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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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
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