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GEARGEARGEARISRELYINGONTHETOOTHMESHINGTORQUEROTAVIRUSMECHANICALPARTSGEARWITHOTHERDENTATEMACHINERYPARTS,SUCHASAWORMGEAR,RACK,TRANSMISSION,WHICHCANREALIZECHANGEDTHEDIRECTIONOFROTATIONSPEEDANDTORQUE,CHANGETHEDIRECTIONOFMOVEMENTANDCHANGETHEMOVEMENTFORMS,ANDOTHERFUNCTIONSOWINGTOTHEHIGHTRANSMISSIONEFFICIENCY,ACCURATEANDADVANTAGESOFLARGERANGEOFPOWERTRANSMISSIONRATIO,GEARMECHANISMISWIDELYUSEDININDUSTRIALPRODUCTS,THEDESIGNANDMANUFACTURELEVELDIRECTLYAFFECTSTHEQUALITYOFINDUSTRIALPRODUCTSGEARTOOTHBUCKLEEACHGEARWILLDRIVETHEOTHERGEARSTOTRANSMITPOWERSEPARATETWOGEARS,CHAINSCANALSOBEAPPLIED,CATERPILLAR,ONBOTHSIDESOFTHEBELTTODRIVEGEARANDTRANSMISSIONPOWERBASICINTRODUCTIONINTHEAPPLICATIONOFTRANSMISSIONGEARAPPEAREDVERYEARLYMORETHANTHREEHUNDREDYEARSBC,THEANCIENTGREEKPHILOSOPHERARISTOTLEINTHEMECHANICALPROBLEMS,ITEXPOUNDSTHEBRONZEORIRONGEARTRANSMISSIONPROBLEMOFROTARYMOTIONINVENTEDINANCIENTCHINA,HASBEENAPPLIEDINTHEENTIREGEARTRAINHOWEVER,THEANCIENTGEARISMADEOFWOODORMETALMOULDS,CANONLYTRANSFERBETWEENSHAFTROTARYMOTION,CANNOTGUARANTEETHESTABILITYOFTRANSMISSION,THEBEARINGCAPACITYOFTHEGEARAREALSOSMALLACCORDINGTOHISTORICALRECORDS,IN400200BCINANCIENTCHINAHASALREADYSTARTEDTOUSEGEAR,SHANXIUNEARTHEDBRONZEGEARSINOURCOUNTRYISBYFARTHEOLDESTGEARHADBEENFOUND,ASAREFLECTIONOFANCIENTSCIENCEANDTECHNOLOGYACHIEVEMENTSOFTHISWORKISTOGEARMECHANISMASTHECOREMECHANISMTHE17THCENTURY,PEOPLESTARTEDTORESEARCH,CANBEDELIVEREDRIGHTTOOTHSHAPEOFTHEMOVEMENTTHE18THCENTURY,EUROPEAFTERTHEINDUSTRIALREVOLUTION,THEAPPLICATIONOFGEARTRANSMISSIONISINCREASINGDAYBYDAYWIDELY;FIRSTTHEDEVELOPMENTOFCYCLOIDALGEAR,THENTHEINVOLUTEGEAR,UNTILTHEBEGINNINGOFTHE20THCENTURY,INVOLUTEGEARHASSETUPAFILEINTHEAPPLICATIONASEARLYASIN1694,FRENCHSCHOLARPHILIPPEDELAHIREFORWARDINVOLUTETOOTHSHAPECURVECANBEUSEDASINTHEFIRSTPLACEIN1733,THEFRENCHMCAMUSPUTFORWARDTHECOMMONNORMALOFTOOTHCONTACTMUSTBEONTHECENTEROFTHENODEAAUXILIARYINSTANTANEOUSCENTERLINERESPECTIVELYALONGTHEBIGWHEELANDLITTLEWHEELOFTHEINSTANTANEOUSCENTERLINEPITCHFORPUREROLLING,ANDTHEAUXILIARYINSTANTANEOUSCENTERLINESOLIDCOUPLINGOFAUXILIARYTOOTHSHAPEONTHEBIGWHEELANDLITTLEWHEELENVELOPEFORMEDBYTWOTOOTHPROFILECURVEISCONJUGATEDTOEACHOTHER,THISISCAMUSTHEOREMITTAKESINTOACCOUNTTHETWOTOOTHSURFACEMESHINGSTATE;CLEARLYESTABLISHEDTHEMODERNCONCEPTABOUTCONTACTTRAJECTORYIN1765,SWISSLEULERINVOLUTEPROFILEANALYTICRESEARCHMATHEMATICALFOUNDATION,ILLUSTRATESAPAIROFMESHINGGEARS,THETOOTHPROFILECURVEOFTHERADIUSOFCURVATUREANDCURVATURECENTERPOSITIONLATER,BABIESFURTHERCOMPLETETHEMETHOD,ANDISNOWTHEEULETBABIESEQUATIONCANCONTRIBUTETOTHEAPPLICATIONOFINVOLUTETOOTHPROFILEISROTEFTWULLS,HEPUTFORWARDTHECENTREDISTANCECHANGEWHENINVOLUTEGEARHASTHEADVANTAGESOFTHEANGULARSPEEDRATIOUNCHANGEDIN1873,AGERMANENGINEERHOPPEISPUTFORWARD,WITHDIFFERENTNUMBEROFTEETHOFINVOLUTETOOTHPROFILEOFGEARINTHEPRESSUREANGLEISCHANGED,THUSLAIDTHEIDEOLOGICALBASISOFMODERNSHIFTGEARTHEENDOFTHE19THCENTURY,GENERATIVEPRINCIPLEOFGEARCUTTINGMETHODANDUSINGTHEPRINCIPLEOFGEARCUTTINGMACHINEANDCUTTINGTOOLAPPEARED,AFTERMAKINGTHEGEARMACHININGWITHTHEMORECOMPREHENSIVEMEANS,INVOLUTEPROFILESHOWSHIGHMOREOPTIMALSEXTEETHMESHASLONGASTHEGEARCUTTINGTOOLSFROMTHENORMALPOSITIONWHENMOVINGSLIGHTLY,CANUSETHESTANDARDCUTTERCUTOUTTHECORRESPONDINGSHIFTGEARSINMACHINETOOLIN1908,THESWISSMAAGDISPLACEMENTMETHODISSTUDIEDANDMANUFACTURINGEXPORTASPROCESSINGGEARSHAPER,LATER,THEBSS,AMERICANAGMA,GERMANYDINSUCCESSIVELYPUTFORWARDMANYKINDSOFMETHODTOCALCULATETHEDEFLECTIONOFGEARINORDERTOIMPROVETHESERVICELIFEOFTHEPOWERTRANSMISSIONGEARANDREDUCEITSSIZE,INADDITIONTOFROMMATERIAL,HEATTREATMENTANDSTRUCTUREIMPROVEMENT,THECIRCULARARCTOOTHPROFILEOFGEAROBTAINEDTHEDEVELOPMENTIN1907,THEBRITISHFRANKHUMPHRISPUBLISHEDACIRCULARARCTOOTHPROFILEATTHEEARLIESTIN1926,RUINATIVESERUESTWILDHABERAPATENTONTHEMETHODOFSURFACEARCTOOTHPROFILEHELICALGEARSIN1955,THESOVIETUNIONSMLNOVIKOVCOMPLETEDPRACTICALRESEARCHOFARCTOOTHPROFILEGEARANDGETTHEORDEROFLENININ1970,THEBRITISHROLHROYCECOMPANYENGINEERSRMSTUDERACHIEVEDDOUBLECIRCULARARCGEARPATENTINTHEUNITEDSTATESTHISKINDOFGEARISNOWINCREASINGLYATTENTIONBYPEOPLE,INTHEPRODUCTIONOFTHESHOWTHEBENEFITSGEARISTOBEABLETOMESHEACHOTHERTOOTHEDMACHINEPART,ITSAPPLICATIONINTHEFIELDOFMECHANICALTRANSMISSIONANDTHEWHOLEMACHINERYISEXTREMELYBROADMODERNGEARTECHNOLOGYHASREACHEDTHEMODULEOFGEARO004100MM;GEARDIAMETERBY1MM150M;ONTHETRANSMITTEDPOWERCANREACHHUNDREDSOFKILOWATTS;SPEEDUPTOHUNDREDSOFTHOUSANDSOFREVOLUTIONSPERMINUTE;THECIRCUMFERENCEOFTHEHIGHESTSPEEDOF300M/SECWITHTHEDEVELOPMENTOFPRODUCTION,THEGEAROPERATIONSTABILITY1674DANISHASTRONOMERROEMERFIRSTWITHOUTERCYCLOIDTOOTHPROFILECURVEISPUTFORWARD,INORDERTOGETSTABLERUNNINGGEARINTHE18THCENTURYINDUSTRIALREVOLUTION,GEARTECHNOLOGYGOTRAPIDDEVELOPMENT,PEOPLEHAVEMADEALOTOFRESEARCHONGEARIN1733THEFRENCHMATHEMATICIANCARDMETERSPUBLISHEDPROFILEMESHINGBASICLAWS;IN1765THESWISSMATHEMATICIANEULERPROPOSEDUSINGINVOLUTETOOTHPROFILECURVEEMERGEDINTHE19THCENTURYGEARHOBBINGMACHINEANDGEARSHAPER,SOLVESTHEPROBLEMOFMASSPRODUCTIONANDHIGHPRECISIONGEARIN1900,FORDFORGEARHOBBINGMACHINEISINSTALLEDONTHEDIFFERENTIALDEVICE,CANWORKOUTHELICALGEARONGEARHOBBINGMACHINE,GEARHOBBINGM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