機040511號馬吟川指導老師：許寶杰1THEDESIGNOFPARALLELKINEMATICMACHINETOOLSUSINGKINETOSTATICPERFORMANCECRITERIA/ftp/arxiv/papers/0705/0705.1038.pdf1.INTRODUCTIONMostindustrialmachinetoolshaveaserialkinematicarchitecture,whichmeansthateachaxishastocarrythefollowingone,includingitsactuatorsandjoints.HighSpeedMachininghighlightssomedrawbacksofsucharchitectures:heavymovingpartsrequirefromthemachinestructurehighstiffnesstolimitbendingproblemsthatlowerthemachineaccuracy,andlimitthedynamicperformancesofthefeedaxes.ThatiswhyPKMsattractmoreandmoreresearchersandcompanies,becausetheyareclaimedtoofferseveraladvantagesovertheirserialcounterparts,likehighstructuralrigidityandhighdynamiccapacities.Indeed,theparallelkinematicarrangementofthelinksprovideshigherstiffnessandlowermovingmassesthatreduceinertiaeffects.Thus,PKMshavebetterdynamicperformances.However,thedesignofaparallelkinematicmachinetool(PKMT)isahardtaskthatrequiresfurtherresearchstudiesbeforewideindustrialusecanbeexpected.ManycriterianeedtobetakenintoaccountinthedesignofaPKMT.WepayspecialattentiontothedescriptionofkinetostaticcriteriathatrelyontheconditioningoftheJacobianmatrixofthemechanism.Theorganisationofthispaperisasfollows:nextsectionintroducesgeneralremarksaboutPKMs,thenisexplainedwhyPKMscanbeinterestingalternativemachinetooldesigns.ThenarepresentedexistingPKMTs.Anapplicationtothedesignofasmall-scalemachinetoolprototypedevelopedatIRCCyNispresentedattheendofthispaper.2.ABOUTPARALLELKINEMATICMACHINES2.1.GeneralRemarksThefirstindustrialapplicationofPKMswastheGoughplatform(Figure1),designedin1957totesttyres1.PKMshavethenbeenusedformanyyearsinflightsimulatorsandroboticapplications2becauseoftheirlowmovingmassandhighdynamicperformances.Sincethedevelopmentofhighspeedmachining,PKMTshavebecomeinterestingalternativemachinetooldesigns3,4.機040511號馬吟川指導老師：許寶杰2Figure1.TheGoughplatformInaPKM,thetoolisconnectedtothebasethroughseveralkinematicchainsorlegsthataremountedinparallel.Thelegsaregenerallymadeofeithertelescopicstrutswithfixednodepoints(Figure2a),orfixedlengthstrutswithglidingnodepoints(Figure2b).Alongwithhigh-speedcuttingsunceasingdevelopment,thetraditionaltandemtypeorganizationconstructstheplatformthestructurerigidityandthetravelingcarriagehighspeedbecomesthetechnologicaldevelopmentgraduallythebottleneck,buttheparallelplatformthenbecomesthebestcandidateobject,butwasoppositeinthetandemenginebed,theparallelworkingplatformhadthefollowingcharacteristicandthemerit:(1)structureissimple,thepriceislowTheenginebedmechanicalsparepartnumberisseriesconnectedconstructstheplatformtoreducelargely,mainlybytheballbearingguidescrew,theHookearticulation,theballarticulation,theservoelectricalmachineryandsooncommonmoduleiscomposed,thesecommonmodulesmaybythespecialfactoryproduction,thusthisenginebedsmanufactureandtheinventorycostaremuchlowerthanthesamefunctionstraditionalenginebed,easytoassembleandthetransporting.(2)structurerigidityishighBecauseusedclosenessstructure(closed-loopstructure)toenableittohavehighrigidandthehighspeedmerit,itsstructuralloadstreamlinewasshort,butshouldereddecomposespulls,thepressurealsotowithstandbysixconnectingrods,bymaterialsmechanicsviewpoint,whentheexternalforcewascertain,thebracketquantitysstressandthedistortionwerebiggest,thebothsidesinsertedthe(build-in)nextbest,cameisagainbothsidesJansupports(simply-supported),nextwasthebearingtwostrengthstructure,whatthestressandthedistortionweresmallestwasthetensitytwostrengthstructure,thereforeithadthehighrigidity.Itsrigidityloadratioishigherthantraditionalthenumerically-controlledmachinetool.