Chapter2StructuralAnalysisofPlanarMechanisms1.Link2.1KinematicChainandMechanisms

Apartisaminimumunitinamachinefromthestandpointofmanufacture,suchasarigidlink,nut,bolt,gearandsoon.Fig.2-1ashowsasinglecylinderfourstrokecycleengine,andFig.2-1bistheschematicdiagram.Fig.2-1cisacoupler.Thecouplerconsistsofseveralpartswhichareconnectedrigidly.Fig.2-1Coupleroftheinternalcombustionengine(內(nèi)燃機(jī)中的連桿)2.KinematicPair

(1)KinematicpairsaccordingtonatureofrelativemotionAccordingtothefeatureofrelativemotionbetweenthetwolinks,kinematicpairsmaybeclassifiedasturningpairsandslidingpairs.

1)Turningpair.Whenonelinkhasaturningorrevolvingmotionrelativetotheotherlink,thesetwolinksconstituteaturningpairorarevolvingpair.

Akinematicpairisajointthatpermitsrelativemotion.Fig.2-2Turningpairs(轉(zhuǎn)動(dòng)副)2)Slidingpair.Iftwolinkshaveaslidingmotionrelativetoeachother,theyformaslidingpairorprismaticpair.Fig.2-3showssomeslidingpairsandtheirsymbols.Fig.2-3Slidingpairs(移動(dòng)副)(2)KinematicpairsaccordingtonatureofcontactAccordingtothefeatureofcontactbetweenthetwolinks,kinematicpairsmaybeclassifiedaslowerpairsandhigherpairs.1)Lowerpair.Whenapairhassurfaceorareacontactbetweentwolinks,itisknownasalowerpair.

2)Higherpair.Whenapairhasapointorlinecontactbetweentwolinks,itisknownasahigherpair.

Fig.2-4Higherpairs(高副)(3)KinematicpairelementThegeometricformsofcontactinapair,suchaspoint,lineorsurface,areknownaspairelements.

Apairismadeupoftwoelements,oneoneachlinkbeingjoined,suchastheoutsidecylindricalsurfaceofshaft1inFig.2-2andinnercylindricalsurfaceofbearing2inFig.2-2arepairelementsrespectively.。3.KinematicChainFig.2-5Closedkinematicchains(閉鏈)

Akinematicchainisanassemblyoflinksinwhichtherelativemotionsofthelinksarepossible.Kinematicchainscanbeclassifiedasclosedchainsandunclosedchains.Ifeverylinkinakinematicchainhasatleasttwopairelements,andlinksformaclosedloop,thiskinematicchainiscalledaclosedchain.Aclosedchainatleasthasoneloop.Fig.2-5showssomeclosedkinematicchains.Fig.2-6Unclosedkinematicchains(開鏈)Fig.2-6showssomeunclosedkinematicchains.Thefirstandthelastlinkhaveonlyonepairelementintheunclosedchain.Fig.2-7Structures(桁架)

Iftherelativemotionofthelinksintheassemblyisimpossible,theassemblyoflinksiscalledastructureorsuperstructure.Fig.2-7showssomestructures.Astructuremaybeconsideredasalink.Fig.2-8Mechanismsinwhichallthepairsarelowerpairs(低副機(jī)構(gòu))4.MechanismIfonelinkofakinematicchainisfixedtotheground,thekinematicchainbecomesamechanism.Ifallthepairsinamechanismarelowerpairs,themechanismiscalledalowerpairmechanism.Ifamechanismhasoneormorehigherpairs,themechanismiscalledahigherpairmechanism.Fig.2-9Mechanismincludinghigherpair(高副機(jī)構(gòu))

Fig.2-9showsahigherpairmechanisminwhichlinks1and2areconnectedbyahigherpairatpointC.2.2SchematicDiagramofMechanisms1.SchematicDiagram

Asimplediagraminwhichthelinksandpairsarerepresentedbysomesimplelinesandpairsymbolstodescribethecompositionofamechanismiscalledaschematicdiagramofmechanisms.Theschematicdiagramtakesoneortwoforms:aschematicdiagramandscaledschematicdiagram.Aschematicdiagramisproportionalbutnotexactlytoscale,whileascaledschematicdiagramrequiresa“strippeddown”stickdiagram,“strippeddown”stickdiagramisusuallyusedforfurthermotionanalysisandforceanalysis.2.SymbolsofCommonUsedLinksandPairs

ThespecialsymbolsusedinaschematicdiagramofmechanismsarelistedinTab.2-1.3.TheProcedureofDrawingaSchematicDiagramofaMechanism

(1)Mechanismnomenclature1)Frame.Linkwhichisfixedinamechanism.2)Drivinglink.Linkactedbythedrivingforceinamechanism.3)Drivenlink.Alltheothermovinglinksexcepttheframeandthedrivinglinksinamechanism.4)Couplerorconnectedrod.Linkswhicharenotconnectedwiththeframeinamechanism.

