INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3,pp.419-427JUNE2010/419DOI:10.1007/s12541-010-0048-61.IntroductionPlatecammechanismisawidelyusedmachinecomponentwiththecontinuouscontactmotionofcamandfollower,andcaneasilyproduceanyfunctionalmotionoffollowerduetotherotationofcam.Cammechanismhasthediversetypesbythecombinationofdifferentshapeofcamandmotionoffollower；plateorcylindricalcam,rollerorflat-facedfollower,andreciprocatingoroscillatingmotion.Inspiteoftheadvantagesofafewnumberoflinks,simplestructure,positivemotion,andcompactsize,cammechanismsrequiretheaccurateshapedesignandprecisemachiningproceduresforsatisfyingthemechanicalrequirements.Underthelowleveleddesignandmanufacturing,cammechanismsgivetheheavyeffectsonvibration,noise,separation,andoverloadingtoanoverallsystem.Toavoidtheseeffects,cammechanismmustbewelldesignedaccuratelyandmachinedprecisely.Actually,ahybridCAD/CAMapproachmaybethebestsolutionthattheshapedatafromthedesignprocessaredirectlycombinedtothemachiningdataforthemanufacturingprocess.Lineinterpolationandcircularinterpolationarecommonlyusedinconstructionofthemachiningdatafromtheprofiledataofcam.LineinterpolationhasthelowaccuracyandcircularinterpolationcannotkeeptheaccuracybecauseofthedisconnectiveradiiofcurvaturesorthediscontinuousslopesattheconnectedpointbytwocirculararcsaspresentedinShinetal.1-3Recently,parametericinterpolationusingB-splineandNURBScurvearesuggestedinJungetal.5andYangetal.6Alsobiarcinterpolationiswidelyusedanddeeplydependentonthedirectionangletowardcentersofbiarccurves.Bolton7describedabiarccurvebasedonthetangentialanglesattwopoints,ParkinsonandMoreton8madeabiarccurvebasedonaquadraticequationatthreepoints,MeekandWalton9usedsplinetypesforconstuctionofbiarccurve.Schonherr10introducedanapproachtominimizetheradiiofbiarccurves.Commonlytheseinterpolationmethodsmakethemachiningpointsincreasingandthentheexcessivedataformachiningacurvedshapemakethemachiningerrorsincreased.Thus,theprecisemachiningprocessrequiresminimizationofthemachiningpointstokeeptheaccuracyunderagivenmachiningtolerance.Thispaperintroduces3stepsofahybridCAD/CAMAHybridApproachforCamShapeDesignandProfileMachiningofGeneralPlateCamMechanismsJoong-HoShin1,Soon-ManKwon1andHyoungchulNam1,#1DepartmentofMechanicalDesign&Manufacturing,ChangwonNationalUniversity,#9,Sarim-dong,Changwon,Kyungnam,SouthKorea,641-773#CorrespondingAuthor/E-mail:nhchulchangwon.ac.kr,TEL:+82-55-267-1106,FAX:+82-55-267-1106KEYWORDS:Platecammechanism,Cam,Follower,Shapedesign,Profilemachining,Contactpoint,NCdata,Instantvelocitycenter,BiarccurvefittingPlatecammechanismcaneasilyproducethepositiveandfunctionalmotionsincontactofcamandfollower.Generallycammechanismisusedinmanyfieldsofmechanicalcontrol,automation,andindustrialmachinery.Toobtaintheaccuratemotionoffollower,theprofileofcammustbedesignedandmachinedprecisely.Thispaperproposesaninstantvelocitycentermethodfortheprofiledesignandabiarcfittingmethodfortheprofilemachiningto4differenttypesofplatecammechanismswithreciprocatingoroscillatingmotionandrollerorflat-facedfollowers.Thekeyofthispaperistheintroductionofahybridsystemcombinedthedesignproceduresandthemanufacturingprocedures.Themainideaisthattheminimummachiningdataarebuiltbytheaccuratebiarccurvesfitteddirectlyfromthedesignparameters.Theradialdirectionanglestowardbiarccentersfortheaccuratebiarccurvefittingcanbedefineddirectlybythecontactangleofcamandfollowergiveninthedesignprocedures.AnapplicationoftheproposedapproachisverifiedtheaccurateprofilesofadesignedcamandamachiningcamusingtheminimumNCdatawithinagivenmachiningtolerance.Manuscriptreceived:July16,2009/Accepted:February18,2010KSPEandSpringer2010420/JUNE2010INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3approach11for4differenttypesofplatecammechanisms.Firstly,theshapeofcamisdeterminedbythekinematicconstraintsatinstantvelocitycentersandthecontactangleatthecontactpointbetweencamandfollower.Thesecondstepistotransformthecontactanglesintothecenterdirectionanglesandthentocalculatetheradiiofbiarccurve.Finally,themachiningdataareminimizedthroughexpandingorcontractingthebiarcsectionwhetherthecamprofilepointsarelocatedinsideoroutsidetherangeofagivenmachiningtolerance.2.ClarificationofAccuracyonBiarcFitting1-3Onlytheprofiledataofcamshapearedefinedincommondesignprocessofaplatecam.Then,themachiningdatamustbedevelopedbyanycurvefittingforNC(Numericalcontrol)process.Thecircularfitting,whichismostwidelyusedinmachining,hasunreliabilityasshowninFig.1.Acircledevelopedbythreepoints1(,P2,P3)Phasaradius1Randtheotherbypoints2(,P3,P4)Phas2.RIntheviewsofcircularfittingtwocirclespasstheprofilepoints1(,P2,P3,P4),Pbutthediscontinuousslopesaremadeatthesepointsandalsothedisconnectiveradiiatpointsinmid-span.Thesedefectsmakethefittedcurveinlowaccuracyandthenhighervibrationinhighspeedoperationofcammechanism.P4P3P2P1O2O1R1R2S1S2SSlope1Slope2Fig.1Defectsoncircularfitting3231R4R2P4P3O4O3S3S2R3S1P2O2O1P1R121112212Fig.2ContinuousfittingbybiarcFig.2showsacontinuouscurvefittedbybiarcs,whichpassestheprofilepoints1(,P2,P3,P4).PThebiarccurvehas4radiiinthiscase.Radius1Rpasses1Pto1,S2Rfor1Sto2.S3Rfor2Sto3,Sand4Rfor3Sto4.PTheslopesofthebiarccurvearecontinuousanduniqueateverypoint.Alsomid-points1(,S2,S3)Sarecontinuouswithoutjumpinradii.Thus,thebiarccurvecankeepthehigherlevelofaccuracy.AsshowninFig.2,biarcfittingishighlydependentonradialdirectionangles().Thecommondesignprocessofcammechanismdefinesonlytheprofiledataandthenmachiningprocessmustusetheanglesfromthecircularfitting.Thisprocessgivestheloweraccuracybecauseoftheincorrectangles.Buttheproposedapproachinthispapercandefinethecorrectangles,whicharegivendirectlybydesignprocessofcamprofile,andthenkeepthehigheraccuracyforthemachiningdata.3.ShapeDesignofPlateCam3.1DisplacementcharacteristicsofcammechanismForaplatecammechanismwithreciprocatingrollerfollowershowninFig.3,thekinematicpropertiesoffollowermotioncanbedefinedaslineardisplacement,Yfirstderivative,YandsecondderivativeYtotherotationalanglecofcam.Andthepropertiesaregivenasangulardisplacementincaseofoscillatingfollower.Theinstantvelocitycentermethodgiveninthispaperusesthedisplacementsandthe1stderivativesfordeterminingthecamshape.CamFollowerContactpointcoordinateCamshapecoordinatecCRSyxFig.3Platecammechanismwithreciprocatingrollerfollower3.2Shapedesignbasedoninstantvelocitycenters4AsshowninFig.4,PointQisdefinedbyalinethroughcontactpointCfromrollercenterandahorizontallineandthenitbecomesinstantvelocitycenter.ThevelocityatpointQisproportionaltoarotatingspeedofcamasinEq.