《机械原理（英汉双语）（第2版）》 课件Chapter 4-6 Force Analysis；Synthesis of Planar Linkages；Design of Cam Mechanisms

Chapter4ForceAnalysisofPlanarMechanism1.ContentsofForceAnalysis1)Knowingtheexternalappliedloads,calculatetheconstraintforceswhichoccurinpairs.Constraintforcescanbeusedtodesignkinematicpairs.2)Knowingtheresistanceactingondrivenlink,calculatetheforcesactingondrivinglink,orknowingthedrivingforce,calculatetheresistanceactingondrivenlink.3)Theforceanalysisisthetheoreticalfoundationtocalculatetheefficiency.4)Makeuseoftheforceanalysis,wecandesignsomeselflockingmechanism.4.1Introduction2.MethodsofForceAnalysis

Therearetwogeneralmethodsofperformingacompleteforceanalysis：Graphicalforceanalysis&Analyticalforceanalysis.1.InertiaForcesFig.4-1Inertiaforceandinertiatorqueintoresultantforce(连杆的惯性力与惯性力矩的合成)4.2ForceAnalysisIncludingInertiaForcesinMechanisms

Fig4-1ashowsaslidercrankmechanism.Becauseoftheconstrainedmotionofthemechanism,accelerations,suchasas2,α2oftheindividuallink2andaC3oftheslider3,maybedeterminedfirst,thentheinertiaforcesFi2andtorqueMs2actingonthelink2canbecalculatedrespectively.2.KinetostaticAnalysisofPlanarMechanism(1)Kinetostaticanalysisofplanarmechanismbygraphicalmethod

Example4-1Fig4-2ashowsaconventionalshapermechanisminwhichtheangularvelocityofthecrankandalldimensionsoflinksareknown.SupposetheweightoftheramisG5,resistanceactingontheramisFr,andinertiaforceactingontheramisFi5.Theotherweightsandinertiaforcesneednottobeconsidered.DeterminetheinputtorqueMbactingonthedrivinglinkandtheconstraintforcesinpairs.Fig.4-2Graphicalforceanalysisofsharper(牛头刨床的动态静力分析)Fig.4-3Analyticalforceanalysis(动态静力分析的解析法)

Example4-2Fig4-3showsaslidercrankmechanismusedinalotofmachines,suchasinternalcombustionengineandreciprocatingcompressors.Allthedimensionsoflinks,angularpositionofthecrankandangularvelocityofthecrankareknown.Thekinematicanalysisisfirstperformedalso.

(2)Kinetostaticanalysisofplanarmechanismbyanalyticalmethod1.FrictioninKinematicPairs(1)FrictioninslidingpairsThefrictioninslidingpairscanbedividedintoplanesurfacefrictionandVsurfacefriction.

4.3ForceAnalysisIncludingFrictioninMechanismsFig.4-4Frictionontheplane

surface(平面中的摩擦)1)Frictiononplanesurface.Aslider1isrestonasmoothplanesurface2whichishorizontal.Supposethattheslider1isslidingrelativetothesurface2totherightataconstantvelocityv12actedbyadrivingforceFwhichisinclinedatanangleαtothenormal,asshowninFig4-4.2)Frictiononinclinedplanesurface.AblockofweightGrestingonaplaneinclinedatanangleαtothehorizontalisactedonbyahorizontalforceFdwhichtendstomovethebodyuptheplanewithauniformvelocityv12.ThisisshowninFig4-5a.Fig.4-5Frictionontheinclinedplanesurface(斜面摩擦)3)FrictiononVplanesurface.IftheblockshowninFig4-6aischangedintoaVblockwithaincludedangle2θshowninFig4-6b,anditsweightisG,therearetwonormalreactionforcesN21,andfromFig4-6c,Fig.4-6FrictiononV-planesurface(槽面摩擦)(2)FrictioninturningpairsThebearingsareusedextensivelyastuningpairsinmachinery,andtheycanbedividedintojournalbearingandthrustbearing.1)Frictioninjournalbearing.Whenashaftrestsinthebearing,theverticalloadGactsthroughtheaxisoftheshaft.ThenormalreactionN21ofthebearingactsinlinewithGintheverticallyupwarddirectionshowninFig4-7a.

