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ORIGINALARTICLEFUNCTIONALSIMULATOROF3AXISPARALLELKINEMATICMILLINGMACHINEMILOSGLAVONJICDRAGANMILUTINOVICSASAZIVANOVICRECEIVED12JULY2007/ACCEPTED27JUNE2008/PUBLISHEDONLINE24JULY2008SPRINGERVERLAGLONDONLIMITED2008ABSTRACTPARALLELKINEMATICMACHINESPKMARERESEARCHANDDEVELOPMENTTOPICINMANYLABORATORIESALTHOUGHMANYOFTHEM,UNFORTUNATELY,HAVENOPKMATALLTHEREFORE,THEUSEOFLOWCOSTBUTFUNCTIONALSIMULATOROFA3AXISPARALLELKINEMATICMILLINGMACHINEISSUGGESTEDASAHELPTOACQUIRETHEBASICEXPERIENCESINTHEPKMFIELDTHEIDEAISBASEDONTHEPOSSIBILITYTHATTHESIMULATORCOULDBEDRIVENANDCONTROLLEDBYACONVENTIONAL3AXISCOMPUTERNUMERICALCONTROLMACHINETOOLCNCTHEPAPERDESCRIBESTHEDEVELOPMENTPROCEDUREOFASIMULATORINCLUDINGTHESELECTIONOFACORRESPONDINGPARALLELMECHANISM,KINEMATICMODELLING,ANDTHEPROGRAMMINGALGORITHMTHEFUNCTIONALSIMULATORIDEAHASBEENVERIFIEDBYSUCCESSFULMAKINGOFSOMESTANDARDIZEDTESTPIECESOFSOFTMATERIAL,UNDERFULLOPERATIONALCONDITIONSKEYWORDSPARALLELKINEMATICMACHINESFUNCTIONALSIMULATORMODELLINGANDTESTING1INTRODUCTIONTHESTRATEGICIMPORTANCEOFEDUCATIONANDTRAINING,ESPECIALLYINTECHNOLOGYANDSCIENTIFICSUBJECTS,ISGROWINGTHROUGHOUTTHEWORLDTHISALSOAPPLIESTOTHEPARALLELKINEMATICMACHINESPKMSWHICHARETODAYRESEARCHANDDEVELOPMENTRDANDEDUCATIONALWORLDWIDETOPICBASICKNOWLEDGEABOUTDIVERSEASPECTSOFPKMHASBEENPUBLISHED1MANYDIFFERENTTOPOLOGIESOFPARALLELMECHANISMSWITH3TO6DOF,INCLUDINGA3DOFTRANSLATIONALORTHOGONALPARALLELMECHANISM,HAVEBEENUSED1–5TODAY,UNFORTUNATELY,THEGREATMAJORITYOFRESEARCHINSTITUTES,UNIVERSITYLABORATORIES,ANDCOMPANIESHAVENOPKMTHEREASON,OBVIOUSLY,ISTHEHIGHCOSTOFEDUCATIONANDTRAININGFORANEWTECHNOLOGY,SUCHASPKMINORDERTOCONTRIBUTETOWARDSTHEACQUISITIONOFPRACTICALEXPERIENCESINMODELLING,DESIGN,CONTROL,PROGRAMMING,ANDTHEUSEOFPKM,ALOWCOSTBUTFUNCTIONALSIMULATOROF3AXISPARALLELKINEMATICMILLINGMACHINEISPROPOSED2THEIDEAISBASEDONTHEPOSSIBILITYTHATTHESIMULATORCOULDBEDRIVENANDCONTROLLEDBYACONVENTIONAL3AXISCNCMACHINETOOLASTHEAXESOFTHECONVENTIONAL3AXISCNCMACHINEAREMUTUALLYORTHOGONAL,DIFFERENT3DOFSPATIALPARALLELMECHANISMSWITHORTHOGONALTRANSLATORYJOINTSMAYBEUSEDTOBUILDTHESIMULATOR2,7THEPAPERDESCRIBESTHEPROCEDUREFORSIMULATORDEVELOPMENTINCLUDINGTHESELECTIONOFACORRESPONDINGPARALLELMECHANISM,KINEMATICMODELLING,ANDTHEPROGRAMMINGALGORITHMTHEIDEAABOUTTHEFUNCTIONALSIMULATORWASVERIFIEDBYSUCCESSFULMAKINGOFSOMESTANDARDIZEDTESTPIECESOUTOFSOFTMATERIALS,MADEUNDERFULLOPERATIONALCONDITIONS2SIMULATOR’SCONCEPTITWOULDBEPOSSIBLE,THANKSTOTHEPREVIOUSKNOWLEDGEABOUTSERIALKINEMATICMACHINESANDAVAILABLERESOURCESFORTHEIRPROGRAMMING,TOMAKETHESIMULATORASAHYBRIDSTRUCTURECONSISTINGOFDRIVINGCONVENTIONAL3AXISCNCMILLINGMACHINEANDDRIVEN3DOFSPATIALPARALLELMECHANISMONEOFTHEPOSSIBLECONCEPTSOFAFUNCTIONALSIMULATORINTJADVMANUFTECHNOL200942813–821DOI101007/S001700081643XMGLAVONJICDMILUTINOVICSZIVANOVICMECHANICALENGINEERINGFACULTY,UNIVERSITYOFBELGRADE,KRALJICEMARIJE16,11120BELGRADE,SERBIAEMAILMGLAVONJICMASBGACYUFOR3DMILLINGOFSOFTERMATERIALS,SHOWNINFIG1,CONSISTSOF▪FULLYPARALLEL3DOFMECHANISMWITHCONSTANTSTRUTLENGTHSANDLINEARJOINTSACTUATEDANDCONTROLLEDBYTHECONVENTIONAL3AXISCNCMACHINETHEMECHANISMISBASEDONLINEARDELTAMECHANISM6BUTWITHORTHOGONALLINEARACTUATEDJOINTSTOFACILITATEITSCONNECTIONWITHXM,YM,ANDZMAXESOFHORIZONTALORVERTICALSERIALKINEMATICMACHINESTHEUNIVERSALPLATFORM,WHICHALWAYSREMAINSPARALLELWITHTHEBASE,ENABLESTHEPLACEMENTOFTHESPINDLEINTHREEDIFFERENTORTHOGONALXP,YP,−ZPDIRECTIONSASSHOWNINFIG1OUTOFSEVERALPOSSIBLECONFIGURATIONSOFTHEMECHANISM,THEONEWITHTHEPLATFORMINSIDETHETRIHEDRONXB,YB,−ZBHASBEENSELECTEDSINCEITENABLESEASYMOUNTINGOFTHEPARALLELMECHANISMONTHESERIALMACHINEXMAXISGUIDEWAYS▪SERIAL2DOFPASSIVEMECHANISMFORDECOUPLINGSERIALMACHINE’SYMANDZMAXESINADDITIONTOTHESELECTIONANDADJUSTMENTOFTHESIMULATOR’SMECHANISMWITHTHECHOSENSERIALMACHINE,THEFOLLOWINGPROCEDURES,MODELS,ALGORITHMS,ANDSOFTWAREHAVETOBEDEFINEDANDDEVELOPED–KINEMATICMODELLINGOFPARALLELMECHANISM,IE,INVERSEANDDIRECTKINEMATICS,JACOBIANMATRICES,ANDSINGULARITYANALYSIS,–WORKSPACEANALYSISANDSELECTIONOFSIMULATORPROPERDESIGNPARAMETERS,–SIMULATORDESIGNANDMANUFACTURING,FIG1FUNCTIONALSIMULATORCONCEPTFIG2THEBASICCONCEPTSOFSIMULATOR’SPARALLELMECHANISM814INTJADVMANUFTECHNOL200942813–821–THEPROCEDUREANDACCESSORIESFORADJUSTMENTOFPARALLELMECHANISM’SREFERENTPOINTSTOSIMPLIFYTHEPROGRAMMING,–ALGORITHMSANDSOFTWAREFORSIMULATORPROGRAMMING,–THEPROCEDUREFORTESTINGOFSIMULATORUNDERWORKINGCONDITIONSBYMACHININGOFVARIOUSTESTPIECESFROMSOFTERMATERIALS3ONSIMULATORMECHANISMSASTHEAXESOFTHEVERTICALANDHORIZONTAL3AXISCNCSERIALMACHINESAREORTHOGONALANDACTUATINGSIMULATOR’SAXESATTHESAMETIME,ITWOULDBETHEBESTIF3DOFSPATIALPARALLELSIMULATOR’SMECHANISMHASORTHOGONALTRANSLATORYJOINTSASWELLASINSERIALCNCMACHINESTHEAXESARECOUPLED,ITWOULDBEESSENTIAL,INAGENERALCASE,TOHAVEATLEASTONE2DOFPASSIVESERIALMECHANISMFORTHEIRDECOUPLINGTHEMOSTCONVENIENTCNCMACHINETOOLSFORTHESIMULATORARETHOSEWITHMOVABLETOOLHOLDERANDWORKINGTABLEINSUCHCONCEPTSTWOOUTOFTHREEAXESARECOUPLEDSOTHATONE2DOFSERIALPASSIVEMECHANISMSUFFICESFORTHEIRDECOUPLINGANDTHEACTUATIONOFTHESIMULATORWITHOUTCLASSIFICATIONOFKINEMATICSTRUCTURESOFHORIZONTALANDVERTICAL3AXISCNCMACHINES,SOMEEXAMPLESOF3DOFSPATIALPARALLELMECHANISMSWITHORTHOGONALTRANSLATORYJOINTS,WHICHHAVEBEENCONSIDEREDANDUSEDFORTHESIMULATOR,AREPRESENTEDINFIG2THESHAPESOFTHEIRWORKSPACESARESHOWNASWELLINTHEFIGURETHEABOVEANDSIMILAREXAMPLESOFTHEMECHANISMARETHERESULTOFTHESOLUTIONVARIANCESOFTHEINVERSEANDDIRECTKINEMATICPROBLEMOFTHEBASICCONCEPTILLUSTRATEDINFIG1THEEXAMPLESOF2DOFPASSIVESERIALMECHANISMSUSEDTODECOUPLETHEMOTIONOFTHEAXESOFDRIVINGSERIALCNCMACHINEARESHOWNINFIG3INSOMESERIALCNCMACHINECONCEPTS,THEIRAXESMAYBEDIRECTLYUSEDASSIMULATOR’SPARALLELMECHANISMTRANSLATORYJOINTSINSUCHCASES,THEGENERALCONCEPTOFTHESIMULATORBASEDONMECHANISMSSHOWNINFIG2MAYBESIMPLIFIEDFIGURE4SHOWSANEXAMPLEOFTHESIMPLIFIEDSIMULATORWITHPARALLELMECHANISMWITHOUTITSOWNJOINTSTHEDRIVINGSERIALCNCMACHINEISAHORIZONTALMACHININGCENTERTHECORRESPONDINGMECHANICALINTERFACESCONNECTJOINTPARALLELOGRAMSWITHDECOUPLEDAXESOFTHEMACHININGCENTRE2DOFSERIALMECHANISMDECOUPLESMACHININGCENTER’SYANDZAXESFIGURE5SHOWSTHEDESIGNOFASIMPLIFIEDSIMULATORFORAVERTICALCNCMILLINGMACHINEWITHTWOCOUPLEDAXESSIMULATOR’SMECHANISMHASONEOWNTRANSLATORYJOINTWHILE2DOFSERIALMECHANISMISALSOUSEDFORDECOUPLINGOFTHEVERTICALCNCMILLINGMACHINEAXES4SIMULATORMODELLINGEXAMPLEDETAILEDKINEMATICANALYSISOFTHESIMULATORFROMFIG1,ISBASEDONITSGEOMETRICMODEL,FIG6ASTHEPLATFORM,BYMECHANISMSNATURE,REMAINSPARALLELWITHTHEBASE,EACHSPATIALPARALLELOGRAM,FIG1,ISREPRESENTEDBYONESTRUTTHEFACTTHATTHECOORDINATEFRAMES,{