机械专业毕业设计论文外文翻译连杆机构.docx

机械专业毕业设计论文外文翻译连杆机构.docx

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机械专业毕业设计论文外文翻译连杆机构

Linkmechanism

Linkagesincludegaragedoormechanisms,carwipermechanisms,gearshiftmechanisms.  Theyareaveryimportantpartofmechanicalengineeringwhichisgivenverylittleattention...

Alinkisdefinedasarigidbodyhavingtwoormorepairingelementswhichconnectittootherbodiesforthepurposeoftransmittingforceormotion.  Ineverymachine,atleastonelinkeitheroccupiesafixedpositionrelativetotheearthorcarriesthemachineasawholealongwithitduringmotion.  Thislinkistheframeofthemachineandiscalledthefixedlink.

Anarrangementbasedoncomponentsconnectedbyrotaryorslidinginterfacesonlyiscalledalinkage.  Thesetypeofconnections,revoluteandprismatic,arecalledlowerpairs.Higherpairsarebasedonpointlineorcurveinterfaces.

Examplesoflowerpairsincludehingesrotarybearings,slideways,universalcouplings.Examplesofhigherpairsincludecamsandgears.

Kinematicanalysis,aparticulargivenmechanismisinvestigatedbasedonthemechanismgeometryplusfactorswhichidentifythemotionsuchasinputangularvelocity,angularacceleration,etc.  Kinematicsynthesisistheprocessofdesigningamechanismtoaccomplishadesiredtask.  Here,bothchoosingthetypesaswellasthedimensionsofthenewmechanismcanbepartofkinematicsynthesis.

Planar,SpatialandSphericalMechanisms

Aplanarmechanismisoneinwhichallparticlesdescribeplanecurvesisspaceandalloftheplanesareco-planar..  Themajorityoflinkagesandmechanismsaredesignedasplanersystems.Themainreasonforthisisthatplanarsystemsaremoreconvenienttoengineer.  Spatialmechanismaarefarmorecomplicatedtoengineerrequiringcomputersynthesis.  Planarmechanismsultilisingonlylowerpairsarecalledplanarlinkages.Planarlinkagesonlyinvolvetheuseofrevoluteandprismaticpairs

Aspatialmechanismhasnorestrictionsontherelativemovementoftheparticles.Planarandsphericalmechanismsaresub-setsofspatialmechanisms..Spatialmechanisms/linkagesarenotconsideredonthispage

Sphericalmechanismshasonepointoneachlinkagewhichisstationaryandthestationarypointofallthelinksisatthesamelocation.  Themotionsofalloftheparticlesinthemechanismareconcentricandcanberepesentedbytheirshadowonasphericalsurfacewhichiscenteredonthecommonlocation..Sphericalmechanisms/linkagesarenotconsideredonthispage

Mobility

Animportantfactorisconsideringalinkageisthemobilityexpressedasthenumberofdegreesoffreedom.  Themobilityofalinkageisthenumberofinputparameterswhichmustbecontrolledindependentlyinordertobringthedevicetoasetposition.  Itispossibletodeterminethisfromthenumberoflinksandthenumberandtypesofjointswhichconnectthelinks...

Afreeplanarlinkgenerallyhas3degreesoffreedom（x,y,θ）.  Onelinkisalwaysfixedsobeforeanyjointsareattachedthenumberofdegreesoffreedomofalinkageassemblywithnlinks=DOF=3（n-1）

Connectingtwolinksusingajointwhichhasonlyondegreeoffreedomaddstwoconstraints.Connectingtwolinkswithajointwhichhastwodegreesoffreedominclude1restrainttothesystems.Thenumberof1DOFjoints=sayj1andthenumberofjointswithtwodegreesoffreedom=sayj2..TheMobilityofasystemisthereforeexpressedasmobility=m=3（n-1）-2j1-j2

Exampleslinkagesshowingthemobilityareshownbelow..

Asystemwithamobilityof0isastructure.Asystemwithamobilityof1canbefixedinpositionmypositioningonlyonelink.Asystemwithamobilityof2requirestwolinkstobepositionedtofixthelinkageposition..

Thisruleisgeneralinnatureandthereareexceptionsbutitcanprovideaveryusefulinitialguideasthethemobilityofanarrangementoflinks...

Grashof'sLaw

Whendesigningalinkagewheretheinputlinkageiscontinuouslyrotatede.g.drivenbyamotoritisimportantthattheinputlinkcanfreelyrotatethroughcompleterevolutions.  Thearrangementwouldnotworkifthelinkagelocksatanypoint.  ForthefourbarlinkageGrashof'slawprovidesasimpletestforthiscondition

Grashof'slawisasfollows:

Foraplanarfourbarlinkage,thesumoftheshortestandlongestlinkscannotbegreaterthanthesumoftheremaininglinksifthereistobecontinuousrelativerotationbetweentwomembers.

Referringtothe4inversionsofafourbarlinkageshownbelow..Grashof'slawstatesthatoneofthelinks（generallytheshortestlink）willbeabletorotatecontinuouslyifthefollowingconditionismet...

b（shortestlink）+c（longestlink）

FourInversionsofatypicalFourBarLinkage

Note:

Iftheaboveconditionwasnotmetthenonlyrockingmotionwouldbepossibleforanylink..