Fig.4-7Frictioninajournalbearing(径向轴承中的摩擦)2)Frictioninthrustbearing.Whenarotatingshaftissubjectedtoanaxialload,thethrustistakenbyacollarbearing,orthrustbearing.Fig4-8ashowsathrustbearingactedbyanaxialloadG.Fig.4-8Frictioninathrustbearing(推力轴承的摩擦)（3）FrictioninhelicalpairsAccordingtothetoothshape,thescrewcanbedividedintosquarethreadsandVthreads.Asquarethreadscrewisusedtotransmitpower,andVthreadedscrewisusedtofastenanelementtoanother.Fig.4-9Frictioninsquarethread(矩形螺纹的摩擦)Fig4-9ashowsasquarethreadedscrew;itmaybethoughtofsimplyasaninclinedplaneorwedgewrappedaroundacylinder.Fig.4-10FrictioninV-thread(三角形螺纹的摩擦)Fig4-10ashowsaVthread;itsthreadangleis2β,andtheanglebetweentheVfacesofthethreadis2θ.Fig4-10bshowsatrianglewhichisthedevelopmentofahelixofdiameterdandleadl.2.ForceAnalysisIncludingFrictionExample4-3Fig4-11showsaslidercrankmechanisminwhichresistantforceFrisappliedtothepiston4.Thecrank1isrotatingintheclockwisedirection;thedimensionsoflinksandthefrictionalcoefficientofpairsareknown.Determinetheconstraintforcesinpairsandtheinputtorque.

Fig.4-11Forceanalysisconsideringthefrictioninaslider-cranklinkage

(考虑摩擦的曲柄滑块机构力分析)Example4-4Fig4-12ashowsacammechanismwithanoscillatingfollowerinwhichresistantforceFrisappliedtothefolloweratpointF.Thecam1isrotatinginthecounterclockwisedirection;thedimensionsofthemechanismandthefrictionalcoefficientofpairsareknown.Determinetheconstraintforcesinpairsandtheinputtorque.

Fig.4-12Forceanalysisconsideringthefrictioninacammechanism

(考虑摩擦的凸轮机构的力分析)1.SelflockinginKinematicPairs4.4FrictionandDesignofSelflockingMechanismsTherearetwoforcesinakinematicpairwhichisusedtoconnecttwolinks;theoneisdrivingforceandtheotherisfrictionforcewhichresiststhemotionofthelink.Ifthedrivingforceactinginapairisinfinite,andthelinkisnotmovable,itiscalledasselflockingofapair.Foraslidingpair,appliedresultantforceactswithinthefrictionalangleofabody,theselflockingwilloccurintheslidingpair.Forarotatingpair,appliedresultantforceactswithinthefrictionalcircleofabody,theselflockingwilloccurintheturningpair.2.SelflockingMechanisms(1)Travelofamechanism

1)Positivetravelofamechanism.AdrivingforceactsonthedriverAshowninFig4-13;theworkisdonebytheresistantforceactingonthedrivenlinkB.Thistravelispositivetravel.Fig.4-13Travelofmechanism

(机构的行程)(2)SelflockingmechanismIfthenegativetravelofamechanismisinselflocking,itiscalledasselflockingmechanism.Selflockingmechanismcanbeusedwidelyinmechanicalengineering.2)Negativetravelofamechanism.IftaketheresistantasadrivingforceanditactsonthelinkB,andtheoriginaldrivinglink,suchasA,becomesadrivenlink,thistravelisnegativetravel.3.DesignofSelflockingMechanismsExample4-5Fig4-14showsawedgeexpellermechanismwhichisusedtocompressabody4withloadedFrbyapplyingahorizontalforceFtothewedge2.Ifthecoefficientoffrictionofthecontactsurfacesareallthesameandknown,analyzetheconditionofselflockingofthewedges.

Fig.4-14Analysisofself-lockingmechanism(自锁机构的分析)Fig.4-15Designofself-lockingmechanism(自锁机构的设计)Example4-6DesignaneccentricdiscclampershowninFig4-15,inwhichthelink1isaneccentricdisc,body2isaworkpiecewhichwillbeclamped.Aftertheworkpiecehasbeenclamped,theforceFactedonthehandlemustberemoved.Andthentheworkpiecewhichhasbeenclampedcannotbeloosed.Determinethepositionofthepivotoftheeccentricdisc.