Fig.2-10Mechanismnomenclature(機(jī)構(gòu)術(shù)語)

1、3—linkconnectedframe(連架桿)2—coupler(連桿)4—frame(機(jī)架)(2)Theprocedureofdrawingaschematicdiagram1)Findoutthedrivinglinksandthedrivenlinks.2)Runthemechanismslowlyforawhile,thenstopitatasuitableposition,andobserveitscomposition.3)Findoutthenumberoflinksandthenumberofpairs,anddeterminethetypeofpairsfrominputlinktotheoutputlink.4)Theplaneonwhichmostlinksmovecanbeselectedasadrawingplane.5)Thedimensionsbetweentwopairsandtheotherkinematicdimensionsmustbemeasured,thenselectproperscaletodrawthesketch.Example2-1Fig.2-11ashowsapump.Drawaschematicdiagramofthepump.

Fig.2-11Schematicdiagramofthepump(泵的機(jī)構(gòu)運(yùn)動(dòng)簡圖)

1—eccentricdisk(偏心輪)2—coupler(連桿)3—slider(滑塊)4—frame(機(jī)架)Example2-2Fig.2-12ashowsashaper.Drawaschematicdiagramoftheshaper.

Fig.2-12Shaperanditsschematicdiagram(牛頭刨床及其機(jī)構(gòu)運(yùn)動(dòng)簡圖)

1、2—gear(齒輪)3—block(滑塊)4—rocker(擺桿)

5—link(連桿)6—slidebar(滑枕)7—frame(機(jī)架)1.GrueblersEquation(1)DegreeoffreedomofalinkDegreeoffreedomisalsocalledthemobility,anditcanbedefinedasthenumberofindependentcoordinatesrequiredtodetermineitsposition.

(2)ConstraintsofakinematicpairTheturningpairshowninFig.213bhastwoconstraints.

(3)DegreeoffreedomofakinematicpairItcanbedefinedasthenumberoftheindependentrelativemotion.

2.3DegreeofFreedomofPlanarMechanismsFig.2-13Constrainsofpair(運(yùn)動(dòng)副的約束)(4)DegreeoffreedomofaplanarmechanismInaplanarmechanism,thefixedlinkhaszerodegreeoffreedom;eachmovinglinkhas3d.o.f.,eachlowerpairhas2constraintsandeachhigherpairhas1constraint.Wesupposethattherearemovinglinksn,lowerpairspl,higherpairsph,thenthedegreeoffreedominaplanarmechanismisasfollows:F=3n-2pl-phExample2-3DeterminethedegreesoffreedomofthemechanismsshowninFig.2-14.

Fig.2-14Thecaculationofdegreeoffreedom(自由度計(jì)算)2.ConditionsHavingPredictableMotioninaMechanismFig.2-15Conditionsofcausingdefiniteandpredictablemotions(機(jī)構(gòu)具有確定運(yùn)動(dòng)的條件)Thedegreeoffreedomofamechanismisthenumberofindependentcoordinatestodefineitsposition,andisalsothenumberofinputlinkswhichneedtobeprovidedinordertocreateapredictableoutputmotion3.PointsforAttentionWhenCalculatingDegreeofFreedom(1)RedundantdegreeoffreedomSometimes,oneormorelinksofamechanismmaybemovedwithoutcausinganymotiontotheotherlinksofthemechanism.

Fig.2-16Partialdegreeoffreedom(局部自由度)(2)MultiplepinjointsTwolinksareconnectedtogetherbyonlyoneturningpair,whichisillustratedinFig.2-17&2-18.Fig.2-17Multiplepinjoints(復(fù)合鉸鏈)Fig.2-18Examplesofmultiplepinjoints(復(fù)合鉸鏈的示例)(3)RedundantconstraintsSometimes,amechanismmayhaveoneormoreredundantconstraintswhichdonoteffectthemovementoflinks,oramechanismmayhaveoneormorelinkswhichdonotintroduceanyextraconstraint.Fig.2-19Redundantconstrainintheparallel-crankmechanism(平行四邊形機(jī)構(gòu)的虛約束)1)Twolinksareconnectedbyseveralturningpairsandtheiraxesarecoincident.

2)Twolinksareconnectedbyseveralslidingpairsandtheirguidelinesareparallel.

3)Twolinksareconnectedbyseveralhigherpairsandtheircommonnormallinesarecoincident.

