ABSTRACTArobotarmcomprisesafirstandasecondlink,thefirstlinkhavingaproximalendandadistalendandthesecondlinkhavingaproximalandadistalend.Afixedpulley,withcircumferentialsurfacesconcentricwiththefirstpivotaxisismountedattheproximalendofthefirstlink.Asecond-linkpulleyisfixedtothesecondlinkforrotationaboutthesecondpivotaxis.Anendeffectorpulleyisfixedtotheendeffectorforrotationaboutthethirdpivotaxis.Afirstbeltdriveisalsoprovidedandincludesoneormorebeltsconnectedbetweenthecircumferentialsurfacesofthefixedpulleyandthesecondlinkpulleysothatratationofthefirstlinkrelativetothefixedpulleyaboutthefirstpivotaxiscausesrotationofthesecondlinkaboutthesecondpivotaxisrelativetothefirstlink.Oneormoreidlerpulleysisprovidedandisrotatablymountedtooneorbothofthelinks.Atleastoneofthebeltdrivesincludesafirstbeltengagedwiththefirstcircumferentialsurfaceofanidlerpulleyandasecondbeltengagedwiththesecondcircumferentialsurfaceofthesameidlerpulley.16Claims,3DrawingSheets1ROBOTARMCROSSREFERENCETORELATEDAPPLICATIONThisapplicationclaimsthebenefitofU.S.ProvisionalpatentapplicationNo.60/122,184filedonMar.1,1999,thedisclosureofwhichisincorporatedbyreference.FIELDOFTHEINVENTIONThepresentinventionrelatestoarobotarmhavinganendeffectorlocatedattheremoteendoftherobotarmmaintamingthesameorientationregardlessofrotationalmovemenuofthearm.Therobotarmalsohasatleastoneidlerpulleylocatedwithinoneofthelinksthatallowthediameterofthejointstobeenlargedsothatwiresorotherelongatedcomponentsmaypassthroughtheinteriorofthejoints.BACKGROUNDOFTHEINVENTIONInthesemiconductorindustry,robotarmshavetypicallybeenemployedtomovesemiconductorwafersfromonelocationtoanother.Itisdesiredinthedesignofarobotarminthesemiconductorindustrytohavetheendeffectormaintainthesameorientationwhenthearmmovesradiallyinwardandoutward.Asdiscussed,forexample,inU.S.Pat.Nos.4,299,533and5,064,340,robotarmshavebeenprovidedwithtwolinksandanendeffectormountedatadistalendofthesecondlink.Theproximalendofthefirstlinkismountedcoaxiallywithapulley,referredtohereinasthe"fixed"pulley.Theproximalendofthesecondlinkispivotallyconnectedtothedistalendofthefirstlink.Afirstbeltconnectsthefixedpulleytoasecondlinkpulleyattheproximalendofthesecond-link,whereasasecondbeltconnectsahousingfixedtothedistalendofthefirstlinktoapulleyontheendeffector.Ifthelengthsofthelinksareequal,andifthepulleysareselectedsothattheratioofrotationoftheendeffectivetorotationofthesecondlinkis一關(guān)andtheratioofrotationofthesecondlinktorotationofthefirstlinkis-2,theendeffectorwillremainingfixedorientationbutwillmoveradiallywhenthefirstlinkrotatesrelativetothefixedpulley.Whilethisapproachiseffective,itimposessomeseriousdesignconstraints.Toprovidethedesiredratios,arelativelylargeendeffectorpulleyisneeded.Fortheendeffectortorotateone-halftherotationofthesecondlink,thepulleyattheendeffectormustbetwiceaslargeasthehousingonthedistalendofthefirstlink.Whenthepulleyattheendeffectorislarge,itaddssignificantmasstotheendoftherobotarm,increasinginertiaandmakingitmuchmoredifficulttocontrolpreciselythemovementsofthearm.Also,toprovidethedesiredratios,thesecondlinkpulleyandthehousingatthedistalendofthesecondlinkmustbeofrelativelysmalldiameter,i.e.,halfthediameterofthefixedpulley.Thismakesitdifficulttoconnecttowires,pneumatictubes,orotherelongatedcomponentsextendingfromthefirsttothesecondneighboringlinkthroughahollowboreattheexitofthesecondlinkpulleyandhousing.Suchwires,tubesandotherelongatedcomponentsareusuallypartofthecontrolsystemforcontrollingtheendeffector.Thus,itwouldbedesiredtocreatearobotarmwithenoughspaceatthejointbetweenthelinkssothatthesewiresandtubescanpassthroughthecenterofthejoint.Therobotarmofthepresentinventionaddressestheproblemssetforthaboveandisdescribedmorefullybelow.SUMMARYOFTHEINVENTIONInaccordancewithoneembodimentofthepresentinvention,arobotarmcomprisesafirstandasecondlink,thefirstlinkhavingaproximalendandadistalendandthesecondlinkhavingaproximalandadistalend.Theproximalendofthefirstlinkispivotallyconnectedtoabaseforrotationrelativetoafirstpivotaxis.Theproximalendofthesecondlinkispivotallymountedtothedistalendofthefirstlinkandiscapableofrotationaboutasecondpivotaxisthatisparalleltothefirstpivotaxis.Anendeffectorispivotallyconnectedtothedistalendofthesecondlinkandiscapableofrotationaboutathirdpivotaxiswhichisparalleltothefirstandsecondpivotaxes.Afixedpulley,withacircumferentialsurfaceconcentricwiththefirstpivotaxisismountedattheproximalendofthefirstlink.Asecond-linkpulleyisfixedtothesecondlinkforrotationwiththesecondlinkaboutthesecondpivotaxis.Thesecondlinkpulleyhasacircumferentialsurfaceconcentricwiththesecondpivotaxis.Ahousingisprovidedandisfixedtothefirstlinkatitsdistalend.Thehousinghasacircumferentialsurfaceconcentricwiththesecondpivotaxis.Anendeffectorpulleyisfixedtotheendeffectorforrotationaboutthethirdpivotaxisandtheendeffectorpulleyhascircumferentialsurfacesconcentricwiththethirdpivotaxis.Afirstbeltdriveisalsoprovidedandincludesoneormorebeltsconnectedbetweenthecircumferentialsurfaceofthefixedpulleyandthecircumferentialsurfaceofthesecond-linkpulleysothatrotationofthefirstlinkrelativetothefixedpulleyaboutthefirstpivotaxiscausesrotationofthesecondlinkaboutthesecondpivotaxisrelativetothefirstlink.Thefirstbeltdriveisarrangedtoprovideafirstratiobetweentherotationofthefirstlinkrelativetothefixedpulleyandrotationofthesecondlinkrelativetothefixedpulley.Asecondbeltdriveincludesoneormorebeltsconnectedbetweenthecircumferentialsurfaceofthehousingandthecircumferentialsurfaceoftheendeffectorpulleysothatrotationofthesecondlinkrelativetothefirstlink,aboutthesecondpivotaxis,causesrotationoftheendeffectoraboutthethirdpivotaxisrelativetothesecondlink.Thesecondbeltdriveisarrangedtoprovideasecondratiobetweentherotationofthesecondlinkrelativetothefirstlinkandrotationoftheendeffectorrelativetothesecondlink.Oneormoreidlerpulleysareprovidedandarerotatablymountedtooneorbothofthelinks.Eachoftheidlerpulleysdefineafirstandsecondcircumferentialsurface.Atleastoneofthebeltdrivesincludesafirstbeltengagedwiththefirstcircumferentialsurfaceofanidlerpulleyandasecondbeltengagedwiththesecondcircumferentialsurfaceofthesameidlerpulley.Preferably,thefirstratiohasavalueof-2whererotationofthefirstlinkthroughanangle8causesthesecondlinkpulleyandthesecondlinktoturnthroughanangleof-26withrespecttothefirstlink.Thus,ifthefirstlinktravelsthrougha450anglecounterclockwise,thiswillresultinthesecondlinkpulleyandthesecondlinkturningthroughanangleof900intheclockwisedirectionrelativetothefirstlink.Itisalsopreferredthatthesecondratiohasavalueof?whererotationofthesecondlinkthroughanangle0causestheendeffectorpulleyandtheendeffectortoturnthroughanangleof-1/z0withrespecttothesecondlink.Forexample,ifthesecondlinkturnsthroughanangleof90degreesintheclockwisedirection,thiswillresultintheendeffectorpulleyandtheendeffectorturningthroughanangleof450inthecounterclockwisedirectionrelativetothesecondlink.Becauseoneormoreofthebeltdrivesincludesanidlerpulleyandtwobelts,thepulleyandhousingdiametersneednotbeselectedasdescribedaboveinconnectionwiththepriorartbeltdrives.Forexample,wheretherobotarmincludesafirstidlerpulleymountedtothefirstlink,thefirstbeltofthefirstbeltdriveengagesthefirstcircumferentialsurfaceoftheidlerpulleyandthecircumferentialsurfaceofthefixedpulley.Thesecondbeltofthefirstbeltdriveengagesthesecondcircumferentialsurfaceofthefirstidlerpulleyandthecircumferentialsurfaceofthesecond-linkpulley.Alsopreferably,therobotarmhasasecondidlerpulleymountedtothesecondlink.Thesecondbeltdrivedesirablycomprisesafirstbeltextendingfromthecircumferentialssurfaceofthehousingtothefirstcircumferentialsurfaceofthesecondidlerpulley.Thesecondbeltdrivedesirablyfurthercomprisesasecondbeltextendingfromthesecondcircumferentialsurfaceofthesecondidlerpulleytotheendeffectorpulley.Preferably,theratioofthediameterofthefirstcircumferentialsurfaceofthesecondidlerpulleytothediameterofthesecondcircumferentialsurfaceofthesecondidlerpulleyismorethan1:1as,forexample2:1.Thisratioofmorethan1:1inthesecondidlerpulleyallowsarelativelysmallerendeffectorpulleyonasmallerhousing,orboth,thanwhatwillbeprovidedintheabsenceofthesecondidlerpulley.Preferably,therobotarmfurtherincludeselongatedcomponentsandthesecondlinkpulleyandhousingincludeaninternalbore.Theelongatedcomponentsdesirablyextendfromthefirstlinkthroughtheboreandintothesecondlink.Theseelongatedcomponentsmayincludewires,fiberopticsorpneumaticorhydraulichosesthatareneededtooperatetherobotarm.Theendeffectorpulleymayalsoincludeaninternalbore,andtheelongatedcomponentscanextendfromthesecondlinktotheendeffector.Preferably,therobotarmfurtherincludesabaseandafirstrotarymotionactuatorthatisconnectedtothebaseofrotationforrotatingthefirstlinkrelativetothefixedpulleyaboutthefirstpivotaxissoastomovetheendeffectorradiallyasdescribedabove.Afurtherrotarymotionactuatormaybeprovidedforrotatingthefixedpulleyandthefirstlinksoastoswingtheentirearmaboutthefirstpivotaxis.BRIEFDESCRIPTIONOFTHEDRAWINGSFIG.1isaperspectiveviewofarobotarminaccordancewithoneembodimentofthepresentinvention.FIG.2isacross-sectionalelevationalviewoftherobotarminFIG.1.FIG.3isatopcross-sectionalviewoftherobotarmofFIG.1withthefirstlinkpartiallyshowninphantom.DE7AILEDDESCRIPTIONOFTHEPREFERREDEMBODIMENTAsshowninFIGS.1一，arobotarm10ismountedtoabase11andhasafirstlink12andasecondlink14.Thefirstlinkhasaproximalend16andadistalend18.Likewise,thesecondlink14hasaproximalend20andadistalend22.Thefirstandsecondlinks12and14arepreferablyhollowandcanbemadeofmetal,plasticoranyothersuitablematerial.Firstlink12ismountedtobase12forrotationrelativetothebaseaboutafirstpivotaxis28ofafirstjoint24attheproximalend16ofthefirstlink12.Afixedpulley26isalsomountedforrotationaboutthefirstpivotaxis28atthefirstjoint24.Thefixedpulley26includesacircumferentialsurface30(FIG.3)thatisconcentricwiththefirstpivotaxis28.Alsoextendingfromthefirstjoint24isashaft32fixedtothefirstpulleyandadrivepulley33fixedtofirstlink12.Drivepulley33isconnectedtoafirstrotarymotionactuator35sothatthefirstactuatorcandrivethefirstlinkinrotationaboutaxis28.Shaft32isconnectedtoasecondactuator37whichcandrivethefixedpulley24inrotationabouttheaxis28concurrentlywithrotationofthefirstlink12orholdthedrivepulleyfixedagainstsuchrotation.Thefirstactuatormayincludeanyconventionalrotaryactuatorsuchas,forexample,asteppedmotor,aconventionalelectricmotor,orthelike.Thesecondactuatormayincludesimilarcomponents,ormayincludeafirstbraketolinkthefixedpulley24toarm12forrotationtherewithandasecondbraketoholdthefixedpulleyinafixedpositionrelativetothehousing.Thefirstandsecondactuatorsarecommandedbyaconventionalcontrolsystem(notshown).Thefirstlink12andthesecondlink14arepivotallyconnectedatasecondjoint34.Thefirstandsecondlinks12and14areabletorotatewithrespecttoeachotheraboutasecondpivotaxis36thatisparalleltothefirstpivotaxis28.Asecond-linkpulley38ismountedonthesecondjoint34andhasacircumferentialsurface40thatisconcentricwiththesecondpivotaxis36.Thesecond-linkpulley38isfixedtothesecondlink14.Ahousing42isalsoprovidedatthesecondjoint34andisfixedtothefirstlink12.Thehousing42alsohasacircumferentialsurface44thatisconcentricwiththesecondpivotaxis36.Athirdjoint46isprovidedatthedistalend22ofthesecondlink14.Anendeffectorpulley48ismountedatthethirdjoint46andisabletorotateaboutathirdpivotaxis50.Theendeffectorpulley48hasacircumferentialsurface52concentricwiththethirdpivotaxis50.Anendeffector54isattachedtotheendeffectorpulley48andiscapableofrotationaboutthethirdpivotaxis50.Theendeffector54mayincludefingersorotherfixturesforholdingaworkpiecetobemoved.Afirstidlerpulley56ismountedtothefirstlink12betweenthefixedpulley26andsecond-linkpulley38.Thefirstidlerpulley56hasafirstcircumferentialsurface58andasecondcircumferentialsurface60.Asecondidlerpulley62ismountedtothesecondlink14andhasafirstcircumferentialsurface64andasecondcircumferentialsurface66.Thefirstandsecondidlerpulleys56and62rotateaboutaxes68and69thatareparalleltothefirst,secondandthirdpivotaxes28,36and50.Afirstbeltdrive71onfirstlink12includesafirstbelt70engagingthecircumferentialsurfaceofthefixedpulley30andthefirstcircumferentialsurfaceofthefirstidlerpulley58,andasecondbelt72extendingfromthesecondcircumferentialsurface66ofthefirstidlerpulley62tothecircumferentialsurface40ofthesecond-linkedpulley.Asecondbeltdrive75onsecondlink14includesafirstbelt74extendingfromthecircumferentialsurface44ofthehousing42tothefirstcircumferentialsurface64ofthesecondidlerpulley62.Asecondbelt76extendsfromthesecondcircumferentialsurface66ofthesecondidlerpulley62tothecircumferentialsurface52oftheendeffectorpulley48.Thefirstandsecondbelts74and76ofthesecondidlerpulley62formthesecondbeltdrive75ofthesecondlink.Thebelts70,72,74and76arepreferablybeltshavingcleatsonteeth,ofthetypecommonlyreferredtoas"timingbelts"andareheldtauttothepulleys.Thepulleyshavematingteethontheircircumferentialsurfaces.Itshouldbeappreciatedbythoseskilledintheartthatthebeltscanbeconventionalfrictiondrivebelts,v-beltsorchainsandthepulleyswouldbeselectedaccordingly.Inoperation,tomovetheendeffectorradially,afirstactuator35causesthefirstlink12torotateaboutthefirstpivotaxis28whilesecondactuator37holdsthefixedpulley26againstrotation.Becausethefixedpulley26isstationarywithrespecttothefirstlink12,therotationofthefirstlink12resultsinthefirstidlerpulley56rotatingintheoppositedirectionasthefirstlink12.AsbestseeninFIG.3,ifforexamplethefirstlinkisrotatedinthecounterclockwisedirection,thefirstidlerpulley56willrotateintheclockwisedirectionwithrespecttothefirstlinkcausingthesecondbelt72ofthefirstbeltdrivetomove.Thesecondbelt72ofthefirstidlerpulley56isengagedwiththesecond-linkpulley38,whichisfixedtothesecondlink14.Themovementofbelt72causesclockwisemovementofthesecond-linkedpulley38sothatthesecondlink14rotatesaboutthesecondpivotaxis36intheclockwisedirectionrelativetothefirstlink12.Theamountofmovementofthesecondlinkrelativetothefirstlinkdependsontheoverallratioprovidedbythefirstbeltdrive71onthefirstlink.Thisinturndependsontheratioofthediametersofthefixedpulley26andthesecond-linkpulley38aswellastheratioofthediameters,ofthefirstcircumferentialsurface58andsecondcircumferentialsurface60ofthefirstidlerpulley56.Intheparticularembodimentshown,thediameterofthefixedpulley26istwicethediameterofthesecond-linkpulley38.Thus,whereasthefirstandsecondcircumferentialsurfaces58and60ofthefirstidlerpulley56havethesamediameter,a450rotationofthefirstlink12inthecounterclockwisedirectionwillresultina900rotationofthesecondlink14intheclockwisedirectionrelativetothefirstlink12.Becausethehousing42isfixedtothefirstlink12,rotationofsecondlink14relatingtofirstlink12causesthefirstbelt74ofthesecondbeltdrive75tomoverelativetothesecondlink14.Forexample,ifthesecondlinkrotatesintheclockwisedirection,thefirstbelt74ofthesecondidlerpulley62willmoveandwillturnthesecondidlerpulley62inthecounterclockwisedirectionrelativetothesecondlink.Thismovesthesecondbelt76,engagedwiththesecondcircumferentialsurface66ofthesecondidlerpulley62,inthecounterclockwisedirection.Asthesecondbelt76ofthesecondbeltdrive75isengagedwiththeendeffectorpulley48,themovementofsecondbelt76resultsintheendeffector54alsoturninginthecounterclockwisedirectionrelativetosecondlink14.AsbestshowninFIG.3,theamountofmovementoftheendErector54relativetothesecondlink14dependsonthediametersofthecircumferentialsurface44ofthehousing42,theratioofdiametersofthefirstandsecondcircumferentialsurfaces64and66ofthesecondidlerpulley62andthediameterofthecircumferentialsurface52oftheendeffectorpulley48.Intheparticularembodimentillustrated,theratioofdiametersbetweenthecircumferentialsurface44ofthehousing42andthefirstcircumferentialsurface64ofthesecondidlerpulley62is1:1.Thus,thesecondlinkturning900intheclockwisedirectionresultsinthesecondidlerpulleyrotating900inthecounterclockwisedirection.Thediameterofthesecondcircumferentialsurface66ofthesecondidlerpulleyis1/zthediameterofthefirstcircumferentialsurface64.A900rotationofthefirstcircumferentialsurface64willresultina900rotationofthesecondcircumferentialsurface66butthelinearmovementofbelt76isonly1/zthelinearmovementofbelt74.Further,theratioofthediametersofthesecondcircumferentialsurface66ofthesecondidlerpulley62tothediameterofthecircumferentialsurface52oftheendeffectorpulley48is1/za.Thus,ifthesecondidlerpulley62rotatesthrough900,theendeffectorpulleywouldonlyrotate450.Becausetheendeffector54isrigidlyattachedtotheendeffectorpulley48,theendeffectoralsorotates450.Thisarrangementtranslatesa900clockwisemovementofthesecondlink14relativetothefirstlinkintoa450counterclockwisemovementoftheendeffector54.Byhavinga-2ratiobetweenthefixedpulley26andthesecond-linkpulley38anda-1/zratiobetweenthehousing42andtheendeffectorpulley48maintainstheorientationoftheendeffector54throughouttherotationalmovementsofthefirstandsecondlinks12and14.Inotherwords,theendeffector54keepsitsorientationwithrespecttothebasellwhilethefirstandsecondlinksarerotating.Forexample,ifthefirstlink12ismoved450counterclockwise,thesecondlinkwillmove900intheclockwisedirectionwhiletheendeffector54rotates450inthecounterclockwisedirection.Theendeffectorsimilarlymovestowardorawayfromthefirstjoint24andbase11.Afurtheradvantageofthisarrangementisthatthehousing42canbemadewitharelativelylargediameterascomparedwiththeendeffectorpulley48.Thisisduetothesecondidlerpulley62creatinga1/zratiobetweenitssecondcircumferentialsurface66andtheendeffectorpulley48.Toestablishthe1/zratiointheabsenceofthesecondidlerpulleywouldrequirethatthediameteroftheendeffectorpulley48betwicethediameterofthecircumferentialsurface44ofthehousing.Asmentionedabove,itisdesiredtohavearelativelysmallendeffectorpulley48.Arelativelylargeendeffectorpulley48wouldproduceincreasetherotationalinertiaofthearmandmakeprecisecontrolofthearm10moredifficult.Also,therelativelylargediameterofhousing42providesadditionalspaceinthecenterofthehousingandsecondlinkpulley38whereabore78canbeprovided.Thebore78allowswires,fiberoptics,pneumaticorhydraulichosesorotherelongatedcomponents90topassfromthefirstlink12tothesecondlink14alongtheinterioroftherobotarm10.Havingthesecomponents90passingalongtheinteriorofthelinks12and14improvestheappearanceoftherobotarm10andeliminatesthepossibilityofthoseelongatedcomponentsbecomingcaughtonsomethingorinterferingwiththemovementoftherobotarm.Anadditionalbore80isprovidedinthecenteroftheendeffectorpulley48.Thisbore80canbeusedfortransferringelongatedcomponents90fromthesecondlink14totheendeffector54.Inafurthermodeofoperation,thefirstandsecondactuators35and37areoperatedtoswingthefirstlink12andfixedpulley24aboutfirstpivotaxis28atthesamerotationalvelocity.Thisswingstheentirearmaroundthefirstpivotaxis,withoutmovingtheendeffectorradially.Thetwomodesofoperationmaybecombined.Thus,theactuatorscanturnthefixedpulleyandthefirstlinksimultaneouslyatdifferentvelocities.Iclaim:1.Arobotabase;armcomprrsmg:afirstlinkandasecondlink,saidfirstlinkhavingaproximalendandadistalend,saidsecondlinkhavingaproximalendandadistalend;saidproximalendofsaidfirstlinkbeingpivotallyconnectedtosaidbaseforrotationrelativetheretoaboutafirstpivotaxis,saidproximalendofsaidsecondlinkbeingpivotallymountedtosaiddistalendofsaidfirstlinkforrotationrelativetheretoaboutasecondpivotaxisparalleltosaidfirstpivotaxrs;anendeffectorpivotallyconnectedtosaiddistalendofsaidsecondlinkforrotationrelativetheretoaboutathirdpivotaxisparalleltosaidfirstandsecondpivotaxes,afixedpulleyrotatablymountedtosaidbaseonsaidfirstpivotaxisdefiningacircumferentialsurfaceconcentricwithsaidfirstpivotaxis;asecond-linkpulleyfixedtosaidsecondlinkforrotationtherewithaboutsaidsecondpivotaxis,saidsecond-linkpulleyhavingacircumferentialsurfaceconcentricwithsaidsecondpivotaxis;ahousingfixedtosaidfirstlinkdefiningacircumferentialsurfaceconcentricwithsaidsecondpivotaxis;anendeffectorpulleyfixedtosaidendeffectorforrotationtherewithaboutsaidthirdpivotaxis,saidendeffectorpulleyhavingacircumferentialsurfaceconcentricwithsaidthirdpivotaxis,afirstbeltdriveincludingoneormorebeltsconnectedbetweensaidcircumferentialsurfacesofsaidfixedpulleyandsaidsecond-linkpulleysothatuponrotationofsaidfirstlinkrclativctosaidfixedpulleyaboutsaidfirstpivotaxis,saidsecondlinkwillrotateaboutsaidsecondpivotaxisrelativetosaidfirstlink,saidfirstbeltdrivebeingarrangedtoprovideafirstratiobetweenrotationofsaidfirstlinkrelativetosaidfixedpulleyandrotationofsaidsecondlinkrelativetosaidfixedpulley;asecondbeltdriveincludingoneormorebeltsconnectedbetweensaidcircumferentialsurfacesofsaidhousingandsaidendeffectorpulleysothatuponrotationofsaidsecondlinkrelativetosaidfirstlinkaboutsaidsecondpivotaxis,saidendeffectorwillrotateaboutsaidthirdpivotaxisrelativetosaidsecondlink,saidsecondbeltdrivebeingarrangedtoprovideasecondratiobetweenrotationofsaidsecondlinkrelativetosaidfirstlinkandrotationofsaidendeffectorrelativetosaidsecondlink;oneormoreidlerpulleysrotatablymountedtooneorbothofsaidlinks,eachofsaididlerpulleysdefiningfirstandsecondcircumferentialsurfaces,atleastoneofsaidbeltdrivesincludingafirstbeltengagedwiththefirstcircumferentialsurfaceofanidlerpulleyandasecondbeltengagedwiththesecondcircumferentialsurfaceofthesameidlerpulley.2.Arobotarmasclaimedinclaim1whereinsaidfirstratiois-2wherebyrotationofsaidfirstlinkthroughangle8causessaidsecond-linkpulleyandsaidsecondlinktoturnthroughangle-26withrespecttosaidfirstlink.3.Arobotarmasclaimedinclaim1,whereinsaidsecondratiois?/zwherebyrotationofsaidsecondlinkthroughangle8causessaidend-efFectorpulleyandsaidend-efFectortoturnthroughangle?/z6withrespecttosaidsecondlink.4.Arobotarmasclaimedinclaim1,whereinsaidfirstandsecondcircumferentialsurfacesofsaididlerpulleyhavedifferentdiameters5.Arobotarmofclaim1,whereinsaidoneormoreidlerpulleyscomprisesafirst-driveidlerpulleymountedonsaidfirstlink,saidfirstbeltdriveincludingsaidfirst-driveidlerpulley.6.Arobotarmasclaimedinclaim5,whereinsaidfirstbeltdrivecomprisesafirstbeltextendingfromsaidcircumferentialsurfaceofsaidfixedpulleytosaidfirstcircumferentialsurfaceofsaidfirstidlerpulley.7.Arobotarmasclaimedinclaim6,whereinsaidfirstbeltdrivecomprisesasecondbeltextendingfromsaidsecondcircumferentialsurfaceofsaidfirstidlerpulleytosaidsecondlinkpulley.8.Arobotarmasclaimedinclaim7,whereinsaidfirstandsecondcircumferentialsurfacesofsaidfirstidlerpulleyhavea1:1diameterratio.9.Arobotarmasclaimedinclaim1,whereinsaidoneormoreidlerpulleysincludeasecond-driveidlerpulleymountedonsaidsecondlink.10.Arobotarmasclaime