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英文原文THESTRUCTUREDESIGNANDKINEMATICSOFAROBOTMANIPULATORml.THEORYKESHENGWANGandTERJEK.LIENProductionEngineeringLaboratory,NTH-SINTEF,N-7034Trondheim,NorwayArobotmanipulatorwithsixdegreesoffreedomcanbeseparatedintotwoparts:thearmwiththefirstthreejointsformajorpositioningandthewristwiththelastthreejointsformajororienting.Ifweconsidertheconsecutivelinkstobeparallelorperpendicular,only12armandtwowristconfigurationsarepotentiallyusefulanddifferentforrobotmanipulatormechanicaldesign.Thiskindofsimplificationcanleadtoageneralalgorithmofinversekinematicsforthecorrespondingconfigurationofdifferentcombinationsofarmandwrist.Theapproachesforcalculatingtheinversekinematicsofarobotmanipulatorareveryefficientandeasy.Theapproachesforcalculatingtheinversekinematicsofarobotmanipulatorareveryefficientandeasy.1.INTROUCTIONArobotmanipulatorconsistsofanumberoflinksconnectedtogetherbyjoints.Inrobotmanipulatordesign,theselectionofthekinematicchainoftherobotmanipulatorisoneofthemostimportantdecisionsinthemechanicalandcontrollerdesignprocess.Inordertopositionandorienttheendeffectoroftherobotmanipulatorarbitrarily,sixdegreesoffreedomarerequired:threedegreesoffreedomforpositionandthreedegreesoffreedomfororient-ation.Eachmanipulatorjointcanprovideonedegreeoffreedom,andthusamanipulatormusthaveaminimumofsixjointsifitistoprovidesixorthogonaldegreesoffreedominpositionandorientation.Theconstructionofmanipulatorsdependsonthedifferentcombinationofjoints.Thenumberofposs-iblevariationsofanindustrialrobotstructurecanbedeterminedasfollows:V=6thwhereV=numberofvariations.DF=numberofdegreesoffreedomTheseconsiderationsshowthataverylargenumberofdifferentchainscanbebuilt,forexamplesixaxis46,656chainsarepossible.6However,alargenumberisnotappropriateforkinematicreasons.Wemaydividethesixdegreesoffreedomofarobotmanipulatorintotwoparts:thearmwhichconsistsofthefirstthreejointsandrelatedlinks;andthewristwhichconsistsofthelastthreejointsandrelatedlinks.Thenthevariationsofkinematicchainswillbetremendouslyreduced.Lienhasdevelopedtheconstructionsofarmandwrist,i.e.20differentconstructionsforthearmandeightforthewrist.2Inthispaper,weabbreviatethe20differentarmsinto12kindsofarmswhichareusefulanddifferent.Weconcludethatfivekindsofarmsandtwokindsofwristsarebasicconstructionsforcommercialindus-trialrobotmanipulators.Thiskindofsimplificationmayleadtoageneralalgorithmofinversekinema-ticsforthecorrespondingconfigurationofdifferentcombinationsofarmandwrist.2.STRUCTUREDESIGNOFROBOTMANIPULATORSInthispaper,foroptimumworkspaceandsim-plicity,weassumethat:(a)Arobotwithsixdegreesoffreedommaybeseparatedintotwoparts:thelinkageconsistingofthefirstthreejointsandrelatedlinksiscalledthearm;thelinkageoftheremainingjointsandrelatedlinksiscalledthewrist.(b)Twolinksareconnectedbyalowerpairjoint.Onlyrevoluteandlinearjointsareusedinrobotmanipulators.(c)TheaxesofjointsareeitherperpendicularorAccordingtotheauthorsknowledge,thisassumptionissuitableformostcommerciallyusedindustrialrobotmanipulators.Wecanconsiderthestructureofarmandwristseparately.2.1.Thestructureofthearmofrobotmanipulator(a)Graphicalrepresentation.Todrawarobotinsidevieworinperspectiveiscomplicatedanddoesnotgiveaclearpictureofhowthevarioussegmentsmoveinrelationtoeachother.Todrawarobotinaplanesketcheddiagramistoosimpleanddoesnotgiveaclearconstructionpicture.Wecompromisethisprobleminasimplethree-dimensionaldiagramtoexpresstheconstructionandmovementsofarobotmanipulator.AtypicalformofrepresentationfordifferentarticulationsisshowninTable1.(b)Combinationofjoints.WeuseRtorepresentarevolutejointandLtorepresentalinearjoint.Differentcombinationsofjointscanbeobtainedasfollows:Accordingtothedifferentcombinationswiththeparallelorperpendicularaxes,eachpreviouscombin-ationhasfourkindsofsub-combination.Thus,32combinationscanbearrivedat:Ifthesecondjointisalinearjointandboththeotherjointsareperpendiculartoit,twochoicesinrelationtothefirstandthethirdjointsareconsideredparal-lelorperpendicular.Inall,thereare36possiblecombinationsofasimplethree-jointarm.Nineof36possiblecombinationsdegenerateintooneortwodegreesoffreedom.Sevenoftheremainderareplanarmechanisms.Thus,thereare20possiblespatialsimplearms.LetusconsiderR11L2IL3inwhichthefirstjointpermitsrotationabouttheverticalaxis,thesecondjointisaverticallinearjoint(i.e.paralleltothefirst),andthethirdjointisahorizontallinearjoint(i.e.perpendiculartothesecond).Thisarmdefinesatypicalcylindricalrobot.Changingthesequentialorderofthejointssothateither(a)theverticallinearjointprecedestherotaryjoint,or(b)theverticallinearjointfollowsthehorizontalone,willresultinnochangeinthemotionofthearm.Inthiscasetherearetwolinkageswhicharebothequivalenttothestandardcylindricallinkage.Inallsuchcaseswheretwoormoreequivalentlinkagesexist,therepresentativeofthegroupwillbetheoneinwhichthelinearjointthatisparalleltoarotaryjointisinthemiddle(jointNo.2).Countingonlyonelinkagetorepresentthegroupofequivalentswilleliminateeightofthe20combinations.Theremaining12categoriesoflinksareusefulanddif-ferentshowninFig.1.WegetthesameresultsasinRef.4.(c)Fivebasictypesofmanipulatorarm.Althoughthereare12usefulanddifferentarm-configurationswhichcanbeusedinthedesignofarobotman-ipulatorarm,inpracticeonlysomeofthemarepracticalandcommonlyused.Wefindthatmostcommerciallyavailableindustrialrobotscanbebrokendownintoo
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