design_and_prototyping_of_a_spherical_parallel_mac

9DesignandPrototypingofaSphericalParallelMachineBasedon3-CPUKinematicsMassimoCallegariDipartimentodiMeccanica,UniversitàPolitecnicadelleMarcheViaBrecceBianche,Ancona,Italy1.IntroductionParallelkinematicsmachines,PKMs,areknowntobecharacterisedbymanyadvantageslikealightweightconstructionandahighstiffnessbutalsopresentsomedrawbacks,likethelimitedworkspace,thegreatnumberofjointsofthemechanicalstructureandthecomplexkinematics,especiallyfor6-dofmachines.ThereforeCallegarietal.(2007)proposedtodecomposefull-mobilityoperationsintoelementalsub-tasks,tobeperformedbyseparateminormobilitymachines,likedonealreadyinconventionalmachiningoperations.Theyenvisagedthearchitectureofamechatronicsystemwheretwoparallelrobotscooperateinordertoperformacomplexassemblytask:thekinematicsofbothmachinesisbaseduponthe3-CPUtopologybutthejointsaredifferentlyassembledsoastoobtainatranslatingparallelmachines(TPM)withonemechanismandasphericalparallelmachine(SPM)withtheother.Inonecase,joints’axesaresetinspacesothatthemobileplatformcanfreelytranslate(withoutrotating)insideits3Dworkspace:thisiseasilyobtainedbyarrangingtheuniversaljointofeachlimbsothattheaxisoftheouterrevolutejointisparalleltothebasecylindricaljoint;suchthreedirectionsaremutuallyorthogonaltomaximisetheworkspaceandgrantoptimalmanipulability.Withadifferentsettingofthejoints,threedegreesoffreedomofpurerotationareobtainedattheterminalofthesphericalwrist:inthiscasetheaxesofthecylindricaljointsandthoseoftheouterrevolutepairsintheuniversaljointsallintersectatacommonpoint,whichisthecentreofthesphericalmotion.Thissolution,atthecostofamoresophisticatedcontroller,wouldleadtothedesignofsimplermachinesthatcouldbeusedalsostand-alonefor3-doftasksandwouldincreasethemodularityandreconfigurabilityoftherobotisedindustrialprocess.ThetworobotshavebeendevelopedtilltheprototypalstagebymeansofavirtualprototypingenvironmentandasketchofthewholesystemisshowninFig.1:whilethetranslatingmachinehasbeenpresentedalreadyelsewhere(Callegari&Palpacelli,2008),thepresentarticledescribesthedesignprocessoftheorientingdeviceandtheoutcomingprototype.ParallelManipulators,NewDevelopments172Fig.1.Architectureoftheassemblysystembasedontwocooperatingparallelrobots2.KinematicsynthesisThedesignofparallelkinematicsmachinesabletoperformmotionsofpurerotation,alsocalledSphericalParallelMachines,SPM’s,isaquiterecentresearchtopics:besidesthepioneeringresearchesbyAsadaandGranito(1985),themostimportantmechanismofthistypeistheagileeyebyGosselinandAngeles(1989),uponwhichmanyprototypemachineshavebeendesignedsincethen.Fewotherstudiesonthesubjectareavailableduringthe90’s,amongwhichtheworkofLeeandChang(1992),InnocentiandParenti-Castelli(1993)andAlizadeetal.(1994).Inthenewmillennium,however,agrowinginterestonsphericalparallelwristsproducedmanyinterestingresults,asnewkinematicarchitecturesorpowerfuldesigntools.Theuseofsynthesismethodsbasedonorscrewtheory,forinstance,hasbeenexploitedbyKongandGosselin(2004aand2004b)thatprovidecomprehensivelistingsofbothoverconstrainedandnon-overconstrainedSPM’s;HervéandKarouia,ontheotherhand,usethetheoryofLiegroupofdisplacementstogeneratenovelarchitectures,asthefourmainfamiliesin(Karouia&Hervè,2002)orthe3-RCC,3-CCR,3-CRCkinematicsspecificallytreatedin(Karouia&Hervè,2005);FangandTsai(2004)usethetheoryofreciprocalscrewstopresentasystematicmethodologyforthestructuralsynthesisofaclassof3-DOFrotationalparallelmanipulators.Moreinterestingarchitectures,asthe3-URC,the3-RUUorthe3-RRS,havebeenstudiedbyDiGregorio(2001a,2001band2004)andalsobyotherresearchers.Followingtheapproachoutlinedin(Karouia&Hervè,2000),Callegarietal.(2004)proposedanewwristarchitecture,basedonthe3-CPUstructure;itisnotedalsothatthe3-CRUvariantischaracterisedbyamuchmorecomplexkinematicsbutcanbeusefulinviewofaDesignandPrototypingofaSphericalParallelMachineBasedon3-CPUKinematics173possibleprototypingatamini-ormicro-scale,asshownbyCallegarietal.(2008).Themainsynthesisstepsofthe3-CPUparallelwristareoutlinedinthefollowingparagraphs.Firstofall,itisnotedthatonlynon-overconstrainedmechanismshavebeensearchedinordertoavoidthestrictdimensionalandgeometrictolerancesneededbyoverconstrainedmachinesduringmanufacturingandassemblyphases.Moreover,theuseofpassivesphericalpairsdirectlyjoiningtheplatformtothebasehasbeenavoidedaswellandforeconomicreasonsonlymodularsolutionscharacterisedbythreeidenticallegshavebeenconsidered.Itmustbesaidthattheseadvantagesareusuallypaidwithamorecomplexstructureandthepossiblepresenceofsingularconfigurations(translationsingularities)inwhichthesphericalconstraintbetweenplatformandbasefails.Fig.2.Limbofconnectivity5abletogenerateasphericalmotionoftheplatformAimingatthiskindofsphericalmachines,asimplemobilityanalysisshowsthataparallelmechanismabletogenerate3-dofmotionsmustbecomposedbythreelimbsofconnectivity5.Withoutlosinggenerality,itissupposedthateachsinglelimbconsistsof4linksand5revolute(R)orprismatic(P)jointsthatconnectthelinksamongthemandthelimbitselftothefixedframeandtothemobileplatform.Ifeachlimb’skinematicchainhas3revolutepairswhoseaxesinter