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MECHANISMSANDMACHINETHEORYAurelianVadean∗,DimitriLeray,JeanGuillotAdeapartmentofMechanicalEngineering,EcolePolytechniquedeMontreal,P.O.Box6079,StationCentre-Ville,Montreal,Québec,CanadaH3C3A7bLaboratoiredeGenieMecaniquedeToulouse-COSAM,INSAToulouse,135AvenuedeRangueil,ToulouseCedex4,Automotivesub-actuatorstoothsideclearanceadjustmentoptimizationtechniques1.IntroductiontoMechanism：Thefunctionofamechanismistotransmitortransformmotionfromonerigidbodytoanotheraspartoftheactionofamachine.Therearethreetypesofcommonmechanicaldevicesthatcanbeusedasbasicelementsofamechanism.1、Gearsystem,inwhichtoothedmembersincontacttransmitmotionbetweenrotatingshafts.2、Camsystem,whereauniformmotionofaninputmemberisconvertedintoanonuniformmotionoftheoutputmember.3、Planeandspatiallinkagesarealsousefulincreatingmechanicalmotionsforapointorrigidbody.Akinematicchainisasystemoflinks,thatis,rigidbodies,whichareeitherjointedtogetherorareincontactwithoneanotherinamannerthatpermitsthemtomoverelativetooneanother.Ifoneofthelinksisfixedandthemovementofanyotherlinktoanewpositionwillcauseeachoftheotherlinkstomovetodefinitepredictableposition,thesystemisaconstrainedkinematicchain.Ifoneofthelinksisheldfixedandthemovementofanyotherlinktoanewpositionwillnotcauseeachoftheotherlinkstomovetoadefinitepredictablepositionthenthesystemisanunconstrainedkinematicchain,Amechanismorlinkageisaconstrainedkinematicchain,andisamechanicaldevicethathasthepurposeoftransferringmotionand/orforcefromasourcetoanoutput.Alinkageconsistsoflinks(orbars),generallyconsideredrigid,whichareconnectedbyjoints,suchaspinCorrevolute)orprismaticjoints,toformopenorclosedchains(orloops).Suchkinematicchains,withatleastonelinkfixed,becomemechanismsifatleasttwootherlinksremainmobility,orstructuresifnomobilityremains.Inotherwords,amechanismpermitsrelativemotionbetweenits"rigidlinks"；astructuredoesnot.Sincelinkagesmakesimplemechanismsandcanbedesignedtoperformcomplextasks,suchasnonlinearmotionandforcetransmissiontheywillreceivemuchattentioninmechanismstudy.Mechanismsareusedinagreatvarietyofmachinesanddevices.Thesimplestclosed-looplinkageisthefour-barlinkage,whichhasthreemovinglinks(plusonefixedlink)andfourpinjoints.Thelinkthatisconnectedtothepowersourceorprimemoverandhasonemovingpivotandonegroundpivotiscalledtheinputlink.Theoutputlinkconnectsanothermovingpivottoanothergroundpivot.Thecouplerorfloatinglinkconnectedthetwomovingpivots,thereby"coupling"theinputtotheoutputlink.Thefour-barlinkagehassomespecialconfigurationscreatedbymakingoneormorelinksinfiniteinlength.Theslider-crank(orcrankandslider)mechanismisafour-barchainwithasliderreplacinganinfinitelylongoutputlink.Theinternalcombustionengineisbuiltbasedonthismechanism.Otherformsoffour-linkmechanismsexistinwhichasliderisguidedonamovinglinkratherthanonafixedlink.Thesearecalledinversionsoftheslider-crank,producedwhenanotherlink(thecrank,coupler,orslider)isfixedlink.Althoughthefour-barlinkageandslider-crankmechanismareveryusefulandfoundinthousandsofapplications,wecanseethattheselinkageshavelimitedperformancelevel.Linkageswithmoremembersareoftenusedinmoredemandingcircumstances.Howeveritisoftendifficulttovisualizethemovementofamultilooplinkage,especiallywhenothercomponentsappearinthesamediagram.Thefirststepinthemotionanalysesofmorecomplicatedmechanismsistosketchtheequivalentkinematicorskeletondiagram.Theskeletondiagramservesapurposesimilartothatoftheelectricalschematicorcircuitdiagram.Organizationmovementanalysissecondstep:Drawsagraphicchart,ismustdeterminetheorganizationthenumberofdegreesoffreedom.Basedondegreeoffreedom,butItalyrefersneedscertainindependentinputsthemovementnumber,bydeterminedorganizationallcomponentsareoppositeinthegroundposition.Thepeoplehavethousandsofdifferenttypesconceivablythelinkmotiongear.Youmayimagineabagcontainingmassivelinkmotiongearthecomponent:Twopolegroups,threepolegroups,fourpolegroupsandsoon,aswellascomponents,rotation,motion,camfollower,gear,toothchain,chainwheel,leatherbelt,beltpulleyandsoon.