Chapter5SynthesisofPlanarLinkages1.TheCharacteristicsofPlanarLinkages1)Alinkagehasasimplestructureanditiseasytomanufacture,soithasalowcost.2)Thepressureinalowerpairwithsurfacecontactislower,sothelinkagehasalargeloadcapacity.3)Alinkagecanachievevariousmotionsbydesigningitsdimensionsofthelinks.4)Alinkagecantransmitmotionwithinalongdistance.5)Itisdifficulttoperformprecisionmotion;thisisadisadvantageoflinkages.5.1CharacteristicsandTypesofPlanarLinkagesFig.5-1Typesoffour-barlinkages(铰链四杆机构的类型)2.TypesofPlanarLinkagesFig.5-2Typesoffour-barlinkageswithaslidingpair(含有一个移动副的四杆机构类型)(1)CrankrockerlinkageIfafourbarlinkageshowninFig5-1aisdesignedsothatlink1canrotatecontinuouslywhilelink3onlyoscillatesthroughanangle,itiscalledacrankrockerlinkage.(2)DoublecranklinkageBothlink2andlink4inFig5-1bcanrotatecontinuouslyrelativetotheframe1;thislinkageiscalledadoublecranklinkage.(3)DoublerockerlinkageBothlink2andlink4inFig5-1ccannotrotatecompletelyrelativetotheframe3;thislinkageiscalledadoublerockerlinkage.(4)ParallelcrankfourbarlinkageIfinafourbarlinkage,twooppositelinksareparallelandequalinlength,asshowninFig5-1d,cranks2and4alwayshavethesameangularvelocity.Thismechanismiscalledaparallelcrankfourbarlinkage.Itiswidelyused,suchasinthecouplingoflocomotivewheels,inpantograph,etc.(5)IsoscelestrapeziumlinkageIftworockersofadoublerockerlinkageareequalinlength,seetheFig5-1e,thislinkageiscalledanisoscelestrapeziumlinkage;itcanbeusedinthesteeringmechanisminautomobiles.(6)SlidercranklinkageThislinkageisshowninFig5-2a,inwhichsidelink1isacrank,andtheothersidelink3isaslider.TurningpairsAandBarefullturningpairs,andCisoscillatingturningpair.(7)RotatingguidebarlinkageIfboththesidelink2andsidelink4canrotatecompletely,thislinkageiscalledarotatingguidebarlinkageshowninFig5-2b,inwhichthecouplerbecomesasliderinshape.(8)RockingblocklinkageThecrankrotatescompletelywhiletheblockonlyoscillatesaboutitspivotcenterC,thislinkageiscalledrockblocklinkageshowninFig5-2c.Itiswidelyusedinhydrauliccylindermechanism.(9)SlidingguidebarlinkageIftheguidelink4reciprocatesalongtheaxisofthefixedblock,andtheothersidelink2oscillatesaboutthepivotC,thelinkageiscalledaslidingguidebarlinkageshowninFig5-2d.Itcanbeusedinsomewaterpumps.(10)RockingguidebarlinkageIfthelink2canrotatesaboutpivotBcompletely,andthelink4oscillatesaboutthepivotAshowninFig5-2e,thislinkageiscalledarockingguidebarlinkage.Itisusedinmachinetoolssuchasshapers.(11)DoubleslidercranklinkageInafourbarlinkage,iftwosidelinks1and3becomesliderswhicharereciprocatingalongeachaxisofcrossframe,andthetwopairsofthesamekindareadjacent,itisknownasadoubleslidercranklinkageshowninFig5-3a.Thislinkagecandrawellipses.(12)DoublerotatingblocklinkageIftwoslidersarerotatingcompletelyabouttheirpivotsAandBrelativetotheframe2,thislinkageiscalledadoublerotatingblockmechanismshowninFig5-3b.ItcanalsobecalledOldhamlinkage,anditisusedtoconnecttwoshaftshavingparallelmisalignment.(13)SinelinkageThislinkagecanalsobecalledaScotchyokelinkage,inwhichthecrank2rotatesaboutitspivot.Acompletely,andlink4reciprocatesinthefixedlink1toproduceasimpleharmonicmotion.ItisshowninFig5-3c.

(14)TangentlinkageInatangentmechanism,thesidelink2oscillatesaboutitspivotA,theotherlink4reciprocatesalongitsaxis,andthelink3isasliderinshape.ItisalsocalledtheRapsonsslidelinkage.Thedisplacementoflink4hasatangentmotion.Fig.5-3Typesoffour-barlinkageswithtwoslidingpairs

(含有两个移动副的四杆机构类型)3.EvolutionandMutationofPlanarLinkages(1)InversionofafourbarlinkageDifferentmechanismscanbeobtainedbyfixingdifferentlinksofamechanism.Thisisknownasinversion.Theprincipleisthattherelativemotionbetweenlinksofafourbarlinkagedoesnotchangeindifferentinversion.

