Receiveddate:2010-01-19Foundationitems:NationalNaturalScienceFoundationofChina(No50875243)；ZhejiangTechniqueInnovationGroupofModernTextileMachinery，China(No2009R50018)；FoundationofEducationDepartmentofZhejiangProvince，China(NoY201019088)；FoundationofNewTextileRDEmphasisedLaboratoryofZhejiangProvince，China(No2009FZD004)*CorrespondenceshouldbeaddressedtoCHENJian-neng，E-mail:jiannengchenzstueducnKinematicAnalysisandTestStudyofElliptic-GearandCrank-RockerBeating-UpMechanismZHAOXiong(趙雄)，RENGen-yong(任根勇)，CHENJian-neng(陳建能)*CollegeofMechanicalEngineeringandAutomation，ZhejiangSci-TechUniversity，Hangzhou310018，ChinaAbstract:Inordertoanalyzethekinematicperformancesofelliptic-gearandcrank-rocker(EGCR)beating-upmechanism，kinematicmathematicmodelsofthemechanismwereestablished，andanaidedanalysisandsimulationsoftwarewerecompiledThissoftwarecandisplaythekinematiccharacteristicsandsimulationmotionofthemechanismaccordingtodifferentparametersItalsosuppliesaplatformforhuman-computerinteractionAgroupofsatisfactoryparameterswereselectedbythesoftwareAtestbedofEGCRbeating-upmechanismwasdevelopedaccordingtotheseparametersThekinematicperformancesofthemechanismwereverifiedbyhigh-speedvideotaperecorderKeywords:beating-upmechanism；elliptic-gear；crank-rocker；kinematicsCLCnumber:TS103135Documentcode:AArticleID:1672-5220(2011)02-0222-04IntroductionBeating-upmechanismisoneofthekeymechanismsofaloomItbeatstheweftwhichisinsertedbyweft-insertionmechanismtoformthefabricItsfunctionistotransformtheconstantspeedrotationoftheloomsspindletothenon-constantspeedreciprocatingswingofthesleyInordertoallowtheweft-insertionmechanismtofinishinsertingthewefts，thesleyofthebeating-upmechanismshouldhaveadequatedwelltimeorrelativedwelltimeinthefrontpositionTheperformancesofbeating-upmechanismdeterminethefabricsquality，andalsodecidethequalityandcompetitivenessofaloom1Nowadays，therearethreegeneralkindsofbeating-upmechanisms:four-barlinkagebeating-upmechanism，six-barlinkagebeating-upmechanism，andconjugatedcambeating-upmechanismGenerally，four-barlinkagebeating-upmechanismisthesimplestmechanismwith65-75relativedwelltimeSix-barlinkagebeating-upmechanismhasabout120relativedwelltimeIthasmorehingeswhichproducelargercumulativeerrorsThedwelltimeofconjugatedcammechanismis220-240，buttheconjugatedcammechanismneedsveryhighprecisionmachiningIftherearesomeprocessingerrorsitwillcausecertainvibration2-4Inthispaper，anewtypeofbeating-upmechanismbasedonelliptic-gearandcrank-rocker(EGCR)wasproduced5，anditskinematicmathematicmodelswereestablishedAtestbedwasdevelopedandthekinematicperformancesofthemechanismwereverifiedbyhigh-speedvideotaperecorder，whichdemonstratedthatthisnewmechanismcouldmeettherequirementsofweftbeating-up1EGCRBeating-UpMechanismFigure1showstheEGCRbeating-upmechanisminitsinitialpositionOisoneofthefocusesoftheactiveelliptic-gear1andtherotationcentreoftheloomsspindleAisoneofthefocusesandtherotationcentreofthedrivenelliptic-gear2CrankAB(l1)isfixedonthedrivenelliptic-gearRockerCD(l3)isdrivenbyBC(l2)andswingsreciprocallySleyDE(l5)isfixedwithCDbyaxisDandswingsreciprocallytogetherwithCDByoptimizingtheeccentricityk(theratiooftheelliptic-gearsminorradius(b)tomajorradius(a)，theangle(theincludedanglebetweenAD(l4)andcrankABwhencrankABandlinkageBCarecollinear，thatisthesleyDEwillbeinthefrontposition)，(theincludedanglebetweenthemajoraxisoftheactiveelliptic-gearandAO)，(theincludedanglebetweenADandx-axis)，andthelengthsoflinkagesincrank-rockermechanism，thekinematicperformancesofthisnovelbeating-upmechanismbecomeexcellent，whicharesimilartothoseoftheconjugatedcambeating-upmechanism1Activeelliptic-gear；2Drivenelliptic-gear；DESleyFig1EGCRbeating-upmechanismwithitsinitialposition2KinematicMathematicModelsofEGCRBeating-UpMechanism21Mathematicalmodelsofthedrivenelliptic-gearInFig1，whentheactivegear1rotatesanticlockwiseataconstantspeed，gear2willrotateclockwiseatanon-constantspeedGiventheangulardisplacementsoftheactivegear11anddrivengear22，thedistancefrommeshpointPtoaxisOisr1andPAisr2Withcalculation，thenr1=b2/(a+ccos1)，(1)r2=b2/(a+ccos2)，(2)where，cisthedistancebetweentheelliptic-gearcenterandthefocus；1rangesfrom0to2，and2from0to26Accordingtothetransmissionprinciplesofelliptic-gearsr1=2ar2，(3)222JournalofDonghuaUniversity(EngEd)Vol28，No2(2011)thatis，cos2=(a+ccos1)b2(2a2+2accos1b2)cac(4)FromEq(4)，therelationshipbetween2and1canbeobtainedAccordingtotheprinciplesofgeartransmission2=1r1r2(5)Giventhatthevelocityofactivegearisconstant，2=1r1r2r1r2r22=2ar2r221(6)TakingthederivativeofEqs(1)and(3)，r1=b2csin1(a+ccos1)21andr2=r1，soinEq(6)r2=b2csin1(a+ccos1)21(7)22KinematicalmodelsofrockerCDSincethecrankisfixedonthedrivenelliptic-gear，itsangularvelocityandangularaccelerationarethesameasthoseofthedrivenelliptic-gearThatistosay，j1=2，j1=2，andj1=+2FromFig2，thefollowingequationscanbededuced7Fig2Crank-rockermechanismj2=arctanyCyBxCxB(8)j4=arctan(yByDxBxD)(9)j3=arccos(l32+(xDxB)2+(yDyB)2l222l3(xDxB)2+(yDyB)槡2)+j4(10)j2=VxBcosj3+VyBsinj3l2sin(j2j3)(11)j3=VxBcosj2+VyBsinj2l3sin(j2j3)(12)j2=c1cosj3+c2sinj3l2sin(j2j3)(13)j3=c1cosj2+c2sinj2l3sin(j2j3)(14)InEqs(13)and(14)，c1=axB+l3j23cosj3l2j22cosj2，(15)c2=ayB+l3j23sinj3l2j22sinj2(16)23KinematicmodelsofEinx-axisdirectiononthesleyDEDisplacementequation:sxE=xD+lDEcos(j3)(17)Velocityequation:VxE=lDEj3cos(j3/2)(18)Accelerationequation:axE=lDEj32cosj3+lDEj3jcos(j3/2)(19)3AidedAnalysisandSimulationSoftwareofMechanismandParameterOptimization31AidedanalyticalsoftwareThevisualizationofthemechanismisanalyzingandoptimizingprocessthatcandisplaymoreinformationoftheprocesstousersUserscanobservethewholeprocessandfindouttheessentialparametersofthemechanismHuman-computerinteractionanalysisandoptimizationcombinethevirtuesofbothhumanandcomputersHumanspossessthecapabilitiesofillegibleillation，judgmentandinnovation，whichcanhelptodisposerandomeventsaswellMeanwhile，computersaregoodataccuratecalculationandrepeativeworkHumanandcomputercanfullydisplaytheirrespectiveadvantagesinhuman-computerinteractionoptimizationThussatisfactoryparameterscanbeeasilyachieved8-10BasedontheabovekinematicmodelsofEGCRbeating-upmechanism，anaidedanalysisandsimulationsoftwarearecompiledwhichisshowninFig3ItcanbeusedtoanalyzetheinfluencesofdifferentmechanismparametersandverifywhetherthereexistinterferencesamongthecomponentsofthemechanismFig3AidedanalysisandsimulationsoftwareofmechanismWiththissoftware，userscaninputmechanismparameterssuchasa，k，l1，l2，l3，l4，androtaryspeedoftheloomsspindleThemechanismmotionsimulationwillbeshownontheleftoftheinterface；thedisplacement，velocity，andaccelerationcurvesofpointEwillbeshownrespectivelyontherightoftheinterface；theoptimalvalueofwillbeshownontheleft-bottomoftheinterfaceThedisplacementcurveshowsthatdwelltimeintherearpositiondecreasesaskincreases；322JournalofDonghuaUniversity(EngEd)Vol28，No2(2011)meanwhiletheaccelerationcurveshowsthatthemaximalaccelerationalsodecreasesaskincreasesForkinematicperformancesofthemechanism，kneedstobeoptimizedaccordingtotherequirementsofthebeating-upweft；l1，l2，l3，andl4alsoneedtobemodifiedbytheuserincompanywithk，soastoachieveidealkinematicperformances32OptimizationresultsanalysisOneofthemostimportantperformancesofbeating-upmechanismisthedwelltimeofsleyIncreasingmechanismparameterkcanprolongdwelltime，meantimethemaximalaccelerationincreasesremarkably，andtheoversizefluctuationofaccelerationwilldegrademechanismdynamicperformanceDesignermustthereforemakeabalancebetweenprolongingdwelltimeandcontrollingaccelerationfluctuationWiththeaboveaidedanalysisandsimulationsoftware，agroupofparameterswasobtained:=4，k=085，=135，a=71233mm，l1=40mm，l2=100mm，l3=180mm，l4=199mm，andlDE=1895mmBasedontheseparameters，whentheloomhasaspeedof300r/min，thekinematicalcurveofthebeatingpointEisshowninFig4Whenthebeating-upmechanismisontherearposition，thedisplacementcurveisalmostflatThedwelltimeofsleyiscloseto200(rangingfrom92to285)，whichwillnotleadtointerferenceofthebeating-upmechanismandweft-insertionmechanismInaddition，duringthisperiod，thecurvesofthevelocityandaccelerationofthesleyarealmostcloseto0Thereforeitwillnotcausevibration，whichwillbenefittheweftsenteryandexitfromshedAttheendofthebeating-up，themaximaldisplacementis85mmandthemaximalaccelerationis6158434m/s2，whichbothcanmeettherequirementsofthebeating-upweftFig4ThekinematiccurvesofEGCRbeating-upmechanism4TestStudyBasedontheaboveparameters，atestbedofEGCRbeating-upmechanismisdeveloped(Fig5)Usingthehigh-speedvideotaperecorderandvideoanalysissoftwareBlastersMAS，thedisplacementandvelocityareobtainedwithloomspindlesrotaryspeedat100r/minTheoreticalandexperimentaldisplacementsofbeatingpointEareshowninFig6，andtheoreticalandexperimentalvelocitiesofbeatingpointEareshowninFig7Theactualmeasureddisplacementcurveisconsistentwiththetheoreticalone，buttheactualmeasuredvelocitycurveshowssomefluctuationTherearetworeasonsforthisfinding:thegapamongthecomponentsofthemechanismcausesvibration；thevideoanalysiscontainserrors422JournalofDonghuaUniversity(EngEd)Vol28，No2(2011)5Conclusions(1)Inthispaper，theEGCRbeating-upmechanismhadbeenproducedItskinematicmathematicmodelshadbeenestablishedandanaidedanalysisandsimulationsoftwarehadbeencompiledbyvisualbasicAgroupofsatisfactoryparametershadbeengotbythissoftware(2)AtestbedoftheEGCRbeating-upmechanismwasdevelopedWiththevideotaperecorder，itskinematicperformanceswereverifiedThisdemonstratedthevalidityofthemodelsandthefeasibilityofthemechanismReferences1ZhuSK，GaoWDWeavingMachineM2ndedBeijing:ChinaTextileApparelPress，2004:267-268(inChinese)2LiangHS，HuQE，WangGC，etalTheFuzzyOptimizationDesignoftheFour-LinkWeftBeat-UpMechanismJMachineDesignandResearch，2005，21(2):72-75(inChinese)3MaSPOptimalDesignandSimulationon6-LinkB