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英文原文THESTRUCTUREDESIGNANDKINEMATICSOFAROBOTMANIPULATORml.THEORYKESHENGWANGandTERJEK.LIENProductionEngineeringLaboratory,NTHSINTEF,N7034Trondheim,NorwayArobotmanipulatorwithsixdegreesoffreedomcanbeseparatedintotwopartsthearmwiththefirstthreejointsformajorpositioningandthewristwiththelastthreejointsformajororienting.Ifweconsidertheconsecutivelinkstobeparallelorperpendicular,only12armandtwowristconfigurationsarepotentiallyusefulanddifferentforrobotmanipulatormechanicaldesign.Thiskindofsimplificationcanleadtoageneralalgorithmofinversekinematicsforthecorrespondingconfigurationofdifferentcombinationsofarmandwrist.Theapproachesforcalculatingtheinversekinematicsofarobotmanipulatorareveryefficientandeasy.Theapproachesforcalculatingtheinversekinematicsofarobotmanipulatorareveryefficientandeasy.1.INTROUCTIONArobotmanipulatorconsistsofanumberoflinksconnectedtogetherbyjoints.Inrobotmanipulatordesign,theselectionofthekinematicchainoftherobotmanipulatorisoneofthemostimportantdecisionsinthemechanicalandcontrollerdesignprocess.Inordertopositionandorienttheendeffectoroftherobotmanipulatorarbitrarily,sixdegreesoffreedomarerequiredthreedegreesoffreedomforpositionandthreedegreesoffreedomfororientation.Eachmanipulatorjointcanprovideonedegreeoffreedom,andthusamanipulatormusthaveaminimumofsixjointsifitistoprovidesixorthogonaldegreesoffreedominpositionandorientation.Theconstructionofmanipulatorsdependsonthedifferentcombinationofjoints.ThenumberofpossiblevariationsofanindustrialrobotstructurecanbedeterminedasfollowsV6thwhereVnumberofvariations.DFnumberofdegreesoffreedomTheseconsiderationsshowthataverylargenumberofdifferentchainscanbebuilt,forexamplesixaxis46,656chainsarepossible.6However,alargenumberisnotappropriateforkinematicreasons.Wemaydividethesixdegreesoffreedomofarobotmanipulatorintotwopartsthearmwhichconsistsofthefirstthreejointsandrelatedlinksandthewristwhichconsistsofthelastthreejointsandrelatedlinks.Thenthevariationsofkinematicchainswillbetremendouslyreduced.Lienhasdevelopedtheconstructionsofarmandwrist,i.e.20differentconstructionsforthearmandeightforthewrist.2Inthispaper,weabbreviatethe20differentarmsinto12kindsofarmswhichareusefulanddifferent.Weconcludethatfivekindsofarmsandtwokindsofwristsarebasicconstructionsforcommercialindustrialrobotmanipulators.Thiskindofsimplificationmayleadtoageneralalgorithmofinversekinematicsforthecorrespondingconfigurationofdifferentcombinationsofarmandwrist.2.STRUCTUREDESIGNOFROBOTMANIPULATORSInthispaper,foroptimumworkspaceandsimplicity,weassumethataArobotwithsixdegreesoffreedommaybeseparatedintotwopartsthelinkageconsistingofthefirstthreejointsandrelatedlinksiscalledthearmthelinkageoftheremainingjointsandrelatedlinksiscalledthewrist.bTwolinksareconnectedbyalowerpairjoint.Onlyrevoluteandlinearjointsareusedinrobotmanipulators.cTheaxesofjointsareeitherperpendicularorAccordingtotheauthorsknowledge,thisassumptionissuitableformostcommerciallyusedindustrialrobotmanipulators.Wecanconsiderthestructureofarmandwristseparately.2.1.ThestructureofthearmofrobotmanipulatoraGraphicalrepresentation.Todrawarobotinsidevieworinperspectiveiscomplicatedanddoesnotgiveaclearpictureofhowthevarioussegmentsmoveinrelationtoeachother.Todrawarobotinaplanesketcheddiagramistoosimpleanddoesnotgiveaclearconstructionpicture.Wecompromisethisprobleminasimplethreedimensionaldiagramtoexpresstheconstructionandmovementsofarobotmanipulator.AtypicalformofrepresentationfordifferentarticulationsisshowninTable1.bCombinationofjoints.WeuseRtorepresentarevolutejointandLtorepresentalinearjoint.DifferentcombinationsofjointscanbeobtainedasfollowsAccordingtothedifferentcombinationswiththeparallelorperpendicularaxes,eachpreviouscombinationhasfourkindsofsubcombination.Thus,32combinationscanbearrivedatIfthesecondjointisalinearjointandboththeotherjointsareperpendiculartoit,twochoicesinrelationtothefirstandthethirdjointsareconsideredparallelorperpendicular.Inall,thereare36possiblecombinationsofasimplethreejointarm.Nineof36possiblecombinationsdegenerateintooneortwodegreesoffreedom.Sevenoftheremainderareplanarmechanisms.Thus,thereare20possiblespatialsimplearms.LetusconsiderR11L2IL3inwhichthefirstjointpermitsrotationabouttheverticalaxis,thesecondjointisaverticallinearjointi.e.paralleltothefirst,andthethirdjointisahorizontallinearjointi.e.perpendiculartothesecond.Thisarmdefinesatypicalcylindricalrobot.Changingthesequentialorderofthejointssothateitheratheverticallinearjointprecedestherotaryjoint,orbtheverticallinearjointfollowsthehorizontalone,willresultinnochangeinthemotionofthearm.Inthiscasetherearetwolinkageswhicharebothequivalenttothestandardcylindricallinkage.Inallsuchcaseswheretwoormoreequivalentlinkagesexist,therepresentativeofthegroupwillbetheoneinwhichthelinearjointthatisparalleltoarotaryjointisinthemiddlejointNo.2.Countingonlyonelinkagetorepresentthegroupofequivalentswilleliminateeightofthe20combinations.Theremaining12categoriesoflinksareusefulanddifferentshowninFig.1.WegetthesameresultsasinRef.4.cFivebasictypesofmanipulatorarm.Althoughthereare12usefulanddifferentarmconfigurationswhichcanbeusedinthedesignofarobotmanipulatorarm,inpracticeonlysomeofthemarepracticalandcommonlyused.Wefindthatmostcommerciallyavailableindustrialrobotscanbebrokendownintoonlyfivegroupsaccordingtothe.characteristicsoftheirarmmotionandgeometricalappearance.ThefivegroupscanbedefinedasfollowsandareshowninFig.6.1.CartesianLILIL2.CylindricalRIIL1L3.SphericalRIRIL4.RevoluteRIRIIR5.DoublecylindricalLIIRIIR.2.2.Thestructureofamanipulatorwrist
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