(1)andthevelocityofrolleratpointRisdefinedinEq.(2)asthelinearvelocityoffollower.cQQdVLdt=(1)cRcdYdYdVdtddt=(2)INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3JUNE2010/421Bythekinematiccharacteristicsofcammechanism,thevelocityattheinstantvelocitycenter,QVissameasthevelocityoffollower.RVThus,thevelocityconditiongivesthelocationoftheinstantvelocitycenterinEq.(3).QcdYLYd=(3)QR(Rx,Ry)LQVQVRcRrYxyC(Cx,Cy)Fig.4ContactpositionofcamandfollowerThecontactangleshowninFig.4isdefinedinEq.(4)byaanglebetweenaslidingvelocitylineandanormallineatacontactpointoffollowerroller.ThecoordinatesofthecontactpointaregiveninEq.(5)wherethecoordinatesofarollercenter(,xR)yRcanbecalculatedfromthedisplacement()Yandthegeometricconditions(primecircleandeccentricity)ofagivencammechanism,andwhererRistheradiusofroller.Finally,thecontactpoint(xCand)yCisgiveninEq.(5)1tanQxyLRR=(4)sinsinxxryyrCRRCRR=+=(5)QLQVQVfcYxC(Cx,Cy)F(Fx,Fy)Fig.5Platecamwithreciprocatingflat-facedfollowerFig.5showsacammechanismwithreciprocatingflat-facedfollower.InstantvelocitycenterQislocatedonthehorizontallineanddefinedinEq.(6)basedonthevelocityconditionsatinstantvelocitycenters.Then,thecontactpointisdefinedinEq.(7)QcdYLd=(6)xQyyCLCF=(7)ForamechanismwithoscillatingrollerfollowerasinFig.6,thedistanceofinstantvelocitycenterfromcamcenterbecomesinEq.(8).ThecontactanglebetweencamandrollerisexpressedinEq.(9)andthenthecontactpointisdefinedinEq.(10).Here,Zxyisthedistancetoapivotfromcamcenter.1fxycQfcdZdLdd=+(8)1tanQxyLRR=(9)sinsinxxryyrCRRCRR=+=(10)fQLQVQVRRZLZxycR(Rx,Ry)xyC(Cx,Cy)RrFig.6PlatecamwithoscillatingrollerfollowerInacaseofcammechanismwithoscillatingflat-facedfollowerasshowninFig.7,thelocationofinstantvelocitycenterisformulatedasinEq.(11)andthecontactpointisgiveninEq.(12)1fxycQfcdZdLdd=+(11)()()2coscossinxxyxyQfyxyQffCZZLCZL=(12)422/JUNE2010INTERNATIONALJOURNALOFPRECISIONENGINEERINGANDMANUFACTURINGVol.11,No.3fQLQVQVfVfZLZxycxyC(Cx,Cy)F(Fx,Fy)Fig.7Platecamwithoscillatingflat-facedfollowerFinally,theprofileofcamshapecanbedeterminedbytransformingthecontactpointwiththereverseangleofcamrotationasinEq.(13),wherexSandySarethecoordinatesofcamprofile.cossinsincosxxcycyxcycSCCSCC=+=+(13)3.3InternalnormalangleatcontactpointThenormallineateachcontactpointisshowninFigs.4-7for4differentcasesoftheplatecammechanisms.Inthispaperaninternalnormalangle()isdefinedasananglebetweenlinesconnectedtocamcenterandtoinstantvelocitycenterfromcontactpointasshowninFig.8.Becausetoolcentersformachiningandbiarccentersforcurvefittingarelocatedonthenormaldirectionlinethroughcontactpoint,theinternalnormalangle