机械专业毕业设计论文外文翻译连杆机构文档格式.docx

机械专业毕业设计论文外文翻译连杆机构文档格式.docx

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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

slawisasfollows:

Foraplanarfourbarlinkage,thesumoftheshortestandlongestlinkscannotbegreaterthanthesumoftheremaininglinksifthereistobecontinuousrelativerotationbetweentwomembers.

Referringtothe4inversionsofafourbarlinkageshownbelow..Grashof'

slawstatesthatoneofthelinks（generallytheshortestlink）willbeabletorotatecontinuouslyifthefollowingconditionismet...

b（shortestlink）+c（longestlink）<

a+d

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..

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