B}AND{P},CONNECTEDTOTHEBASEANDTHEPLATFORMAREPARALLELANDTHATTHEYARE,ATTHESAMETIME,PARALLELWITHTHEREFERENTSERIALMACHINECOORDINATEFRAME{M}ENABLESGENERALIZATIONOFTHEMODELLINGOFTHEENTIRESIMULATORTHISMEANSTHATITISFEASIBLETOSEPARATETHEMODELLINGOFTHEPARALLELMECHANISMITSELF,REGARDLESSOFITSMOUNTINGONTHEHORIZONTALORVERTICALSERIALMACHINEANDTHEPOSITIONOFTHESPINDLEONFIG3THEEXAMPLESOFSERIALMECHANISMSFORDECOUPLINGOFDRIVINGMACHINE’SAXESFIG4THEEXAMPLEOFTHESIMULATORWITHOUTOWNTRANSLATORYJOINTSINTJADVMANUFTECHNOL200942813–821815ITSPLATFORMVECTORSVREFERENCEDINFRAMES{B}AND{P}AREDENOTEDBYBVANDPVVECTORSDEFINEDBYSIMULATORPARAMETERS–THEPOSITIONVECTORSOFTHEMIDPOINTSCIBETWEENJOINTCENTERSATMOBILEPLATFORMAREDEFINEDINTHEFRAME{P}AS,PPCI；I1；2；3–THEPOSITIONVECTOROFTHETOOLTIPISDEFINEDINTHEFRAME{P}ASPPT；XTPYTPZTPC138T,WHEREZTPC0H–THEPOSITIONVECTORSOFSIMULATOR’SDRIVINGAXESREFERENCEPOINTSRIAREDEFINEDAS,BPRI；I1；2；3JOINTCOORDINATESVECTOR–LL1L2L3C138T,L1,L2,ANDL3ARESCALARVARIABLESPOWEREDANDCONTROLLEDBYSERIALCNCMACHINEWITHINTHERANGEOFLMINC20LIC20LMAX,WHILEBAIAREUNITVECTORS,BA1100C138T；BA2010C138TANDBA300C01C138TWORLDCOORDINATESVECTORBPTXTYTZTC138TREPRESENTSTHEPROGRAMMEDPOSITIONVECTOROFTHETOOLTIP,WHILEXBPOPXPYPZPC2C3TREPRESENTSTHELOCATIONOFTHEPLATFORM,IE,THEORIGINOPOFTHECOORDINATEFRAME{P}ATTACHEDTOITTHERELATIONSHIPBETWEENTHESETWOVECTORSISOBVIOUSSINCECOORDINATEFRAMES{B}AND{P}AREALWAYSPARALLEL,IE,BPTBPOPPPT1OTHERVECTORSANDPARAMETERSAREDEFINEDASSHOWNINFIG6,WHEREBWIANDBQIAREUNITVECTORSWHILECISFIXEDLENGTHOFJOINTPARALLELOGRAMSTHERELATIONSHIPSBETWEENTHESIMULATOR’SJOINTCOORDINATESVECTORLL1L2L3C138TANDTHESERIALMACHINEJOINTCOORDINATESMX0MYMZMC2C3T,ASSHOWNINFIG6,AREX0ML3；YML2；ZMC0112ONTHEBASISOFGEOMETRICRELATIONSSHOWNINTHEFIG6,THEFOLLOWINGEQUATIONSAREDERIVEDKBIWIBPOPPBPCIC0BPRI3KBIWILBIAICBQI4BYTAKINGTHESQUAREOFBOTHSIDESINEQ4THEFOLLOWINGRELATIONISDERIVEDC2K2IL2IC02LIBAIKBIWIC0C15BYADOPTINGPBPCIC0BPRI06INEQ3,KINEMATICMODELLINGISVERYSIMPLIFIEDINORDERTOFULFILLTHISREQUIREMENT,SPECIFICCALIBRATIONMETHOD,IE,SETTINGOFREFERENCEPOINTSRIHASBEENDEVELOPEDBYFIG6GEOMETRICMODELOFTHESIMULATORFIG5EXAMPLEOFASIMULATORONTHEVERTICALCNCMILLINGMACHINE816INTJADVMANUFTECHNOL200942813–821