MechanicalAdvantageof4barlinkage

Themechanicaladvantageofalinkageistheratiooftheoutputtorqueexertedbythedrivenlinktotherequiredinputtorqueatthedriverlink.  ItcanbeprovedthatthemechanicaladvantageisdirectlyproportionaltoSin（β）theanglebetweenthecouplerlink（c）andthedrivenlink（d）,andisinverselyproportionaltosin（α）theanglebetweenthedriverlink（b）andthecoupler（c）.  Theseanglesarenotconstantsoitisclearthatthemechanicaladvantageisconstantlychanging.

Thelinkagepositionsshownbelowwithanangleα=0oand180ohasanearinfinitemechanicaladvantage.  Thesepositionsarereferredtoastogglepositions.  Thesepositionsallowthe4barlinkagetobeusedaclampingtools.

Theangleβiscalledthe"transmissionangle".  Asthevaluesin（transmissionangle）becomessmallthemechanicaladvantageofthelinkageapproacheszero.  Intheseregionthelinkageisveryliabletolockupwithverysmallamountsoffriction.  Whenusingfourbarlinkagestotransfertorqueitisgenerallyconsideredprudenttoavoidtransmissionanglesbelow450and500.

Inthefigureaboveiflink（d）ismadethedriverthesystemshownisinalockedposition.  Thesystemhasnotogglepositionsandthelinkageisapoordesign

Freudenstein'sEquation

Thisequationprovidesasimplealgebraicmethodofdeterminingthepositionofanoutputleverknowingthefourlinklengthsandthepositionoftheinputlever.  

Considerthe4-barlinkagechainasshownbelow..

Thepositionvectorofthelinksarerelatedasfollows

l1+l2+l3+l4=0

Equatinghorizontaldistances

l1cosθ1+l2cosθ2+l3cosθ3+l4cosθ4=0

EquatingVerticaldistances

l1sinθ1+l2sinθ2+l3sinθ3+l4sinθ4=0

Assumingθ1=1800thensinθ1=0andcosθ1=-1Therefore

-l1+l2cosθ2+l3cosθ3+l4cosθ4=0

and..l2sinθ2+l3sinθ3+l4sinθ4=0

Movingalltermsexceptthosecontainingl3totheRHSandSquaringbothsides

l32cos2θ3=（l1-l2cosθ2-l4cosθ4）2

l32sin2θ3=（-l2sinθ2-l4sinθ4）2

Addingtheabove2equationsandusingtherelationships

cos（θ2-θ4）=cosθ2cosθ4+sinθ2sinθ4）  and  sin2θ+cos2θ=1

thefollowingrelationshipresults..

Freudenstein'sEquationresultsfromthisrelationshipas

K1cosθ2+K2cosθ4+K3=cos（θ2-θ4）

K1=l1/l4    K2=l1/l2    K3=（l32-l12-l22-l24）/2l2l4

Thisequationenablestheanalyticsynthesisofa4barlinkage.  Ifthreepositionoftheoutputleverarerequiredcorrespondingtotheangularpositionoftheinputleveratthreepositionsthenthisequationcanbeusedtodeterminetheappropriateleverlengthsusingthreesimultaneousequations...

VelocityVectorsforLinks

Thevelocityofonepointonalinkmustbeperpendiculartotheaxisofthelink,otherwisetherewouldbeachangeinlengthofthelink.

OnthelinkshownbelowBhasavelocityofvAB=ω.ABperpendiculartoA-B." Thevelocityvectorisshown...

Consideringthefourbararrangementshownbelow.Thevelocityvectordiagramisbuiltupasfollows:

∙AsAandDarefixedthenthevelocityofDrelativetoA=0aanddarelocatedatthesamepoint

∙ThevelocityofBrelativetoaisvAB=ω.ABperpendiculartoA-B.Thisisdrawntoscaleasshown

∙ThevelocityofCrelativetoBisperpediculartoCBandpassesthroughb

∙ThevelocityofCrelativetoDisperpediculartoCDandpassesthroughd

∙ThevelocityofPisobtainedfromthevectordiagrambyusingtherelationshipbp/bc=BP/BC

Thevelocityvectordiagramiseasilydrawnasshown...

VelocityofslidingBlockonRotatingLink

ConsiderablockBslidingonalinkrotatingaboutA.TheblockisinstantaneouslylocatedatB'onthelink..

ThevelocityofB'relativetoA=ω.ABperpendiculartotheline.ThevelocityofBrelativetoB'=v.Thelinkblockandtheassociatedvectordiagramisshownbelow..

AccelerationVectorsforLinks

Theaccelerationofapointonalinkrelativetoanotherhastwocomponents:

∙1）thecentripetalcomponentduetotheangularvelocityofthelink.ω2.Length

∙2）thetangentialcomponentduetotheangularaccelerationofthelink....

∙Thediagrambelowshowshowtotoconstructavectordiagramfortheaccelerationcomponentsonasinglelink.

Thecentripetalaccelerationab'=ω2.ABtowardsthecentreofrotation.  Thetangentialcomponentb'b=α.ABinadirectionperpendiculartothelink..

Thediagrambelowshowshowtoconstructanaccelerationvectordrawingforafourbarlinkage.

∙ForAandDarefixedrelativetoeachotherandtherelativeacceleration=0（a,daretogether）

∙TheaccelerationofBrelativetoAaredrawnasfortheabovelink

∙ThecentripetalaccelerationofCrelativetoB=v2CBandisdirectedtowardsB