(3)processingspeedishigh,theinertiaislowIfthestructurewithstandsthestrengthwillchangethedirection,(willbesituatedbetweentensityandpressure),twostrengthcomponentswillbemostsavethematerialthestructure,butitwillmovetothemovingpartsweighttoreducetolowlyandsimultaneouslywillactuatebysixactuatingunits,thereforemachineveryeasyhighspeed,andwillhavethelowinertia.(4)workingaccuracyishighBecauseitforthemultiplespindleparallelorganizationcomposition,sixexpandablepolepoleslongalonehasaneffecttocuttingtoolspositionandtheposture,thus機040511號馬吟川指導老師：許寶杰3doesnothavethetraditionalenginebed(i.e.connectsenginebed)thegeometricalerroraccumulationandtheenlargementphenomenon,evenalsohasthebeinguniformeffect(averagingeffect)；Ithasthehotsymmetricalstructuraldesign,thereforethethermaldeformationissmall；Thereforeithasthehighaccuracymerit.(5)multi-purposeflexibleIsconvenientasaresultofthisenginebedorganizationsimplecontrol,easilyaccordingtoprocessingobject,butdesignsitthespecialpurposemachine,simultaneouslymayalsodevelopthegeneralenginebed,withrealizesthemilling,boring,processingsandsoongrinding,butmayalsoprovidetheessentialmeasuringtooltocomposeitthemeasuringengine,realizesenginebedsmulti-purpose.Thiswillbringtheverybigapplicationandthemarketprospect,hastheverybroadapplicationprospectinthenationaldefenseandthecivilaspect.(6)servicelifeislongBecausethestressstructureisreasonable,themovingpartattritionissmall,anddoesnothavetheguiderail,doesnothavetheironfilingseithertherefrigerantenterstheguiderailinteriortocauseittoscratch,theattritionorthecorrosionphenomenon.(7)StewartplatformsuitsinthemodularproductionRegardingthedifferentmachinescope,onlyneedchangetheconnectingrodlengthandthecontactposition,maintainsalsoeasily,doesnotneedtocarryonpartsremakingandtoadjust,onlyneedtheneworganizationparameterinput.(8)transformationcoordinatesystemisconvenientBecausedoesnothavetheentitycoordinatesystem,theenginebedcoordinatesystemandtheworkpiececoordinatesystemtransformdependonthesoftwaretocompletecompletely,isconvenient.WhentheStewartplatformappliesintheenginebedandtherobot,mayreducethestaticerror(,becausehighrigidity),aswellasdynamicerror(becauselowinertia).ButStewarttheplatforminferiorityliesinitsworkingspacetobesmall,andithasthesingularpointlimitintheworkingspace,buttheserialoperationplatform,thecontrollermeetstimethesingularpoint,accountantwillfigureouttheactuationorderwhichthedriveisunabletoachievetocreatetheningerror,buttheStewartplatformwilllosethesupportpartialdirectionsinthestrangepositionthestrengthormomentofforceability,willbeunabletocompletetheconstantloadobject.Figure2a.AbipodPKM機040511號馬吟川指導老師：許寶杰4Figure2b.AbiglidePKM2.2.SingularitiesThesingularconfigurations(alsocalledsingularities)ofaPKMmayappearinsidetheworkspaceoratitsboundaries.Therearetwotypesofsingularities5.Aconfigurationwhereafinitetoolvelocityrequiresinfinitejointratesiscalledaserialsingularity.Aconfigurationwherethetoolcannotresistanyeffortandinturn,becomesuncontrollable,iscalledaparallelsingularity.Parallelsingularitiesareparticula