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http//pic.sagepub.com/EngineeringScienceEngineers,PartCJournalofMechanicalProceedingsoftheInstitutionofMechanicalhttp//pic.sagepub.com/content/219/7/687TheonlineversionofthisarticlecanbefoundatDOI10.1243/095440605X315086872005219ProceedingsoftheInstitutionofMechanicalEngineers,PartCJournalofMechanicalEngineeringScienceHaoWang,CeZhangandGuanlongChenKHVIndexingCamMechanismANewIntermittentMechanismPublishedbyhttp//www.sagepublications.comOnbehalfofInstitutionofMechanicalEngineerscanbefoundatScienceProceedingsoftheInstitutionofMechanicalEngineers,PartCJournalofMechanicalEngineeringAdditionalservicesandinformationforhttp//pic.sagepub.com/cgi/alertsEmailAlertshttp//pic.sagepub.com/subscriptionsSubscriptionshttp//www.sagepub.com/journalsReprints.navReprintshttp//www.sagepub.com/journalsPermissions.navPermissionshttp//pic.sagepub.com/content/219/7/687.refs.htmlCitationsWhatisThisJul1,2005VersionofRecordatZHEJIANGUNIVERSITYonJanuary5,2013pic.sagepub.comDownloadedfromKHVindexingcammechanismanewintermittentmechanismHaoWang1C3,CeZhang2,andGuanlongChen11SchoolofMechanicalEngineering,ShanghaiJiaoTongUniversity,Shanghai,PeoplesRepublicofChina2SchoolofMechanicalEngineering,TianjinUniversity,Tianjin,PeoplesRepublicofChinaThemanuscriptwasreceivedon13September2004andwasacceptedafterrevisionforpublicationon5April2005.DOI10.1243/095440605X31508AbstractTheKHVindexingcammechanismisanewtypeintermittentmechanismthathasastructuresimilartotheKHVplanetarygeartransmissiononetypeoftheplanetarydrivewithsmallteethdifference,whereKindicatesthesungear,Hindicatesthepivotedarm,andVindicatestheoutputmechanism.Thispaperfocusesonthegenerationofapitchcurveandacamprofileinsuchanewmechanism.ThreetypesoftheKHVindexingcammechanismarecomparedanddiscussed,andtheequationsofcamspitchcurvesarederived.ThecamsprofileisgeneratedbyBooleanoperationsontheoffsetsofthecamspitchcurve.Afterthis,thecuspsonthecamprofileareeliminatedandreplacedbyaparticularHermitecurve.Theanimationsofallthreetypesareillustrated,andaprototypeofsuchmechanismisreported.Keywordsintermittentmechanism,indexingcammechanism,planetarytransmission1INTRODUCTIONIndexingcammechanismsarewidelyusedintheindustry.Threetypesofsuchmechanisms,theparallelindexingcammechanism,theFergusonindexingcammechanism,andthebarrelindexingcammechanism,arethetraditionaltypeswellknowntoday1–8.Inrecentyears,somenewtypesofindexingcammechanismshavealsobeenreported,e.g.thesynthesisofthesphericalindexingcammechanismwithdirectcontactbetweencamandfollowerwasreportedbyGonzalezPalaciosandAngeles9.Theyextendedthisconcepttothesphericalindexingcammechanismincludingrollers10.GonzalezPalaciosandAngeles11alsoproposedaunifiedapproachaimingatthesynthesisofindexingcammechanismswithdirectcontacttransmission.AnewtypeofparallelindexingcammechanismwithaninternalcamwasreportedbyNishiokaandNishimura12.Zhang13,14createdanewconceptofindexingcammechanisms–theplanetaryindexingcammechanism–andpresentedtwotypesofit.Inthispaper,theconceptisextendedtotheKHVindexingcammechanism,whichisanintermittentmechanismthathasalayoutofKHVplanetarygeartransmission