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机040511号马吟川指导老师许宝杰1THEDESIGNOFPARALLELKINEMATICMACHINETOOLSUSINGKINETOSTATICPERFORMANCECRITERIAhttp//arxiv.org/ftp/arxiv/papers/0705/0705.1038.pdf1.INTRODUCTIONMostindustrialmachinetoolshaveaserialkinematicarchitecture,whichmeansthateachaxishastocarrythefollowingone,includingitsactuatorsandjoints.HighSpeedMachininghighlightssomedrawbacksofsucharchitecturesheavymovingpartsrequirefromthemachinestructurehighstiffnesstolimitbendingproblemsthatlowerthemachineaccuracy,andlimitthedynamicperformancesofthefeedaxes.ThatiswhyPKMsattractmoreandmoreresearchersandcompanies,becausetheyareclaimedtoofferseveraladvantagesovertheirserialcounterparts,likehighstructuralrigidityandhighdynamiccapacities.Indeed,theparallelkinematicarrangementofthelinksprovideshigherstiffnessandlowermovingmassesthatreduceinertiaeffects.Thus,PKMshavebetterdynamicperformances.However,thedesignofaparallelkinematicmachinetoolPKMTisahardtaskthatrequiresfurtherresearchstudiesbeforewideindustrialusecanbeexpected.ManycriterianeedtobetakenintoaccountinthedesignofaPKMT.WepayspecialattentiontothedescriptionofkinetostaticcriteriathatrelyontheconditioningoftheJacobianmatrixofthemechanism.TheorganisationofthispaperisasfollowsnextsectionintroducesgeneralremarksaboutPKMs,thenisexplainedwhyPKMscanbeinterestingalternativemachinetooldesigns.ThenarepresentedexistingPKMTs.AnapplicationtothedesignofasmallscalemachinetoolprototypedevelopedatIRCCyNispresentedattheendofthispaper.2.ABOUTPARALLELKINEMATICMACHINES2.1.GeneralRemarksThefirstindustrialapplicationofPKMswastheGoughplatformFigure1,designedin1957totesttyres1.PKMshavethenbeenusedformanyyearsinflightsimulatorsandroboticapplications2becauseoftheirlowmovingmassandhighdynamicperformances.Sincethedevelopmentofhighspeedmachining,PKMTshavebecomeinterestingalternativemachinetooldesigns3,4.机040511号马吟川指导老师许宝杰2Figure1.TheGoughplatformInaPKM,thetoolisconnectedtothebasethroughseveralkinematicchainsorlegsthataremountedinparallel.ThelegsaregenerallymadeofeithertelescopicstrutswithfixednodepointsFigure2a,orfixedlengthstrutswithglidingnodepointsFigure2b.Alongwithhighspeedcuttingsunceasingdevelopment,thetraditionaltandemtypeorganizationconstructstheplatformthestructurerigidityandthetravelingcarriagehighspeedbecomesthetechnologicaldevelopmentgraduallythebottleneck,buttheparallelplatformthenbecomesthebestcandidateobject,butwasoppositeinthetandemenginebed,theparallelworkingplatformhadthefollowingcharacteristicandthemerit1structureissimple,thepriceislowTheenginebedmechanicalsparepartnumberisseriesconnectedconstructstheplatformtoreducelargely,mainlybytheballbearingguidescrew,theHookearticulation,theballarticulation,theservoelectricalmachineryandsooncommonmoduleiscomposed,thesecommonmodulesmaybythespecialfactoryproduction,thusthisenginebedsmanufactureandtheinventorycostaremuchlowerthanthesamefunctionstraditionalenginebed,easytoassembleandthetransporting.2structurerigidityishighBecauseusedclosenessstructureclosedloopstructuretoenableittohavehighrigidandthehighspeedmerit,itsstructuralloadstreamlinewasshort,butshouldereddecomposespulls,thepressurealsotowithstandbysixconnectingrods,bymaterialsmechanicsviewpoint,whentheexternalforcewascertain,thebracketquantitysstressandthedistortionwerebiggest,thebothsidesinsertedthebuildinnextbest,cameisagainbothsidesJansupportssimplysupported,nextwasthebearingtwostrengthstructure,whatthestressandthedistortionweresmallestwasthetensitytwostrengthstructure,thereforeithadthehighrigidity.Itsrigidityloadratioishigherthantraditionalthenumericallycontrolledmachinetool.3processingspeedishigh,theinertiaislowIfthestructurewithstandsthestrengthwillchangethedirection