外文翻译-斜齿轮、蜗杆、圆锥齿轮

HELICAL,WORMANDBEVELGEARSINTHEFORCEANALYSISOFSPURGEARS,THEFORCESAREASSUMEDTOACTINASINGLEPLANEINTHISLESSONWESHALLSTUDYGEARSINWHICHTHEFORCESHAVETHREEDIMENSIONSTHELESSONFORTHIS,INTHECASEOFHELICALGEARS,ISTHATTHETEETHARENOTPARALLELTOTHEAXISOFROTATIONANDINTHECASEOFBEVELGEARS,THEROTATIONALAXESARENOTPARALLELTOEACHOTHERTHEREAREALSOOTHERREASONS,ASWESHALLLEARNHELICALGEARSAREUSEDTOTRANSMITMOTIONBETWEENPARALLELSHAFTSTHEHELIXANGLEISTHESAMEONEACHGEAR,BUTONEGEARMUSTHAVEARIGHTHANDHELIXANDTHEOTHERALEFTHANDHELIXTHESHAPEOFTHETOOTHISANINVOLUTEHELICOIDIFAPIECEOFPAPERCUTINTHESHAPEOFAPARALLELOGRAMISWRAPPEDAROUNDACYLINDER,THEANGULAREDGEOFTHEPAPERBECOMESAHELIXIFWEUNWINDTHISPAPER,EACHPOINTONTHEANGULAREDGEGENERATESANINVOLUTECURVETHESURFACEOBTAINEDWHENEVERYPOINTONTHEEDGEGENERATESANINVOLUTEHELICOIDSTHEINITIALCONTACTOFSPURGEARTEETHISALINEEXTENDINGALLTHEWAYACROSSTHEFACEOFTHETOOTHTHEINITIALCONTACTOFHELICALGEARTEETHISAPOINT,WHICHCHANGESINTOALINEASTHETEETHCOMEINTOMOREENGAGEMENTINSPURGEARSTHELINEOFCONTACTISPARALLELTOTHEAXISOFTHEROTATIONINHELICALGEARS,THELINEISDIAGONALACROSSTHEFACEOFTHETOOTHITISTHISGRADUALENGAGEMENTOFTHETEETHANDTHESMOOTHTRANSFEROFLOADFROMONETOOTHTOANOTHER,WHICHGIVEHELICALGEARSTHEABILITYTOTRANSMITHEAVYLOADSATHIGHSPEEDSHELICALGEARSSUBJECTTHESHAFTBEARINGSTOBOTHRADIALANDTHRUSTLOADWHENTHETHRUSTLOADSBECOMEHIGHORAREOBJECTIONABLEFOROTHERREASONS,ITMAYBEDESIRABLETOUSEDOUBLEHELICALGEARSADOUBLEHELICALGEARHERRINGBONEISEQUIVALENTTOTWOHELICALGEARSOFOPPOSITEHAND,MOUNTEDSIDEBYSIDEONTHESAMESHAFTTHEYDEVELOPOPPOSITETHRUSTREACTIONSANDTHUSCANCELOUTTHETHRUSTLOADWHENTWOORMORESINGLEHELICALGEARSAREMOUNTEDONTHESAMESHAFT,THEHANDOFTHEGEARSSHOULDBESELECTEDSOASTOPRODUCETHEMINIMUMTHRUSTLOADCROSSEDHELICAL,ORSPIRAL,GEARSARETHOSEINWHICHTHESHAFTCENTERLINESARENEITHERPARALLELNORINTERSECTINGTHETEETHOFCROSSEDHELICALGEARSHAVEPOINTCONTACTWITHEACHOTHER,WHICHCHANGESTOLINECONTACTASTHEGEARSWEARINFORTHISREASONTHEYWILLCARRYOUTVERYSMALLLOADSANDAREMAINLYFORINSTRUMENTALAPPLICATIONS,ANDAREDEFINITELYNOTRECOMMENDEDFORUSEINTHETRANSMISSIONOFPOWERTHEREISNODIFFERENCEBETWEENACROSSEDHELICALGEARANDAHELICALGEARUNTILTHEYAREMOUNTEDINMESHWITHEACHOTHERTHEYAREMANUFACTUREDINTHESAMEWAYAPAIROFMESHEDCROSSEDHELICALGEARSUSUALLYHAVETHESAMEHANDTHATIS,ARIGHTHANDDRIVERGOESWITHARIGHTHANDDRIVENINTHEDESIGNOFCROSSEDHELICALGEARS,THEMINIMUMSLIDINGVELOCITYISOBTAINEDWHENTHEHELIXANGLEAREEQUALHOWEVER,WHENTHEHELIXANGLEARENOTEQUAL,THEGEARWITHTHELARGERHELIXANGLESHOULDBEUSEDASTHEDRIVERIFBOTHGEARSHAVETHESAMEHANDWORMGEARARESIMILARTOCROSSEDHELICALGEARSTHEPINIONORWORMHASASMALLNUMBEROFTEETH,USUALLYONETOFOUR,ANDSINCETHEYCOMPLETELYWRAPAROUNDTHEPITCHCYLINDERTHEYARECALLEDTHREADSITSMATINGGEARISCALLEDAWORMGEAR,WHICHISNOTATRUEHELICALGEARAWORMANDWORMGEARAREUSEDTOPROVIDEAHIGHANGULARVELOCITYREDUCTIONBETWEENNONINTERSECTINGSHAFTSWHICHAREUSUALLYATRIGHTANGLETHEWORMGEARISNOTAHELICALGEARBECAUSEITSFACEISMADECONCAVETOFITTHECURVATUREOFTHEWORMINORDERTOPROVIDELINECONTACTINSTEADOFPOINTCONTACTHOWEVER,ADISADVANTAGEOFWORMGEARINGISTHEHIGHSLIDINGVELOCITIESACROSSTHETEETH,THESAMEASWITHCROSSEDHELICALGEARSWORMGEARINGAREEITHERSINGLEORDOUBLEENVELOPINGASINGLEENVELOPINGGEARINGISONEINWHICHTHEGEARWRAPSAROUNDORPARTIALLYENCLOSESTHEWORMAGEARINGINWHICHEACHELEMENTPARTIALLYENCLOSESTHEOTHERIS,OFCOURSE,ADOUBLEENVELOPINGWORMGEARSTHEIMPORTANTDIFFERENCEBETWEENTHETWOISTHATAREACONTACTEXISTSBETWEENTHETEETHOFDOUBLEENVELOPINGGEARSWHILEONLYLINECONTACTBETWEENTHOSEOFSINGLEENVELOPINGGEARSTHEWORMANDWORMGEAROFASETHAVETHESAMEHANDOFHELIXASFORCROSSEDHELICALGEARS,BUTTHEHELIXANGLESAREUSUALLYQUITEDIFFERENTTHEHELIXANGLEONTHEWORMISGENERALLYQUITELARGE,ANDTHATONTHEGEARVERYSMALLBECAUSEOFTHIS,ITISUSUALTOSPECIFYTHELEADANGLEONTHEWORM,WHICHISTHECOMPLEMENTOFTHEWORMHELIXANGLE,ANDTHEHELIXANGLEONTHEGEARTHETWOANGLESAREEQUALFORA90DEGSHAFTANGLEWHENGEARSARETOBEUSEDTOTRANSMITMOTIONBETWEENINTERSECTINGSHAFTS,SOMEFORMOFBEVELGEARISREQUIREDALTHOUGHBEVELGEARSAREUSUALLYMADEFORASHAFTANGLEOF90DEGTHEYMAYBEPRODUCEDFORALMOSTANYSHAFTANGLETHETEETHMAYBECAST,MILLED,ORGENERATEDONLYTHEGENERATEDTEETHMAYBECLASSEDASACCURATEINATYPICALBEVELGEARMOUNTING,ONEOFTHEGEARISOFTENMOUNTEDOUTBOARDOFTHEBEARINGTHISMEANSTHATSHAFTDEFLECTIONCANBEMOREPRONOUNCEDANDHAVEAGREATEREFFECTONTHECONTACTOFTHETEETHANOTHERDIFFICULTY,WHICHOCCURSINPREDICTINGTHESTRESSINBEVELGEARTEETH,ISTHEFACTTHATTHETEETHARETAPEREDSTRAIGHTBEVELGEARSAREEASYTODESIGNANDSIMPLETOMANUFACTUREANDGIVEVERYGOODRESULTSINSERVICEIFTHEYAREMOUNTEDACCURATELYANDPOSITIVELY,ASINTHECASEOFSPURGEARS,HOWEVER,THEYBECOMENOISYATHIGHERVALUESOFTHEPITCHLINEVELOCITYINTHESECASESITISOFTENGOODDESIGNPRACTICETOGOTOTHESPIRALBEVELGEAR,WHICHISTHEBEVELCOUNTERPARTOFTHEHELICALGEAR,ASINTHECASEOFHELICALGEARS,SPIRALBEVELGEARSGIVEAMUCHSMOOTHERTOOTHACTIONTHANSTRAIGHTBEVELGEARS,ANDHENCEAREUSEFULWHEREHIGHSPEEDAREENCOUNTEREDITISFREQUENTLYDESIRABLE,ASINTHECASEOFAUTOMOTIVEDIFFERENTIALAPPLICATIONS,TOHAVEGEARINGSIMILARTOBEVELGEARSBUTWITHTHESHAFTOFFSETSUCHGEARSARECALLEDHYPOIDGEARSBECAUSETHEIRPITCHSURFACESAREHYPERBOLOIDSOFREVOLUTIONTHETOOTHACTIONBETWEENSUCHGEARSISACOMBINATIONOFROLLINGANDSLIDINGALONGASTRAIGHTLINEANDHASMUCHINCOMMONWITHTHATOFWORMGEARSTOPOLOGICALEXPRESSIONMODELOFSATELLITEGEARMECHANISMABSTRACTBYINVESTIGATIONOFTHETOPOLOGICALCHARACTERISTICSOFTHEKINEMATICSTRUCTUREOFSATELLITEGEARMECHANISMSGMWITHGRAPHTHEORY，THEGRAPHMODELOFSGMISANALYZED，ANDATOPOLOGICALEXPRESSIONMODELBETWEENINPUTANDOUTPUTOFSGMISESTABLISHEDBASEDONSYSTEMATICDESIGNPOINTMEANWHILE，THEMATHEMATICALEXPRESSIONFORSGMISDEDUCEDBYINTEGRATINGMATRIXTHEORYANDGRAPHTHEORY；THUS，THETOPOLOGICALCHARACTERISTICSOFTHEKINEMATICSTRUCTUREOFSGMCALLBECONVERTEDINTOAMATRIXMODEL，ANDTHETOPOLOGICALDESIGNPROBLEMOFSGMINTOAMATRIXOPERATIONPROBLEMINADDITION，ABRIEFDISCUSSIONABOUTTHEMEASURESFORIDENTIFICATIONOFISOMORPHISMOFTHEGRAPHMODEISMADEKEYWORDSSATELLITEGEARMECHANISM；GRAPHMODEL；TOPOLOGICALEXPRESSIONINTR0DUCTIONBECAUSEOFTHEIRCOMPACTNESSANDINTERESTINGPOWERTOWEIGHTRATIO，EPICYCLICGEARMECHANISMSEGMSAREWIDELYUSEDINROBOTICS，AERONAUTICS，ANDAUTOMOTIVE，MARINEANDINDUSTRIALPOWERTRANSMISSIONSSATELLITEGEARMECHANISMSGMISACOMPLEXEGMWHICHHASATLEASTONESATELLITEGEAR，ANDTHESATELLITEGEARISDEFINEDASTHEGEARWHOSEAXISREVOLVESAROUNDTHEAXISOFTHEPLANETGEARINTHEEARLYSTAGEOFDESIGNINGAUTOMOTIVEAUTOMATICTRANSMISSION，ITISDESIRABLETOENUMERATEALLTHEPOSSIBLEEGMSFORTHESUBSEQUENTSTAGEOFDETAILDESIGNIN1988TSAIETALIDENTIFIEDSOMEOFTHESTRUCTURALCHARATERISTICSREQUIREDBYANEPICYCLICGEARTRAINEGTTOQUALIFYFORAUTOMATICTRANSMISSIONSIN1994,CHATTERJEEANDTSAIDEFINEDTHECANONICALGRAPHOFEGMSTOFORMULATEASYSTEMATICMETHODOLOGYFORTHEENUMERATIONOFEGMSTHEIRMETHODOLOGYCONSISTSOFTWOPHASESONEISTOENUMERATEALLTHELABELEDTREESGENERATED；ANDTHEOTHERISTOADDGEAREDEDGESTOTHESETREESTOCREATECANONICALGRAPHSALTHOUGHTHISMETHODOLOGYISFEASIBLE，ITISTEDIOUSANDPRONETOHUMANERRORASTHENUMBEROFLINKSGROWSTHEREFORE，ITISNECESSARYTODEVELOPANEFICIENTMETHODOLOGYFORTHETOPOLOGICALEXPRESSIONOFEGMSTWOMAJORPROBLEMSAREFREQUENTLYENCOUNTEREDINTHEINTEHIGENTCADFORDESIGNOFKINEMATICCHAINS，ESPECIALLYFOREGMSONEISHOWTOENUMERATEALLTHEPOSSIBLEKINEMATICSTRUCTURESWHICHCANMEETTHEDESIGNDEMAND；THEOTHERISHOWTODETECTTHEPOSSIBLESTRUCTURALISOMORPHISMBETWEENTWOGIVENCHAINSTHEREFORE，ARELIABLEANDEFICIENTSYSTEMATICMODELINGMETHODOLOGYANDANALGEBRAICTESTINGALGORITHMFORSOLVINGTHESEPROBLEMSAREPARTICULARLYNECESSARYFORTHESTRUCTURALSYNTHESISPROCEDURETOBEIMPLEMENTEDOFTHEDIGITALCOMPUTERORTOFORMTHEINTELLIGENTCADSYSTEMGRAPHTHEORYHASBEENAPPLIEDTOTHESTRUCTURALANALYSISANDSYNTHESISOFMECHANISMFORMANYYEARS，ANDHASPROVENTOBEANEFECTIVEANDSYSTEMATICMODELINGAPPROACHINTHESEARCHOFNEWMECHANISMALTHOUGHTHISMETHODOLOGYISFEASIBLE，ITSTILLHASTWODISADVANTAGESTHEMETHODCANNOTADAPTTOENUMERATIONOFTHEROTATIONGRAPHSFOREGM，ANDCANNOTADAPTTOTHEEGMWHICHHASEMBEDDEDSTRUCTURESANDNONCOAXIALLINKSBEINGUSEDASINPUT，OUTPUTORFIXEDLINKTOOVERCOMETHESEDISADVANTAGES，WEMUSTINTRODUCESOMEMOREEFFICIENTCONCEPSANDRULESFORGRAPHREPRESENTATIONOFEGM；ESPECIALLY，THEYMUSTADAPTTOTHELINKSGROWINGANDTHEEMBEDDEDSTRUCTURESANDNONCOAXIALLINKSUSEDASINPUT，OUTPUTORFIXEDLINK，ETC；ANDCONSTITUTETHEMOREEFFICIENTENUMERATIONSGMISANEWTYPEOFEGMWITHVARIOUSTYPESOFGEARINGSINWHICHTHECOUPLINGBETWEENTHEGEARANDPLANETISACCOMPLISHEDBYINGENIOUSTACTICSTHISDESIGNISANATTRACTIVEALTERNATIVETRANSMITTINGMOTIONANDPOWERFORSOMESPECIALDEMANDCOMPAREDWITHTHEPLANETARYGEARMECHANISM，SGMCANGETAMORECOMPACTNEDSTRUCTUREINAXIALDKECTIONUNDERTHESAMETRANSMITTINGRATIO，ANDCANOBTAINABROADERTRANSMITTINGRATIOUNDERTHESAMETRANSMITTINGPOWERWHATSMORE，SGMCANPRODUCESOMECOMPLICATEDOUTPUTTRJECTORIESWHENTHESATELLITECOMPONENTISUSEDASTHEOUTPUTCOMPONENT，ANDITALSOHASSOMENESTINGSTRUCTURESWITHGEARPAIRSTHEAIMOFTHISPAPERISTOPROVIDEATENTATIVEPROCEDURETOPERFORMTOPOLOGICALEXPRESSIONFORSGMBYINVESTIGATIONOFTHETOPOLOGICALCHARACTERISTICSOFTHEKINEMATICSTRUCTUREOFSGMWITHGRAPHTHEORY，THEGRAPHMODELOFSGMISANALYZED，ANDTHETOPOLOGICALEXPRESSIONMODELOFSGMISESTABLISHEDBASEDONSYSTEMATICDESIGNPOINTINADDITION，THEIDENTIFICATIONOFISOMORPHISMOFSGMISDISCUSSEDPRLIMINARILY1TOPOLOGICALEXPRESSIONOFKINEMATICSTRUCTUREOFSGM11BASICCONCEPTSTOREALIZEAUTOMATICANALYSISOFTHEKINEMATICCHARACTERISTICSOFTHECOMPLEXEGMSBYCOMPUTER，FOREXAMPLE，THOSEOFSGMS，WEINTRODUCEANEWTOPOLOGICALEXPRESSIONMETHODWITHGRAPHMODETHEPROPOSEDMETHODISBASEDONTHETRADITIONALMETHOD，BUTITINTRODUCESGEMELFINESTOREPRESENTSINGLETURNINGPAIRANDINTRODUCESSOLIDFINESTOREPRESENTTHETURNINGPAIRTAKINGPARTINCOMPOSITIONOFTHECOMPLEXTURNINGPAIR，WHILETHECOMPLEXTURNINGPAIRCANCONSTRUCTAPOLYGONWITHOTHERSOLIDLINESTHISPRINCIPLECANDISTINGUISHTHESINGLETURNINGPAIRFROMCOMPLEXTURNINGPAIRSBASICASSUMPTIONSAREASFOLLOWSIFVERTEXIISADJACENTTOVERTEXJWITHATURNINGPAIREDGE，AIJ1IANDJREPRESENTTHELINKS；IFTHETURNINGPAIRTAKESPARTINTHECOMPLEXTURNINGPAIRWHICHCANCONSTRUCTAPOLYGONINPROGRESS，THENAIJMMISTHENUMBEROFTHEPOLYGONSINTHEMEANTIME，AIJ2IFVERTEXIISADJACENTTOVERTEXJWITHAGEARPAIREDGE，ANDAIJ0OTHERWISEFURTHERMORE，AIJ0IN1972，FREUDENSTEINETA1FIRSTDEFINEDTHEROTATIONGRAPHANDDISPLACEMENTGRAPHOFAPLANETARYGEARMECHANISMTOIDENTIFYTHEROTATIONALANDLINEARISOMORPHISMSHEALSOESTABLISHEDTHECORRESPONDENCEBETWEENTHECANONICALGRAPHREPRESENTATIONANDTHEDISPLACEMENTEQUATIONOFAPLANETARYGEARMECHANISMIN1994HSUFURTHERMODIFIEDTHEDEFINITIONSOFROTATIONGRAPHSANDDISPLACEMENTGRAPHS，ANDUSEDTHEMTOCHARACTERIZETHEKINEMATICSTRUCTUREINTHEFOLLOWING，THETOPOLOGICALEXPRESSIONMODEOFSGMWILLBEBUILTBYUSINGTHESEBASICCONCEPTS12GRAPHMODELOFSGMANDITSMATHEMATICALDESCRIPTIONTHEGRAPHMODELOFSGMISSHOWNINFIG1，WHEREFIGS1AANDBSHOWTHEFUNCTIONDIAGRAMOFTHEORDINARYSATELLITEGEARMECHANISMOSGM，ANDFIGS1CTOFSHOWTHEGRAPHMODELREPRESENTATIONOFSGMTHEDISPLACEMENTGRAPHOFOSGMISSHOWNINFIG1C，WHERETHEVERTICES1，2，3，4，5，AND6CORRESPONDTOTHELINKS1，2，3，4，5，AND6INFIG1A，RESPECTIVELY；THESIXSOLIDEDGES14，16，25，24，45，46CORRESPONDTOTHETUMINGPAIRSCONNECTINGTOLINKSBETWEEN1AND4，1AND6，2AND5，2AND4，4AND5，AND4AND6，RESPECTIVELYTHENTHEEDGES14，16AND46FORMATRIANGLEINWHICHAL4AL6A463；THEEDGES24，25，AND45FORMANOTHERTRIANGLEINWHICHA24A25A453THEGEMELLINEBETWEENVERTICES3AND5REPRESENTSTHECORRESPONDINGSINGLETURNINGPAIRWHICHWILLNOTTAKEPARTINCOMPOSINGACOMPLEXTURNINGPAIRTHEREAREFOURFUNDAMENTALCIRCUITSINFIG1CTHEFUNDAMENTALCIRCUITS5325AND5345WHERETHEVERTEX5ISTHETRANSFERVERTEXANDTHEFUNDAMENTALCIRCUITS4214AND4564WHEREVERTEX4ISTHETRANSFERVERTEXTHEROTATIONGRAPHOF0SGMISSHOWNINFIG1D，WHERETHEVERTICES1，2，3，4，5，AND6CORRESPONDTOTHELINKS1，2，3，4，5，AND6FIG1A，RESPECTIVELY；THETHREESOLIDEDGES24，25，AND45CORESPONDTOTHETURNINGPAIRSCONNECTINGTOTHELINKSBETWEEN2AND4，2AND5，AND4AND5，RESPECTIVELYTHENTHEEDGES24，25，AND45FORMATRIANGLEINWHICHA24A25A453THEGEMELLINEBETWEENVERTICES1AND4，4AND6，AND3AND5REPRESENTTHECORESPONDINGSINGLETURNINGPAIRWHICHWILLNOTTAKEPARTINCOMPOSINGACOMPLEXTURNINGPAIRSIMILARLY，THEREAREFOURFUNDAMENTALCIRCUITSTHEFUNDAMENTALCIRCUITS4564AND4214WHERETHEVERTEX4ISTHETRANSFERVERTEXANDTHEFUNDAMENTALCIRCUITS5325AND5345WHERETHEVERTEX5ISTHETRANSFERVERTEXTHEDISPLACEMENTGRAPHOFTHECLOSEDSATELLITEGEARMECHANISMCSGMISSHOWNINFIG1E，WHERETHEVERTICES1，2，3，4，5，6，AND7CORESPONDTOTHELINKS1，2，3，4，5，6，AND7INFIG1B，RESPECTIVELY；THEFOURSOLIDEDGES27，25，37，AND35CORESPONDTOTHETURNINGPAIRSCONNECTINGTOTHELINKSBETWEEN2AND7，2AND5，3AND7，AND3AND5，RESPECTIVELYTHENTHEEDGES27，25，37，AND35FORMAPOLYGONWITHFOUREDGESINWHICHA27A37A35A254THETHREESOLIDEDGES17，67，AND16CORESPONDTOTHETURNINGPAIRSCONNECTINGTOTHELINKSBETWEEN1AND7，6AND7，AND1AND6，RESPECTIVELYTHENTHEEDGES17，67AND16FORMATRIANGLEWITHTHREEEDGESINWHICHA17AL6A673THEGEMELLINESBETWEENVERTICES5AND4，1AND7，AND6AND7REPRESENTTHECORESPONDINGPAIRTHATISTHESINGLETURNINGPAIRWHICHWILLNOTTAKEPARTINCOMPOSINGACOMPLEXTURNINGPAIRSIMILARY，THEREAREFOURFUNDAMENTALCIRCUITSINFIG1ETHECIRCUITS7317AND7627WHERETHEVERTEX7ISTHETRANSFERVERTEXANDTHECIRCUITS5245AND5345WHEREVERTEX5ISTHETRANSFERVERTEXTHEROTATIONGRAPHOFCSGMWHERETHEVERTICES1，2，3，4，5，6，AND7CORESPONDTOTHELINKS1，2，3，4，5，6，AND7INFIG1B，RESPECTIVELY；THEFOURSOLIDEDGES27，25，37，AND35CORRESPONDTOTHETURNINGPAIRSCONNECTINGTOTHELINKSBETWEEU2AND7，2AND5，3AND7，AND3AND5，RESPECTIVELYTHENTHEEDGES27，25，37，AND35FORMAPOLYGONWITHFOUREDGESINWHICHA27A37A35A254THEGEMELLINESBETWEENVERTICES5AND4，1AND7，AND6AND7REPRESENTTHECORRESPONDINGSINGLETURNINGPAIRWHICHWILLNOTTAKEPARTINCOMPOSINGACOMPLEXTURNINGPAIRSIMILARLY，THEREAREFOURFUNDAMENTALCIRCUITSINFIG1FTHECIRCUITS7317AND7627WHERETHEVERTEX7ISTHETRANSFERVERTEX，ANDTHECIRCUITS5245AND5345WHERETHEVERTEX5ISTHETRANSFERVERTEXBASEDONTHEABOVEANALYSIS，THEADJACENCYMATRIXESAREEXPRESSEDASFOLLOWS2IDENTIFCATIONOFISOMORPHISMTHECLASSICALIDENTIFICATIONOFISOMORPHISMISTHELINKAGECHARACTERISTICPOLYNOMIALMETHODITSBASICIDEACANBEDESCRIBEDASFOLLOWSALINKAGECHARACTERISTICPOLYNOMIALISBUILTBASEDONEVERYGRAPH，ANDTHENISRESOLVEDACOMPARISONISMADEAMONGTHESELINKAGECHARACTERISTICPOLYNOMIA1STODECIDEWHETHERTHEYAREOFISOMORPHISMACCORDINGTOTHECRITERIONWHETHERTHEYCANGETTHESAMEVALUEWHENADEQUATEVALUESOFTHEINDEPENDENTVARIABLEARESELECTEDTSALETA1APPLIEDTHECONCEPTOFLINKAGECHARACTERISTICPOLYNOMIALTODETECTTHEISOMORPHISMOFEGTSHOWEVER，SOMECOUNTEREXAMPLESHAVEBEENFOUND，WHERETHELINKAGECHARACTERISTICPOLYNOMIALMETHODFALLSTODETECTTHEDISPLACEMENTISOMORPHISMOFPLANETARYGEARTRAINSMOREOVER，THEMETHODTODECIDEISOMORPHISMISTOOTIMECONSUMINGONCOMPUTERBECAUSETHEVALUESOFTHELINKAGECHARACTERISTICPOLYNOMIALHAVETOBEDETERMINEDWHENTHEREAREAGREATMANYINDEPENDENTVARIABLESTOBEPICKEDTHEREFORE，ITISNOTTHEFEASIBLEANDRELIABLEMETHOD，ANDSOMENEWMETHODTOMEETTHEOBJECTIVESSHOULDBEDEVELOPEDATPRESENT，SOMESCHOLARSARESTUDYINGTHEIDENTIFICATIONOFISOMORPHISMWITHTHERANDOMSEARCHALGORITHMFOREXAMPLE，THEANTALGORITHMANDTHEGENETICALGORITHMHAVEALREADYBEENUSEDINTOTHERESEARCHTOPICASTHERESEARCHINTERESTOFTHEAUTHOR，IDENTIFICATIONOFTHEISOMORPHISMWITHTHEANTALGORITHMISJUSTUNDERWAY，ANDTHERELEVANTPROBLEMSWILLBEDISCUSSEDINANOTHERPAPER3CONCLUSIONSBASEDONTHEINVESTIGATIONOFTHETOPOLOGICALCHARACTERISTICSOFTHEKINEMATICSTRUCTUREOFSGMWITHGRAPHTHEORY，THEGRAPHMODELOFSGMISANALYZED，ANDANEWGRAPHEXPRESSIONISPRESENTEDFORSGMTHETOPOLOGICALEXPRESSIONMODELOFSGMISESTABFISHEDFORINTELLIGENTDESIGNOFSGMINTHEMEATIME，THEMATHEMATICALEXPRESSIONFORSGMISDEDUCEDBYINTEGRATINGMATRIXTHEORYANDGRAPHTHEORYTHUS，THETOPOLOGICALCHARACTERISTICSOFTHEKINEMATICSTRUCTUREOFSGMCANBECONVERTEDINTOAMATRIXMODE1ANDTHETOPOLOGICALDESIGNPROBLEMOFSGMINTOAMATRIXOPERATIONPROBLEMINADDITION，SOMEMEASURESFORTHEIDENTIFICATIONOFISOMORPHISMOFSATELLITEGEARMECHANISMAREDISCUSSEDINHOPEOFLAYINGATHEORETICALBASISFORTHEFUTUREWORKOFKINEMATICCHARACT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