Fig.5-4Evolutionfromturningpairtoslidingpair(转动副向移动副的演化)(2)ConvertingaturningpairintoaslidingpairIftheradiusofthepinDisincreasedtoalengthoflDC,andtherocker3ismadeasliderwithacurvewhichradiusislDC,thenthismechanismbecomesacurveslidercrankmechanismshowninFig5-4b.IfthelDCweremadeinfiniteinlength,thenpointCwouldhaverectilinearmotionandlink3couldbereplacedbyaslider,asshowninFig5-4c.Fig.5-5Eccentricdiskmechanism(偏心盘机构)(3)ExpansionofpinsizeinaturningpairIfweincreasethesizeofthecrankpinBshowninFig5-5auntilitislargerthanthelengthofthecrank,thisenlargedcrankpiniscalledaneccentricdiskandcanbeusedtoreplacethecrankshowninFig5-5a.ThecrankconsistsofacirculardiskwithcenterB,whichispivotedoffcenteratAtotheframe.Thediskrotatesinsidetheringendofcoupler2.4.ApplicationsofPlanarLinkages(1)ApplicationsoflinkagesconsistedofturningpairsFig5-6aisajawcrusher.Itconsistsofacrankrockerlinkage.Theconnectingrodisthemovingjawusedtocrushtherocks.ItskinematicdiagramisshowninFig5-6b.Fig5-6cshowsadoughmixingmachine;itconsistsofacrankrockerlinkagealso.Fig.5-6Applicationsofcrank-rockerlinkage(曲柄摇杆机构的应用)

1—eccentricdisk(偏心盘)2—beltwheel(带轮)3—movingjaw(动鄂)4—movingjawboard(动鄂板)

5—fixedjawboard(静鄂板)6—rocker(摆杆)7—spring(弹簧)Fig.5-7Applicationsofdouble-rockerlinkage(双摇杆机构的应用)Fig5-7ashowsacranewhichisusedinports.Itconsistsofadoublerockerlinkage.ThepointEoncouplercanmovealongastraightline.ornearlyalongastraightline,thereforetheliftedbodymaymovesteadilyalongthispath.Fig.5-8Applicationsofdouble-cranklinkage(双曲柄机构的应用)Fig5-8ashowsainertiavibratingscreen.Itisadoublecranklinkage,andisalsocalledadraglinklinkage.IfthedriverACrotatescounterclockwisewithconstantangularvelocity,theslidermakesaslowstrokeandreturnswithaquickstroke.Theinertiaforcescancausevibrationofthescreentoperformseparationofthematerials.Fig5-8bshowsaparalleldoublecranklinkageusedinthecoupleroflocomotivewheels,andFig5-8cshowsahydraulicliftwithtwosetsofparalleldoublecranklinkages.(2)ApplicationsofslidercranklinkageSlidercranklinkagesareusedwidelyinvariousmulticylinderengines.Fig5-9aisaVenginewitheightcylinders.Thisengineconsistsofeightslidercranklinkages.Fig5-9bshowsashearingmachine.Itconsistsofoneslidercranklinkage.Fig.5-9Applicationsofslider-cranklinkage(曲柄滑块机构的应用)(3)ApplicationofcranksliderquickreturnlinkageFig5-10aisashaper;itconsistsofgearmechanismandslidingguidebarlinkage.Fig5-10bisashapertoo;itconsistsofrotatingguidebarlinkage.Fig.5-10Applicationsrockingguide-barlinkageandrotatingguide-barlinkage

(摆动导杆机构和转动导杆机构)Fig.5-11Applicationsofslidingguide-barlinkageandrocking-blocklinkage

(移动导杆机构和曲柄摇块机构的应用)

1—handle(手柄)2—link(连杆)3—cylinder(简体)4—plunger(活塞)Fig5-11ashowsahandpump,inwhichlink4ismadeintheformofacylinderandaplungerfixedtothelink3reciprocatesinit；itconsistsofslidingguidebarlinkage.Fig5-11bshowsaselfloadingtruck,inwhicharockingblocklinkageisusedtoperformselfloadingwork.