,willbesituatedbetweentensityandpressure,twostrengthcomponentswillbemostsavethematerialthestructure,butitwillmovetothemovingpartsweighttoreducetolowlyandsimultaneouslywillactuatebysixactuatingunits,thereforemachineveryeasyhighspeed,andwillhavethelowinertia.4workingaccuracyishighBecauseitforthemultiplespindleparallelorganizationcomposition,sixexpandablepolepoleslongalonehasaneffecttocuttingtoolspositionandtheposture,thus机040511号马吟川指导老师许宝杰3doesnothavethetraditionalenginebedi.e.connectsenginebedthegeometricalerroraccumulationandtheenlargementphenomenon,evenalsohasthebeinguniformeffectaveragingeffectIthasthehotsymmetricalstructuraldesign,thereforethethermaldeformationissmallThereforeithasthehighaccuracymerit.5multipurposeflexibleIsconvenientasaresultofthisenginebedorganizationsimplecontrol,easilyaccordingtoprocessingobject,butdesignsitthespecialpurposemachine,simultaneouslymayalsodevelopthegeneralenginebed,withrealizesthemilling,boring,processingsandsoongrinding,butmayalsoprovidetheessentialmeasuringtooltocomposeitthemeasuringengine,realizesenginebedsmultipurpose.Thiswillbringtheverybigapplicationandthemarketprospect,hastheverybroadapplicationprospectinthenationaldefenseandthecivilaspect.6servicelifeislongBecausethestressstructureisreasonable,themovingpartattritionissmall,anddoesnothavetheguiderail,doesnothavetheironfilingseithertherefrigerantenterstheguiderailinteriortocauseittoscratch,theattritionorthecorrosionphenomenon.7StewartplatformsuitsinthemodularproductionRegardingthedifferentmachinescope,onlyneedchangetheconnectingrodlengthandthecontactposition,maintainsalsoeasily,doesnotneedtocarryonpartsremakingandtoadjust,onlyneedtheneworganizationparameterinput.8transformationcoordinatesystemisconvenientBecausedoesnothavetheentitycoordinatesystem,theenginebedcoordinatesystemandtheworkpiececoordinatesystemtransformdependonthesoftwaretocompletecompletely,isconvenient.WhentheStewartplatformappliesintheenginebedandtherobot,mayreducethestaticerror,becausehighrigidity,aswellasdynamicerrorbecauselowinertia.ButStewarttheplatforminferiorityliesinitsworkingspacetobesmall,andithasthesingularpointlimitintheworkingspace,buttheserialoperationplatform,thecontrollermeetstimethesingularpoint,accountantwillfigureouttheactuationorderwhichthedriveisunabletoachievetocreatetheningerror,buttheStewartplatformwilllosethesupportpartialdirectionsinthestrangepositionthestrengthormomentofforceability,willbeunabletocompletetheconstantloadobject.Figure2a.AbipodPKM机040511号马吟川指导老师许宝杰4Figure2b.AbiglidePKM2.2.SingularitiesThesingularconfigurationsalsocalledsingularitiesofaPKMmayappearinsidetheworkspaceoratitsboundaries.Therearetwotypesofsingularities5.Aconfigurationwhereafinitetoolvelocityrequiresinfinitejointratesiscalledaserialsingularity.Aconfigurationwherethetoolcannotresistanyeffortandinturn,becomesuncontrollable,iscalledaparallelsingularity.Parallelsingularitiesareparticularlyundesirablebecausetheyinducethefollowingproblemsahighincreaseinforcesinjointsandlinks,thatmaydamagethestructure,adecreaseofthemechanismstiffnessthatcanleadtouncontrolledmotionsofthetoolthoughactuatedjointsarelocked.Figures3aand3bshowthesingularitiesforthebiglidemechanismofFig.2b.InFig.3a,wehaveaserialsingularity.Thevelocityamplificationfactoralongtheverticaldirectionisnullandtheforceamplificationfactorisinfinite.Figure3bshowsaparallelsingularity.Thevelocityamplificationfactorisinfinitealongtheverticaldirectionandtheforceamplificationfactorisclosetozero.Notethatahighvelocityamplificationfactorisnotnecessarilydesirablebecausetheactuatorencoderresolutionisamplifiedandthustheaccuracyislower.Figure3a.Aserialsingularity
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