.Thenewmechanismissuitablefortheworkingconditionswherealargenumberofstopsareneeded.Asmostoftherollerscanbeengagedwiththecaminthemechanism,ahigherstrengthandmorecompactdesigncanbeobtained.Thisnewmechanismcouldexpandtheapplicablerangesoftheindexingdriverstowiderindustryapplications.Thispaperfocusesonthegenerationofthepitchcurveandtheprofileofthecaminsuchamechanism.Thestructureofthispaperisasfollows.First,section2,discussesthreetypesoftheKHVindexingcammechanism,namely,typeI,typeII,andtheretrogressedmechanismthenthegenerationofthecamspitchcurveandcamprofileareexplainedandtheanimationofthemechanismtypeIandtypeIIisillustratedinsections3,4,and5,respectively,afterabriefintroductionoftheretrogressedmechanisminsection6.Finallyaprototypeofthemechanismispresentedinsection7.C3CorrespondingauthorAutobodyManufacturingTechnologyCentre,SchoolofMechanicalEngineering,ShanghaiJiaoTongUniversity,Shanghai200030,PeoplesRepublicofChina.687C16204IMechE2005Proc.IMechEVol.219PartCJ.MechanicalEngineeringScienceatZHEJIANGUNIVERSITYonJanuary5,2013pic.sagepub.comDownloadedfrom2STRUCTUREOFTHEDEVICEThestructureofaKHVindexingcammechanismissimilartoacycloidspeedreducer,whoseschemeisdepictedinFig.1.Acycloidspeedreduceriscomposedofanepitrochoidplanetgearg,aninputshaftHpivotedarmwithaneccentricity,andanumberofrollersfixedinsungearb.ForpurerotationalmotionoftheoutputshaftV,theeccentricwobbleoftheplanetgeargisfilteredoutbydeviceW,whichisaparallelogrammechanism.AsthelayoutofaKHVindexingcammechanismissimilartothecycloidspeedreducer,Fig.1isalsousedastheschemeofthenewmechanism.Insuchamechanism,thepairofplanetgearsgandtherollersinsungearbarereplacedbyacam–rollerpairtoimplementtheintermittentmotion.Inthemotionprocess,theinputshaftHrotatesataconstantspeed,whiletherotationoftheplanetgeargisintermittent.TherotationalmotionoftheplanetgeargisalsofilteredoutbydeviceWtooutputshaftV.TheKHVindexingcammechanismcanbedesignedastwodifferenttypesaccordingtothelayoutofthecam–rollerspair,namely,typeI,inwhichplanetgeargisacamandtherollersarefixedinsungearb,andtypeII,inwhichtherollersarefixedintheplanetgeargandthesungearbisaninternalcam.Whentheoutputshaftisthesungearb,andVisfixed,themechanismisnolongeraplanetarymechanism,butanordinarygeartrainretrogressedfromtheplanetarymechanismFig.2.Becausesucharetrogressedmechanismcouldalsofulfillthetaskofanintermittentmotion,itiscataloguedastheretrogressedtypeoftheKHVindexingmechanism.ResearchworkhasbeenreportedearlierontypeIIofthemechanismbyZhang13.Inthispaper,attentionisfocusedonthesynthesisofallthreetypes.3PITCHCURVEOFTHECAM3.1EquationofthepitchcurveOnthebasisofthelayoutofthemechanismmentionedearlierandtherelativemotionofitscomponents,thecoordinatesystemandtheparametersintypeIareconstructedasinFig.3.Considerthreebodiesg,playingtheroleoftheplanetcam,bbeingthesungearwithrollers,andHbeingtheinputshaftwithaneccentricity.ObandOgdenotethecentreofsungearbandplanetcamg,respectively.ThefixedcoordinatesystemObXbYbisrigidlyfixedonthesungearb,andtheinputshaftHrotatesaroundthepointObwithaconstantangularvelocity.ArelativecoordinatesystemOgXgYgrigidlyconnectedtotheplanetcamgisalsosetup,andOgalsorepresentstherotationalcentreoftheplanetcamg.Weassumethaterepresentstheeccentricityintheinputshaft,andtheradiusofthesungearbthedistancesbetweenObandthecentreofrollersMiisRz.Thenumberofrollersinthesungearbisz.TheangulardisplacementoftheinputshaftHisuH,andthatoftheplanetcamgisug.LetMii¼1,...,zrepresentthecentreoftherollers,respectively.Threepositionvectors,Rzi,H,andRTi,arealsoshowninFig.3,whereRziisfixedonthesungearbandorientedtowardsthecentreoftherollerMiwiththeoriginOb,HisfixedontheinputshaftandorientedtowardsthecentreoftheplanetcamOgwiththeoriginObalso,andRTirepresentsthepositionofthecampitchcurvewiththeoriginOg.Fig.1SchemeofaKHVindexingcammechanismtypeIandtypeIIFig.2SchemeofaKHVindexingcammechanismtheretrogressedmechanismFig.3CoordinatesystemoftypeI688HaoWang,CeZhang,andGuanlongChenProc.IMechEVol.219PartCJ.MechanicalEngineeringScienceC16204IMechE2005atZHEJIANGUNIVERSITYonJanuary5,2013pic.sagepub.comDownloadedfromTheirrelationshipyieldsRTit¼RziþH¼RzejaiC0ugtC0eejuHtC0ugtt½0,TC138,i¼1,2,...,z1FortypeII,thecoordinatesystemandtheparametersareasconstructedinFig.4.Insuchtype,gplaystheroleoftheplanetrollergear,bisaninternalcam,andHistheinputshaftwithaneccentricity.ObandOgdenotethecentreofsungearbandrollergearg,respectively.ThefixedcoordinatesystemObXbYbisalsorigidlyconnectedtotheinternalcamb,andtheinputshaftHrotatesaboutthepointObwithaconstantangularvelocity.ThemovingcoordinatesystemOgXgYgisrigidlyconnectedtotherollergearg,andOgistherotationcentreoftherollergearg.Also,erepresentstheeccentricity,andtheradiusoftherollergeargisRz.Thenumberofrollersinthesungearbisz.TheangulardisplacementoftheinputshaftHisuH,andthatoftheplanetcamgisug.LetMii¼1,...,zrepresentthecentreoftherollers,respectively.Threepositionvectors,Rzi,H,andRTi,arealsousedhereandhavethesamedenotionaswithtypeI.IntypeII,theyyieldadifferentrelationshipasRTit¼HþRzi¼eejuHtþRzejaiþugtt½0,TC138,i¼1,2,...,z23.2RelationsbetweentheinputandtheoutputofthemechanismFromequations1and2,itisseenthatthepitchcurveofeithertypeiscomposedofseveralcurvesthataredeterminedbyeveryequationinthesetcorrespondingly.Everycurvehastobeconnectedtoeachothertomakesurethatthepitchcurveofthecamiscontinuous.Then,theparametersinequations1and2shouldsatisfyRTiT¼RTiþ103RTnT¼RT104Fromequations3and4,fortypeI,thefollowingexpressionisobtainedn¼z5iHg¼C0zC016Then,thedisplacementoftheinputshaftandtheoutputshaftaredefinedbythefollowingequationuHt¼uH0þ2nC01ptnT7ugt¼C02pSn8FortypeII,anotherexpressionisobtainedn¼z9iHg¼C0z10thedisplacementoftheinputshaftandtheoutputshaftintypeIIhasadifferentdefinitionuHt¼uH0þ2ptT11ugt¼C02pSn12Figures5and6provideexamplesofthepitchcurveoftypeIandtypeII,respectively.Inbothtypes,Rz¼100,n¼12,modifiedsinemotionisusedtogeneratethepitchcurve.Figure5alsoshowstheconnectionpointbetweeneverypieceofcurve,withanasterisk,withd¼0.83andK1¼1.2,andinFig.6,d¼1andK1¼1.92.Fig.4CoordinatesystemoftypeIIFig.5PitchcurveoftypeIKHVindexingcammechanism689C16204IMechE2005Proc.IMechEVol.219PartCJ.MechanicalEngineeringScienceatZHEJIANGUNIVERSITYonJanuary5,2013pic.sagepub.comDownloadedfrom
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