(4)ApplicationoffourbarlinkageswithtwoslidingpairsFig5-12ashowsanellipticaltrammelinwhichthefixedlink1isintheformofguidesforsliders2and4.Fig5-12bshowsanOldhamscoupling,anditconsistsofadoublerotatingblocklinkageshowninFig5-3b.Fig5-12cshowsamechanismwhichisusedtodrivetheneedleofasewingmachine;itisasinelinkage.Fig.5-12Applicationsoffour-barlinkageswithtwoslidingpairs(含有两个移动副机构的应用)1.GrashofCriteria5.2FundamentalFeaturesofFourbarLinkagesFig.5-13Grashoflaw(曲柄存在条件)Fig5-13showsafourbarlinkageABCD,andifthelinkABcanrotatethroughafullrevolutionwithanangularvelocityωclockwise,itmustpassthroughthepositionsAB1andAB2.Thelink1whichcanrotatethroughafullrevolutionmustbetheshortestlink;thesumofthelengthofshortestlinkandthelongestlink(theremustbealongestlinkamongb,c,d)cannotbegreaterthanthesumoftheremainingtwolinks.

TheGrashofcriteriacanbestatedasfollowing:

1)Alinkage,inwhichthesumofthelengthoftheshortestandlongestlinksislessthanthesumofthelengthoftheothertwolinks,musthaveacrank.2)Thecrankmustbetheshortestlink.2.QuickreturnMotion

Whenthecrankrotatesthroughafullrevolutionwithanangularvelocityωclockwise,andtherockeronlyoscillatesthroughanangleψ,thecrankandcouplerwillformastraightlineateachextremeposition.Fig-14showsacrankrockerlinkageinthetwoextremepositionsofthedrivenlink.Fig.5-14Quick-returncharacteristics(急回特性)3.PressureAngleandTransmissionAngleFig.5-15Transmissionangleandpressureangle(传动角和压力角)Thepressureangleαistheacuteanglebetweenthedirectionofthestaticforcetransferredthroughthecouplerandtheabsolutevelocityoftheoutputlinkattheconnectedpoint,suchasatC.Sincethecouplerisatwoforcelink,thedirectionofthestaticforceofthecouplerisalongthelineofitspinjoints.

TheacuteangleγbetweenthecouplerandoutputlinkisknownastransmissionangleshowninFig5-15.Noticethatinthiscase,α+γ=90.Fig.5-16Transmissionangleinaslider-cranklinkage(曲柄滑块机构的传动角)ThetransmissionangleinaslidercranklinkageisshowninFig5-16.4.DeadPointFig5-17showsacrankrockerlinkage.Whenthecrankrotatescompletely,thereisnodangerofthelinkagelocking,becausethetransmissionanglecannotbezeroatanypositions.However,iftherockerbecomesadrivinglink,thecrankisadrivenlink,andthentherockermovestotheextremepositionDC1andDC2,thetransmissionanglesbecomezero,thelinkagelockingwilloccur.Wecallthesepositionsasdeadpointsortogglepositions.Therockerwillthenhavetobedriventogetthelinkageoutofthetoggleposition.Fig.5-17Deadpoints(死点)Fig.5-18Overcomedeadpointbyusingflywheel

(利用飞轮克服死点)

1—flywheel(飞轮)2—crankshaft(曲轴)

3—camshaft(凸轮轴)4—valve(气门)

5—piston(活塞)6—connectlink(连杆)Fig5-18showsasinglecylinderenginewithfourstrokecycle.Theflywheelcancarrythepistonthroughtheenginesexhauststroke,intakestrokeandcompressionstroke.Fig5-19isadrivingmechanismofthelocomotivewheels;thephaseangleofthecranksis90°.Ifoneofthemisatthedeadposition,theothercanbedriveneasily.Fig.5-19Overcomedeadpointsbyusingdifferentphase(错位排列克服死点)Fig.5-20Self-lockingclamp(自锁夹具)Fig5-20showsaclampingdevice,inwhichafterasmallforceFappliedonthecouplerhasbeenremoved,thereactionforceoftheclampedworkpiecetothelinkABcannotdrivethelinkagetomoveatall.Wecanalsodesignmanydevicesusingthedeadpointposition.1.Introduction（1）MotiongenerationFig5-21ashowsaoverturningdeviceusedinacastingworkshop.ThisdeviceisdesignedtoguidethesandboxwhichisfixedtothecouplerintwopositionsB1C1andB2C2.Fig5-21bshowsaspeedchangedevicewhichiscontrolledbyhand.Itisdesignedtoactualizetheinputandoutputlinksthroughthethreepositions.

