)定位點(diǎn)的方法，是基于枚舉算法的。莊等人[4]，探討了對(duì)于某一個(gè)給定夾具配置的模型和某一工件存在的組合夾具解決方案，并提出了一類不能用固定銷系統(tǒng)的模塊化夾具來定位的多邊形。Wallack和Canny[5]開發(fā)出一種自動(dòng)設(shè)計(jì)算法的一個(gè)工具包，所謂的裝夾夾具簽證，其中涉及到兩個(gè)夾具板裝在一個(gè)簽證上的關(guān)鍵點(diǎn)和模塊化了的夾具元件。他們還提出了一個(gè)敏捷輸出的算法。該算法首先列舉了所有四個(gè)一組的具有提供封閉力能力的指定關(guān)鍵點(diǎn)邊緣部分，然后為每個(gè)邊緣組列舉所有的夾具位置組，驗(yàn)證力的封閉性，并產(chǎn)生所有模塊裝夾工具包配置，能夠固定某一給定的柱狀目標(biāo)。Penev和Requicha[6]研究多邊形工件的傻瓜校對(duì)夾具，并且為簡(jiǎn)單校核定位銷的位置確定提出了一個(gè)合適的算法，使這種不正確的位置確定情況成為不可能的。奧維馬斯等人[7]提出了一個(gè)點(diǎn)/邊的夾具范例，其中的物體的固定的，由一個(gè)邊和兩個(gè)點(diǎn)相互結(jié)合的接觸。Wagner等人[8]研究的方法，裝夾零件的三維面與7個(gè)模塊化的支撐。吳等人[9,10]介紹了一個(gè)組合夾具分析方法的幾何性，準(zhǔn)確性，夾緊和無障礙性系統(tǒng)的方法。在他們的方法中，三個(gè)定位點(diǎn)的工件接觸的情況決定于定位面的類型和定位器接觸面的類型，并且定位器和工件之間的裝配關(guān)系是用三個(gè)三角函數(shù)方程描述的。通過求解三個(gè)方程，工件和夾具之間的位置關(guān)系以及三個(gè)定位器的位置就可以得到了?；诙S物體自由度的分析，一步一步算法逐步發(fā)展起來，該方法就是要找出夾緊位置的可能性，通過列舉了所有可能的夾緊力邊緣。他們的方法是可行的和系統(tǒng)的，但是它的復(fù)雜性和其計(jì)算效率需要進(jìn)一步改善。對(duì)夾具設(shè)計(jì)的優(yōu)化算法的研究，同樣也關(guān)系到這方面的工作。在這方面，King和Hutter[11]介紹了一種為夾具布局進(jìn)行優(yōu)化設(shè)計(jì)的方法，該方法是通過一個(gè)夾具-工件系統(tǒng)的剛體模型，但是計(jì)算接觸剛度。DeMeter[12,13]用了一個(gè)剛體夾具-工件模型和Min-Max的負(fù)荷標(biāo)準(zhǔn)，以達(dá)到合成的優(yōu)化夾具布局和最低夾緊強(qiáng)度，并提出了有限元為基礎(chǔ)的方法，支持布局優(yōu)化。然而，這些非線性規(guī)劃的方法，既不能達(dá)到“總體性”或“近總體性”最佳解決方案，也不能確定定位器和夾緊的位置明確性。此外，該模型在初步可行的夾具布局中的使用是非常敏捷的。在過去十年中，有幾個(gè)研究人員利用傳統(tǒng)算法來解決這個(gè)問題。吳和陳[14]用遺傳算法，以確定最穩(wěn)定的靜態(tài)夾具布局。Ishikawa和Aoyama[15]通過遺傳算法為彈性工件確定最佳的夾緊條件。Krishnakumar和Melkote[16]提出了一種方法，利用遺傳算法實(shí)現(xiàn)夾具布局優(yōu)化，就是通過一個(gè)有限元的算法來評(píng)估所產(chǎn)生的夾具布局。王和佩利內(nèi)斯庫[17]研究出一種算法的夾具布局優(yōu)化的基礎(chǔ)上準(zhǔn)確定位，最小的定位接觸力和平衡的定位接觸力。