InternationalJournalofMachineTools&Manufacture42(2002)505520Five-axismillingmachinetoolkinematicchaindesignandanalysisE.L.J.Bohez*DepartmentofDesignandManufacturingEngineering,AsianInstituteofTechnology,P.O.Box4,KlongLuang,12120Pathumthani,ThailandReceived23May2000；receivedinrevisedform12September2001；accepted13September2001AbstractFive-axisCNCmachiningcentershavebecomequitecommontoday.ThekinematicsofmostofthemachinesarebasedonarectangularCartesiancoordinatesystem.Thispaperclassifiesthepossibleconceptualdesignsandactualexistingimplementationsbasedonthetheoreticallypossiblecombinationsofthedegreesoffreedom.Someusefulquantitativeparameters,suchastheworkspaceutilizationfactor,machinetoolspaceefficiency,orientationspaceindexandorientationangleindexaredefined.Theadvantagesanddisadvantagesofeachconceptareanalyzed.Criteriaforselectionanddesignofamachineconfigurationaregiven.NewconceptsbasedontheStewartplatformhavebeenintroducedrecentlyinindustryandarealsobrieflydiscussed.2002ElsevierScienceLtd.Allrightsreserved.Keywords:Five-axis；Machinetool；Kinematicchain；Workspace；CNC；Rotaryaxis1.IntroductionThemaindesignspecificationsofamachinetoolcanbededucedfromthefollowingprinciples:L50539Thekinematicsshouldprovidesufficientflexibilityinorientationandpositionoftoolandpart.L50539Orientationandpositioningwiththehighestposs-iblespeed.L50539Orientationandpositioningwiththehighestposs-ibleaccuracy.L50539Fastchangeoftoolandworkpiece.L50539Savefortheenvironment.L50539Highestpossiblematerialremovalrate.Thenumberofaxesofamachinetoolnormallyreferstothenumberofdegreesoffreedomorthenumberofindependentcontrollablemotionsonthemachineslides.TheISOaxesnomenclaturerecommendstheuseofaright-handedcoordinatesystem,withthetoolaxiscorre-spondingtotheZ-axis.Athree-axismillingmachinehasthreelinearslidesX,YandZwhichcanbepositionedeverywherewithinthetravellimitofeachslide.Thetoolaxisdirectionstaysfixedduringmachining.Thislimits*Tel.:+66-2-524-5687；fax:+66-2-524-5697.E-mailaddress:bohezait.ac.th(E.L.J.Bohez).0890-6955/02/$-seefrontmatter2002ElsevierScienceLtd.Allrightsreserved.PII:S0890-6955(01)00134-1theflexibilityofthetoolorientationrelativetothework-pieceandresultsinanumberofdifferentsetups.Toincreasetheflexibilityinpossibletoolworkpieceorien-tations,withoutneedofre-setup,moredegreesoffree-dommustbeadded.Foraconventionalthreelinearaxesmachinethiscanbeachievedbyprovidingrotationalslides.Fig.1givesanexampleofafive-axismillingmachine.Fig.1.Five-axismachinetool.506E.L.J.Bohez/InternationalJournalofMachineTools&Manufacture42(2002)5055202.KinematicchaindiagramToanalyzethemachineitisveryusefultomakeakinematicdiagramofthemachine.Fromthiskinematic(chain)diagramtwogroupsofaxescanimmediatelybedistinguished:theworkpiececarryingaxesandthetoolcarryingaxes.Fig.2givesthekinematicdiagramofthefive-axismachineinFig.1.Ascanbeseenthework-pieceiscarriedbyfouraxesandthetoolonlybyoneaxis.Thefive-axismachineissimilartotwocooperatingrobots,onerobotcarryingtheworkpieceandonerobotcarryingthetool.Fivedegreesoffreedomaretheminimumrequiredtoobtainmaximumflexibilityintoolworkpieceorien-tation,thismeansthatthetoolandworkpiececanbeorientedrelativetoeachotherunderanyangle.Theminimumrequirednumberofaxescanalsobeunder-stoodfromarigidbodykinematicspointofview.Toorienttworigidbodiesinspacerelativetoeachother6degreesoffreedomareneededforeachbody(toolandworkpiece)or12degrees.Howeveranycommontrans-lationandrotationwhichdoesnotchangetherelativeorientationispermittedreducingthenumberofdegreesby6.Thedistancebetweenthebodiesisprescribedbythetoolpathandallowseliminationofanadditionaldegreeoffreedom,resultinginaminimumrequirementof5degrees.3.LiteraturereviewOneoftheearliest(1970)andstillveryusefulintro-ductionstofive-axismillingwasgivenbyBaughman1clearlystatingtheapplications.TheAPTlanguagewasthentheonlytooltoprogramfive-axiscontouringappli-cations.TheproblemsinpostprocessingwerealsoFig.2.Kinematicchaindiagram.clearlystatedbySim2inthoseearlierdaysofnumeri-calcontrolandmostissuesarestillvalid.BoydinRef.3wasalsooneoftheearlyintroductions.Beziersbook4isalsostillaveryusefulintroduction.Held5givesaverybriefbutenlighteningdefinitionofmulti-axismachininginhisbookonpocketmilling.Arecentpaperapplicabletotheproblemoffive-axismachinework-spacecomputationisthemultiplesweepingusingtheDenawit-HartenbergrepresentationmethoddevelopedbyAbdel-MalekandOthman6.Manytypesanddesignconceptsofmachinetoolswhichcanbeappliedtofive-axismachinesarediscussedinRef.7butnotspecificallyforthefive-axismachine.ThenumberofsetupsandtheoptimalorientationofthepartonthemachinetableisdiscussedinRef.8.AreviewaboutthestateoftheartandnewrequirementsfortoolpathgenerationisgivenbyB.K.Choietal.9.GraphicsimulationoftheinteractionofthetoolandworkpieceisalsoaveryactiveareaofresearchandagoodintroductioncanbefoundinRef.10.4.Classificationoffive-axismachineskinematicstructureStartingfromRotary(R)andTranslatory(T)axesfourmaingroupscanbedistinguished:(i)threeTaxesandtwoRaxes；(ii)twoTaxesandthreeRaxes；(iii)oneTaxisandfourRaxesand(iv)fiveRaxes.Nearlyallexistingfive-axismachinetoolsareingroup(i).Alsoanumberofweldingrobots,filamentwindingmachinesandlasermachiningcentersfallinthisgroup.Onlylim-itedinstancesoffive-axismachinetoolsingroup(ii)existforthemachiningofshippropellers.Groups(iii)and(iv)areusedinthedesignofrobotsusuallywithmoredegreesoffreedomadded.Thefiveaxescanbedistributedbetweenthework-pieceortoolinseveralcombinations.Afirstclassi-ficationcanbemadebasedonthenumberofworkpieceandtoolcarryingaxesandthesequenceofeachaxisinthekinematicchain.Anotherclassificationcanbebasedonwheretherotaryaxesarelocated,ontheworkpiecesideortoolside.ThefivedegreesoffreedominaCar-tesiancoordinatesbasedmachineare:threetranslatorymovementsX,Y,Z(ingeneralrepresentedasTTT)andtworotationalmovementsAB,ACorBC(ingeneralrep-resentedasRR).Combinationsofthreerotaryaxes(RRR)andtwolinearaxes(TT)arerare.Ifanaxisisbearingtheworkpieceitisthehabitofnotingitwithanadditionalaccent.Thefive-axismachineinFig.1canbecharacterizedbyXH11032YH11032AH11032BH11032Z.TheXYABaxescarrytheworkpieceandtheZ-axiscarriesthetool.Fig.3showsamachineofthetypeXYZAH11032BH11032,thethreelinearaxescarrythetoolandthetworotaryaxescarrythework-piece.507E.L.J.Bohez/InternationalJournalofMachineTools&Manufacture42(2002)505520Fig.3.XYZAH11032BH11032machinery.4.1.ClassificationbasedonthesequenceofworkpieceandtoolcarryingaxesTheoreticallythenumberofpossibleconfigurationsisquitelargeiftheorderoftheaxesinthetwokinematicchainsofthetoolandworkpiececarryingaxesiscountedasadifferentconfiguration.Alsothecombinationswithonlytwolinearaxesandthreerotaryaxesareincluded.Onetoolcarryingaxisandfourworkpiececarryingaxescanbecombinedinafive-axismachineasfollows:foreachpossibletoolcarryingaxisX,Y,Z,A,B,Ctheotherfourworkpiececarryingaxescanbeselectedfromthefiveremainingaxes.Sothenumberofcombinationsoffouraxesoutoffivewithconsideringdifferentpermu-tationasanotherconfigurationis54!=120foreachpossibletoolaxisselection(1outof6or6possibilities).Sotheoreticallythereare6120=720possiblefive-axismachineswithonetoolcarryingaxis.Thesameanalysiscanbedoneforallothercombinations.Withtthenum-beroftoolcarryingaxesandwthenumberofworkpiececarryingaxes(w+t=5)thetotalnumberofcombinationsisasfollows.Ncomb=H208736tH20874t!H208736twH20874w!tH113493,t+w=5(1)Ncomb=H208736wH20874w!H208736wtH20874t!tH110223,t+w=5(2)Thevalueofthisequationisalwaysequalto6!or720whenw+t=5.Someofthese720combinationswillbecontainingonlytwolinearaxis.Ifonlyfive-axismachineswiththreelinearaxesareconsidered,only35!=360combinationsarestillpossible.ThesetGtofcombinationsischaracterizedbyafixedvalueoft.ThissetisidenticaltothesetGH11032wcharac-terizedbyafixedvalueofw,w=5H11002t.Usingabovedefi-nitionsfollowingsubgroupsoffive-axismachinesexist:(i)GroupG0/GH110325；(ii)GroupG1/GH110324；(iii)GroupG2/GH110323；(iv)GroupG3/GH110322；(v)GroupG4/GH110321；(vi)GroupG5/GH1103.G5/G0H11032machineAllaxescarrythetoolandtheworkpieceisfixedonafixedtable.Fig.4showsamachinewithallthefiveaxescarryingthetool.ThekinematicchainisXBYAZ(TRTRT).Thismachinewasoneoftheearliestmodelsoffive-axismachinestohandleveryheavyworkpieces.Astherearemanylinksinthetoolcarryingkinematicchain,therecanbeaconsiderableerrorduetoelasticdeformationsandbacklashintheslides.4.1.2.G0/G5H11032machineAllaxescarrytheworkpieceandthetoolisfixedinspace.Thisconstructionisbestusedforverysmallworkpieces(seeSection6.3).Fig.4.XBYAZmachine.508E.L.J.Bohez/InternationalJournalofMachineTools&Manufacture42(2002)5055204.1.3.G4/G1H11032machineFouraxescarrythetoolandoneaxiscarriesthework-piece.Therearebasicallytwopossibilities,thework-piececarryingaxiscanbeRH11032orTH110.G1/G4H11032machineOneaxiscarriesthetoolandtheotherfouraxescarrytheworkpiece.Therearebasicallytwopossibilities,thesingleaxiskinematicchaincanbeRorT.Fig.1isanexampleofsuchamachine,withthesingletool