4)Redundantlinks.

theredundantconstraintsandlinks:Fig.2-20Redundantconstrainsofturningpairs(轉(zhuǎn)動(dòng)副的虛約束)Fig.2-21RedundantconstrainsofSlidingpairs(移動(dòng)副的虛約束)Fig.2-22RedundantconstrainsofHigherpairs(高副機(jī)構(gòu)的虛約束)Fig.2-23Redundantconstraints(虛約束)Fig.2-24Redundantconstrainproducedbyconnectingtwoequidistancepoints

(連接等距點(diǎn)產(chǎn)生的虛約束)Example2-4CalculatethedegreeoffreedomofthemechanismshowninFig.2-25.Fig.2-25Degreeoffreedomofthecomplexmechanism(復(fù)雜機(jī)構(gòu)的自由度)Example2-5CalculatethedegreeoffreedomoftheshearingmechanismshowninFig.2-26a.Fig.2-26Degreeoffreedomoftheshearingmechanism(剪床機(jī)構(gòu)的自由度)1.LinkGroupAnalysis(1)DrivinglinkThedrivinglinkmayrotateaboutitsaxisortranslatealongaguideline,andithasonedegreeoffreedom.Fig.2-27showstwokindsofdrivinglinks.

2.4MechanismAnalysisandInnovationFig.2-27Drivinglinks(原動(dòng)件)Fig.2-28Diridingoflinkgroups(拆分桿組)(2)LinkgroupAnymechanismconsistsofdrivinglink,drivenlinkandaframe.Thenumberofdrivinglinksisequaltothenumberofdegreesoffreedom.Forexample,Fig.2-28showsaonedegreeoffreedommechanism,andthedrivinglinkiscrankAB.AfterthedrivinglinkABandtheframehavebeenremovedfromthemechanism,thedegreeoffreedomofthelinkgroupBCDEFiszero.Fig.2-29ClassⅡlinkgroups(Ⅱ級(jí)桿組)

Whentherearetwolinksandthreelowerpairsinthelinkgroup,thislinkgroupiscalledclassⅡlinkgroup.Thereisonepairwhichconnectstwolinksinthelinkgroupandtwopairswhichwillconnecttheotherlinks.TheclassⅡlinkgroupsareillustratedinFig.2-29.Fig.2-30ClassⅢlinkgroups(Ⅲ級(jí)桿組)

Whentherearefourlinksandsixlowerpairsinthelinkgroup,thelinkgroupiscalledclassⅢlinkgroup.Therearethreepairswhichconnectlinksinthelinkgroupandthreepairswhichwillconnecttheotherlinks.ThecommonclassⅢlinkgroupsareillustratedinFig.2-30.Fig.2-31ClassⅣlinkgroup(Ⅳ級(jí)桿組)AnotherlinkgroupinwhichtherearefourlinksandsixlowerpairsisillustratedinFig.2-31.Therearefourpairswhichconnectlinksinthelinkgroupandtwopairswhichwillconnecttheotherlinks.WecalledthislinkgroupasclassIVlinkgroup.Thiskindoflinkgroupisusedrarely.Fig.2-32Shapermechanismdesign(牛頭刨床的組合過程)2.PrincipleofMechanismComposition

Anymechanismcanbedesignedbyconnectingbasiclinkgroupinwhichthedegreeoffreedomiszerowiththedrivinglinkandtheframe.ThisisillustratedinFig.2-32.

3.ReplacementofHigherPairbyLowerPairsWhenamechanismincludingahigherpairmustbeanalyzed,wecanreplacethehigherpairbylowerpairs.Therefore,wecanusetheprincipleoflinkgrouptoanalyzethemechanismconnectedwithlowerpairs.Asweknowthatahigherpairhasoneconstraint,andalowerpairhastwoconstraints,sothatwecanusealinkwithtwoturningpairstoreplacethehigherpair.Fig.2-33Replacementofhigherpairbylowerpairs(高副低代)Fig.2-33showssomehigherpairmechanisms;thehigherpaircanbereplacedbyonebinarylinkwithtwoturningpairs.ThecentersofcurvaturesatthecontactpointPofthetwoprofileslieatC1andC2;thelinkC1C2withturningpairsatC1andC2replacesthehigherpair.4.StructuralAnalysisofPlanarMechanism

Whendeterminingaclassofamechanism,thefollowingproceduremustbenoticed.1)Removetheredundantdegreeoffreedomandredundantconstraints.2)Thehigherpairsarereplacedbylowerpairs.3)Calculatethedegreeoffreedom,anddeterminethedrivinglinks.4)FindouttheclassIIlinkgroupsfirstandremovethemfromthemechanism.IfthereisnotanyclassIIlinkgroup,theclassIIIlinkgroupmustbeconsidered.5)Thelastlinkswhichhavebeenleftmustbethedrivinglinks,andtheyareequaltothenumberofthedegreesoffreedom.Fig.2-34Mechanismanalysis(機(jī)構(gòu)的分析)Example2-6Determinetheclassoftheshearingmechanismas