(Spheremovement,screwvice-aswellasthepermissionthreedimensionalrelativemotionotherconnectionsnotyetincludes,here,discussesinparallelplanesmerelyplanemotion).Moreoveryouconceivableputthesecomponentsvarioustypeslinkmotiongearpossibilitywhichformsinthesameplace.Howexistshelpsthepeopletocontrolformstheseorganizationstherule?Infact,themajorityorganizationdutyisrequestsasoleinputtotransmittoasoleoutput.Thereforethesingledegreeoffreedomorganizationusesmostonekindoforganizationtype.Forexample,namelymayseebytheintuition:Fourpoleorganizationsareasingledegreeoffreedomlinkmotiongear.Thepicturemotiondiagramandthedeterminationorganizationdegreeoffreedomprocess,isthemovementanalysisandthesynthesisprocessfirststage.Inthemovementanalysis,addsonitscharacteristicaccordingtotheorganizationgeometryshapewhichpossiblyknew(forexampleinputangle,speed,angleaccelerationandsoon)studiesthedeterminationconcreteorganization.Ontheotherhand,themovementsynthesisisdesignsanorganizationtocompletethedutyprocesswhichaninstituterequests.Inthis,choosestheneworganizationthetypeandthesizeisamovementsynthesispart.Conceivestherelativemotionability,canguessthereasonthatdesignsanorganizationthereasonandmakestheimprovementtoaconcretedesignabilityislikethisasuccessfulorganizationscientist'ssymbol.Althoughtheseabilitiescomefromthecongenitalcreativity,howevermoreisbecausehasgraspedthetechnologywhichenhancesfromthepractice.1.1Themovementanalysis：simpleoneofmostusefulorganizationsisfourpoleorganizations.Inonfollowingelaborationmajorityofcontentcentralismdiscussionlinkmotiongear,butthisprocedureisalsosuitableforthemorecomplexlinkmotiongear.Wealreadyknewfourpoleorganizationshaveadegreeoffreedom.Aboutfourpoleorganizations,hastheusefulmorecontentswhichmustknow?Indeedissome!ThesepulltheXiaohusbandcriterionincludingthestandard,thetransformationconcept,theblindspotposition(divergencepoint),branchoffice,transmissionangle,withtheirsmovementcharacteristic,includingposition,speedandacceleration.Fourpoleorganizationsmayhaveonekindofbeingcalledascrankrockerorganizationform,onekindofdoublerockingleverorganization,onekindofdoublecrank(tensionbar)doestheorganization,whichoneformsendiniscalledastheorganization,isdecidedintwopolemovementscopeswhich(fixedcomponent)connectswiththerack.Thecrankrockerorganizationinputcomponent,thecrankmayrevolvethrough360°andthecontinuousrotation,butoutputsthecomponenttomaketheundulationmerely(i.e.swingmember).Asanexceptionalcase,intheparallelfourpoleorganization,inputsthepolethelengthtobeequaltooutputsthepolethelength,thego-betweenlengthandthefixedlink(rack)length,alsoisequal.Itsinputandtheoutputallmaymakethecompletealternationrotationortransformthebeingcalledasantiparallelquadrangleorganizationtheoverlappingstructure.ThestandardpullstheXiaohusbandcriterion(theorem)toindicatethat,Ifinfourpoleorganizations,betweentwopolescandowillfullyrelativelyrotatescontinuously,that,itslongestpolelengthissmallerthansumofwiththeshortestpolelengthorisequaltosumoftheothertwopolelength.Shouldpayattention:Thesamefourpoleorganization,mayhavethedifferentform,whichpoleisthisdecidedinwasstipulated(i.e.makesfixedlink)astherack.Themovementtransformationprocessisinthefixedorganizationtransmissionchaindifferentmemberhasthedifferentorganizationrateprocess.Besideshasaboutthecomponentrotationscopeknowledge,butalsomusthavehowcausestheorganizationbeforethemanufactureonenergy“therevolution”thegoodmeasure,thatwillbeveryuseful.Hardenbergh(Hartenberg)speaksof:“Therevolution”isterminology,itssignificancepassestooutputsthecomponentthemovementvalidity.Itmeanttherevolutionissteady,inwhichcaninoutputinthecomponenttohaveastrengthorthetorquebiggestforcecomponentiseffective.Notonlyalthoughthefinaloutputstrengthorthetorquearetheconnectingrodgeometricfigurefunctions,moreoveralsoisgenerallythepowerortheforceofinertiaresult,thatisfrequentlybigtolikestaticstrengthseveraltimes.Inordertoanalyzetheidlingorinordertoeasytoobtainhowcancauseanyorganization“therevolution”theindex,thetransmissionangleconceptisextremelyuseful.Inorganizationmovementperiod,thetransmissionanglevalueischanging.Thetransmissionangle0°mayoccurinthespecialposition.Willoutputthepolebutinthisspecialpositionthemovementwithnottoexertinputsonthepolethestrengthmanytohavenothingtodowithgreatly.Infact,asaresultofthemovementvice-frictioninfluence,thegeneralbasispracticalexperience,withthetransmissionangleplanningboardwhichisbiggerthantherating.Theweightlinkmotiongeartransmissionmovementabilitymatrixfoundationdefinitionalreadystudied.Adeterminingfactorvalue(itincludesregardingsomeassignsorganizationgraph,positionoutputmovementvariabletoinputvariablederivative)isathislinkmotiongearinconcretepositionmobilitycriterion.Iftheorganizationhasadegreeoffreedom(e.g.fourpoleorganizations),thenstipulatedalocationparameter,iftheinputangle,completelydeterminedthisorganizationstopsposition(neglectbranchoffice'spossibility).Wemaystudyoneaboutfourpoleorganizationcomponentabsoluteangularpositionanalysisexpression.Whenanalyzescertainpositionsand(or)certaindifferentorganizationtime,thiswillbemustbemuchmoreusefulthanthegeometricfigureanalysisprogram,becausethisexpressionwillcausetheautomatedcomputationeasytoprogram.Therealizationorganizationspeedanalysisrelativevelocitylawisthespeedpolygonisoneofseveraleffectivemethods.Thisend(goesagainst)thespottorepresentontheorganizationallspots,hasthezerospeed.Fromthisthelinewhichstipplesrespectivelytothespeedpolygoninisrepresentingtheabsolutespeedwhichthisorganizationphotographwellshouldselectrespectively.Inalineconnectionspeedpolygonrandomtwopointsrepresentsistakingonthisorganizationtwocorrespondingspotrelativevelocity.Othermethodistheinstantaneouscenterlaw,namelytheinstantaneouscenterlaw,thismethodisextremelyusefulmoreoverisfrequentlywhenthecomplexlinkmotiongearanalysisquickmethod.Theinstantaneouscenterisaspot,thisspotinthatflash,onbetweentheorganizationtwocomponentsdoesnothavetherelativemotion.Inordertodiscoverknownorganizationcertaininstantaneouscenterstheposition,Kennedythe(Kennedy)threecentertheoriesextremelyareuseful.Itissaidthat,Eachotherrelativemotionthreeobjectthreeinstantaneouscentersaresurelyinastraightline.Theorganizationvariouscomponentsaccelerationismakesonebeinterested,becauseitaffectstheforceofinertia,subsequentlyaffectsthemachinepartthestress,thebearingload,thevibrationandthenoise.Becausethefinalgoalisthemachineandtheorganizationforceofinertiaanalysis,theallaccelerationvariouscomponentsallshouldthedisposablepicture--intheorganizationfixedcomponentinertialcoordinatesystemexpressintheidenticalcoordinatesystem.Shouldpayattention:Isoppositeinrotatesonthevice-rotationrigidbodyanaccelerationcomponentusuallytohavetwofixedly.Aforcecomponentdirectioncutsinthispath,itsdirectionissamewiththisobjectangleaccelerationdirection,andiscalledthetangentialacceleration.Itsexistenceiscompletelybecausetheangularspeedrateofchangecauses.Anothercomponent,alwaysaimsattheobjectthecenterofrotation,iscalledthestandardthecentripetalacceleration,becausethiscomponentthevelocityvectordirectionhasthechangetoexist.ThemovementcomprehensiveGanizationisformsmanymechanismsthebasicgeometrystructuralunits,thesemechanismsincludingautomaticpackaging,printer,mechanicaltoy,textilemachineryandothermachineriesandsoon.Thetypicalorganizationmustdesigncausesthemovementwhichtherigidcomponentrelativedatumcomponentproduceshoped.Theorganizationmovementdesignisthemovementsynthesis,firststepfrequentlydesignstheentiremachinefirst.Whenconsiderationstress,mustaskdynamicsaspectquestion,thebearingload,thestress,thelubricationandsoonthesimilarquestion,butthemajorproblemisthemachinestructurequestion..Themovementscientistdefinesthekinematicsas“thedevelopmentfacilitymovementandthefoundationorganizationmethod”.Thisdefinitionfirstpartinvolvesthekinematicanalysis.Theknownorganization,itsconstitutionstateofmotiondeterminedbythekinematicanalysis.Thenarrationmovementanalysisdutycontainstheorganizationbetweenthemaindimension,thecomponentlinksmutuallywiththeinputmovementtechnicalcharacteristicortheactuationmethod.Thegoalismustdiscoverthedisplacement,thespeed,theacceleration,theimpactorthebeat(twostepaccelerations),withvariouscomponentshigherorderaccelerationwhichpossiblyoccursaswellasdescribesthediametermarkandthemovementwhichrealizesbycertaincomponents.Thedefinitionsecondpartofavailablefollowingtwoaspectexplained：1.researchproduceswiththeaidoftheorganizationassignsthemovementthemethod.2.researchconstructiontobeabletoproduceassignsthemotionthemethod,butintwoplans,themovementisassignstheorganizationisthefoundation.Thisisthemovementsynthesisessence.Suchmovementsynthesisinvolvestoforassignstheperformancetheorganizationsystemdesign.Themovementsynthesisaspectmaysumupasfollowingtwokinds:1.typesarecomprehensive.Thestipulationrequeststheperformance,howisonekindoftypeorganizationappropriate?(Toothgeartrain,linkmotiongear?Camgear?)Howmanycomponentsbutshouldtheorganizationhave?Howmanydegreesoffreedomneeds?Howoutlinestructureishoped?.Aboutthemembernumberandthedegreeoffreedomconsiderationwasusuallyconsideredisinthetypesynthesisisbeencalledasforaquantitysynthesisbranchdomain.2.sizesarecomprehensive.Themovementsynthesissecondpredominanttypeisthebestmethodwhichdeterminedthroughthegoallaw.Thesizesynthesisattemptstodeterminetheorganizationtheimportantsizeandthestartingposition,thisorganizationisconceivesbeforehandfortherealizationstipulationdutyandtheanticipatedperformance.Oftheso-calledimportantsizemeaningsarereferabouttwopoles,threepolesandsoonbetweenthelengthorthepoleareawayfrom,anglebetweennumberofarticlesandspoolthread,camcontoursize,camfollowerdiameter,eccentricity,gearquotaandsoon.Expectedtheorganizationtypepossiblyisthecrankslideorganization,fourpoleorganizations,thetapereelfromthemovingpartscamgear,butorisnon-hassomekindofstructureshapemorecomplexlinkmotiongearbecausebytheanalysissitusmethodwhichtheinferioranalyticmethoddetermined.Iscomprehensiveregardingthemovement,intheconventionhasthreeduties:Functionproduction,pathproductionandmovementproduction..Inputsandoutputsthecomponentinthefunctionproductionorganizationtherotationorthemigrationmustbetheinterdependence.Regardingarbitraryfunctiony=f(x),amovementsynthesisdutypossiblyisdesignsalinkmotiongeartocausetheinputandtheoutputestablishestherelationsinordertocauseinthexo

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