默文等人[18]介紹了一種方法自動(dòng)合成的組合夾具設(shè)計(jì)，通過使用一個(gè)漸進(jìn)的搜索算法實(shí)現(xiàn)夾具的設(shè)計(jì)。一般的來說，電腦輔助組合夾具設(shè)計(jì)目前的所取得成就同機(jī)械行業(yè)的渴望仍然存在一定距離。目前工程的主要局限性包括：（1）因?yàn)槎ㄎ黄骱凸ぜg的定位關(guān)系并沒有在分析方法中被描述，目前的確定位置的方法是枚舉性質(zhì)的，因而非常耗費(fèi)時(shí)間;（2）目前的做法，以測(cè)定一側(cè)夾緊位置是較為復(fù)雜的;（3）現(xiàn)行的夾具設(shè)計(jì)品質(zhì)指標(biāo)并不考慮工件的幾何結(jié)構(gòu)和工件與定位器之間的裝配關(guān)系，這也影響到質(zhì)量的位置圖。

在本文中，我們提出了一種新的接近自動(dòng)規(guī)劃的帶有固定銷的模塊化夾具。該辦法利用四桿機(jī)構(gòu)的理論確定了工件所有替代的位置規(guī)劃，以及組成的平面和圓柱所面對(duì)的普遍和有效的方式，并且執(zhí)行可接近性和可夾持性的分析，并基于幾個(gè)新的概念通過有效的方法夾具規(guī)劃當(dāng)中產(chǎn)生具有可行性的夾持位置。在這種方法中，定位器、側(cè)邊的夾持點(diǎn)以及工件之間的裝配關(guān)系是用一種分析方法來描述的。這種方法的應(yīng)用正逐步變的更為寬泛和更為強(qiáng)大。2．確定預(yù)選定位規(guī)劃方案2．1問題陳述和方法說明在本文中，我們假定在一個(gè)工件上已經(jīng)確定了一個(gè)主要的定位面，而這個(gè)定位面有可能是由一個(gè)單一的平面構(gòu)成的或則是由兩個(gè)或是三個(gè)高度不同的平行面組成的，并且假設(shè)第二個(gè)和第三定位面與之前確定的那個(gè)主要定位面之間相互垂直，但是又不同于那些3-2-1定位方案，他們之間不需要相互垂直對(duì)方。考慮到在大多數(shù)夾具設(shè)計(jì)，只有平面和圓柱面的被確定為定位平面，特別是在組合夾具的應(yīng)用上[10]，在這種方法中，只限用于那些以平面或是圓柱面作為夾緊邊的工件。在不否定一般情況的情況下，我們不妨進(jìn)一步假設(shè)組合夾具底板的上表面是工件的支持面并且是與工件的主要定位面共面的。這樣的話，當(dāng)一個(gè)工件放到組合夾具的底板上時(shí)，它的三個(gè)自由度就完全被約束了。在為了使工件完全固定，工件的其余三個(gè)自由度也需要加以約束。因?yàn)橐粋€(gè)帶有定位銷和3個(gè)圓周定位器的組合夾具要完全固定一個(gè)工件，必須使每個(gè)銷子都插入到銷孔當(dāng)中并且有一個(gè)面與工件接觸。能夠完全使工件定位的三個(gè)定位器就叫做工件的定位方案。很顯然，并不是任意3定位器插入到任意三個(gè)銷孔都可以形成一個(gè)工件定位方案。因此，一個(gè)人如何可以判別出所有的可替換的定位方案就成為了首先要解決的問題了?；诘诙€(gè)和第三定位面與之前確定的那個(gè)主要定位面之間相互垂直這樣的假設(shè)，工件定位方案的判別問題就可以轉(zhuǎn)換為二維問題。圖1就是用來說明這一點(diǎn)的，圖上表明組合夾具的底板上表面上固定著定位銷，以及工件在底板上表面上的投影圖，和一個(gè)定位方案的備選方案。在這個(gè)圖形中，“O”代表著用來固定圓形定位器的定位孔，“X”是指用來連接夾具元素的孔，虛線指以工件的剖面線在底板上的偏移量。在這里，偏移距離等于定位器的半徑。借助圖1，判別一個(gè)定位方案的預(yù)選方案的問題，我們可以很清楚地描述如下：找到一個(gè)定位方案的預(yù)選方案，就是要在底板上