（2）PathgenerationAcoupleristhemostinterestinglinkinamechanism.5.3SynthesisofFourbarLinkagesFig.5-21Problemsofsynthesisofafour-barlinkage1(四杆机构设计基本问题1)Fig5-22ashowsafourbarlinkagewhichisontheextremepositions,andfromthisfigurewehave:a=（AC1－AC2）/2Thisformulaforcalculatingthelengthofthecrankisveryusefultodesignafourbarlinkage.

Fig.5-22Problemsofsynthesisoffour-barlinkages2(四杆机构设计基本问题2)Fig.5-23Guidingabodythroughtwocouplerpositions(按连杆的两个位置设计四杆机构)1)Twoprescribedlinkpositions.Fig5-23ashowstwopositionsofacouplerBC.Itisdesiredtodesignamechanismwhichwillcarrythelinkthroughthesetwopositions.(1)DesignofafourbarmechanismforspecifiedcouplerpositionsGuidingabodythroughtwoorthreelinkpositionsareoftenusedtodesignafourbarlinkage.2.GraphicalSynthesisofFourbarLinkage

2)Threeprescribedlinkpositions.Theprocedureissimilartotheaboveprocesses(Fig5-24).Fig.5-24Guidingabodythroughthreecouplerpositions(按连杆的三个位置设计四杆机构)Fig.5-25Guidingabodythroughanumberoflinkplanepositions

(按连杆平面位置设计四杆机构)3)Twoorthreeprescribedpositionsofthecouplerplane.ThreeprescribedpositionsofacouplerplaneareshowninFig5-25.

Fig.5-26Principleofinversion(反转法的原理)（2）Designofafourbarlinkageforcorrelatedangularpositionsofinputandoutputlinks1)Inversionmethod.Fig5-26showsafourbarlinkage;themotionoftheinputlinkABfromtheφ1toφ2causesamotionoftheoutputlinkDCfromψ1toψ2.Fig.5-27Coordinationofthepositionsoftheinputandoutputlinks

(按两连架杆的三组对应位置设计四杆机构)2)Threeprescribedangularpositionsoftheinputandoutputlinks.Fig5-27illustratesaprobleminwhichitisdesiredtodeterminethedimensionsofalinkageinwhichtheoutputlinkistooccupythreeangularpositionsψ1,ψ2andψ3correspondingtothethreegivenpositionsφ1,φ2andφ3oftheinputlink.

（3）DesignofafourbarlinkageforquickreturnmotionSomeexternalworkisbeingdonebythelinkageontheforwardstroke,andthereturnstrokeneedstobeaccomplishedasrapidlyaspossiblesothatamaximumtimewillbeavailableforworkingstroke.1)Crankrockerlinkage.SynthesizingacrankrockerlinkageforspecifiedvalueofK,thelengthofrockerDCandtheangleψbetweenthetwoextremepositionsoftherockerareknown.TheproceduresareinFig5-28.

Fig.5-28Synthesisofacrank-rocker

linkageforagivenK(已知K设计

曲柄摇杆机构)Fig.5-29Synthesisofaslider-crank

linkageforagivenK(已知K值设计

曲柄滑块机构)2)Slidercranklinkage.

Fig.5-30Synthesisofaguide-bar

linkageforagivenK

(已知K值设计导杆机构)3)Guidebarmechanism.Fig.5-31Couplercurve(连杆曲线)（4）DesignofafourbarlinkageforspecifiedtracingpathCouplercurvescanbecapableofapproximatingstraightlinesandlargecirclearcswithremotecenters,sotheyarequiteusefulpathmotionsformachinedesign.Fig5-31showsafourbarlinkage,inwhichthepointFonthecouplercangenerateaclosepath.3.AnalyticalSynthesisofFourbarLinkage(1)DesignofafourbarlinkageforspecifiedcouplerpositionsFig5-32showsthreepositionsofacouplerBCinwhichthecoordinatesofthepointBandCareshowninFig5-32.Itisdesiredtodesignamechanismwhichwillcarrythelinkthroughthesepositionsbyusinganalyticalmethod.

Fig.5-32Guidingabodythroughanumberoflinkpositions(按连杆的对应位置设计四杆机构)Fig.5-33Coordinationofthepositionsoftheinputandoutputlinks(按连架杆的对应位置设计四杆机构)(2)DesignofafourbarlinkageforcorrelatedpositionsofinputandoutputlinksUsuallythelengthsofthelinkABandtheframeADaregivenbyadesigner.

（3）DesignofafourbarlinkageforquickreturnmotionFig5-34showsafourbarlinkageintheextremepositions.

Fig.5-34Synthesisofafour-barlinkage

foragivenK(已知K设计四杆机构)（4）DesignofafourbarlinkageforcouplercurveAfourbarlinkageABCDwithacouplerpointPisshowninFig5-35.ThepositionofpointPonthecouplermaybelocatedbylengthofe,fandangleγshowninFig5-35.

Fig.5-35Designofafour-barlinkagefor

couplercurve(按连杆曲线设计四杆机构)Chapter6DesignofCamMechanisms1.CompositionandCharacteristicsofCamMechanisms6.1IntroductionFig.6-1Cammechanisms(盘形凸轮机构)Acammechanismconsistsofcam,followerandframe,anditbelongstothecategoryofhigherpairmechanism.Fig6-1showstwokindsofcammechanisms，inwhichFig6-1ashowsadiskcamwithatranslatingfollower,andFig6-1bshowsadiskcamwithanoscillatingfollower.Cammechanismiswidelyusedinautomaticmachines,internalcombustionengines,machinetools,printingmachines,andsoon.Comparedtolinkages,camsareeasierdesignedtogiveaspecificoutputmotion.Camsalsohaveasimplestructureandreliableperformance.2.TypesofCamMechanisms(1)Typesofcams

(2)

Typesoffollowershapes

（Fig6-4）

(3)

Typesoffollowermotion

（Fig6-4、Fig6-5）

(4)

Typesofmotionconstraints

Disccam（Fig6-1）

Translatingcam（Fig6-2）

Spatialcam（Fig6-3）Knifeedgefollower

Rollerfollower

Flatfacedfollower

SphericalfacedfollowerReciprocatingfollowerOscillatingfollowerForceclosure（Fig6-6）Formclosure（Fig6-7）Fig.6-2Translatingcammechanisms(移动凸轮机构)Fig.6-3Spatialcammechanisms(空间凸轮机构)Fig.6-4Followertypes(从动件的分类)Fig.6-5Disccamwithradialfollower

(直动从动件盘形凸轮机构)Fig.6-6Force-closedcammechanism

(力封闭凸轮机构)Fig.6-7Form-closedcammechanism(形封闭式凸轮机构)3.CamsTerminology1)Camprofile

2)Basiccircle

3)Tracepoint

4)Pitchcurveofthecam

5)Primecircle

6)Pressureangle

7)Risetravel

8)Returntravel

9)Stroke

10)Angleofascent

11)Angleofdescent

12)Angledweltatthehighestposition

13)Angledweltatthelowestposition14)Camangle

15)FollowerdisplacementFig.6-8Nomenclaturesofcammechanism(凸轮机构名词术语)

1—follower(从动件)2—pressureangle(压力角)3—tracepoint(轨迹点)

4—pitchcurve(理论廓线)5—camprofile(凸轮实际廓线)

6—primecircle(理论廓线基圆)7—basecircle(实际廓线基圆)Fig.6-9Camangleandfollowerdisplacement(凸轮转角与从动件的位移)Fig.6-10Motionofthefollower(凸轮机构运动循环图)1.BasicTypesofFollowerMotions(1)Polynomialmotions

6.2BasicTypesofFollowerMotionandDesign1)ConstantvelocitymotionFig.6-11Constant-velocitycurve

(等速运动规律)2)ConstantaccelerationanddecelerationmotionFig.6-12Constantaccelerationanddeceleration

curve(等加速等减速运动规律)3）The3-4-5polynomialmotionFig.6-133-4-5polynomialcurve

(五次多项式运动规律)(2)TrigonometricmotionsThemotionsoftrigonometricformaresimpleharmonicmotionwhichhasacosineaccelerationcurveandcycloidmotionwhichhasasineaccelerationcurve.1)Simpleharmonicmotion

Fig.6-14Simpleharmonicmotion(简谐运动)Fig.6-15Cosineacceleration

curve(余弦运动规律)2)CycloidmotionFig.6-17Sineaccelerationcurve(正弦运动规律)Fig.6-16Cycloi