機(jī)電專業(yè)畢業(yè)設(shè)計(jì)中英文翻譯資料-圓柱凸輪的設(shè)計(jì)和加工

英文資料翻譯英文原文：DesignandmachiningofcylindricalcamswithtranslatingconicalfollowersByDerMinTsayandHsienMinWeiAsimpleapproachtotheprofiledeterminationandmachiningofcylindricalcamswithtranslatingconicalfollowersispresented.Onthebasisofthetheoryofenvelopesfora1-parameterfamilyofsurfaces,acamprofilewithatranslatingconicalfollowercanbeeasilydesignedoncethefollower-motionprogramhasbeengiven.Intheinvestigationofgeometriccharacteristics,itenablesthecontactlineandthepressureangletobeanalysedusingtheobtainedanalyticalprofileexpressions.Intheprocessofmachining,therequiredcutterpathisprovidedforataperedendmillcutter,whosesizemaybeidenticaltoorsmallerthanthatoftheconicalfollower.Anumericalexampleisgiventoillustratetheapplicationoftheprocedure.Keywords:cylindricalcams,envelopes,CAD/CAMAcylindricalcamisa3Dcamwhichdrivesitsfollowerinagroovecutontheperipheryofacylinder.Thefollower,whichiseithercylindricalorconical,maytranslateoroscillate.Thecamrotatesaboutitslongitudinalaxis,andtransmitsatransmitsatranslationoroscillationdisplacementtothefolloweratthesametime.Mechanismsofthistypehavelongbeenusedinmanydevices,suchaselevators,knittingmachines,packingmachines,andindexingrotarytables.Inderivingtheprofileofa3Dcam,variousmethodshaveused.Dhandeetal.1andChakrabortyanddhande2developedamethodtofindtheprofilesofplanarandspatialcams.Themethodusedisbasedontheconceptthatthecommonnormalvectorandtherelativevelocityvectorareorthogonaltoeachotheratthepointofcontactbetweenthecamandthefollowersurfaces.Borisov3proposedanapproachtotheproblemofdesigningcylindrical-cammechanismsbyacomputeralgorithm.Bythismethod,thecontourofacylindricalcamcanbeconsideredasadevelopedlinearsurface,andthereforethedesignproblemreducestooneoffindingthecentreandsideprofilesofthecamtrackonadevelopmentoftheeffectivecylinder.Instantaneousscrew-motiontheory4hasbeenappliedtothedesignofcammechanisms.Gonzalez-Palaciosetal.4usedthetheorytogeneratesurfacesofplanar,spherical,andspatialindexingcammechanismsinaunifiedframework.Gonzalez-PalaciosandAngeles5againusedthetheorytodeterminethesurfacegeometryofsphericalcam-oscillatingroller-followermechanisms.Consideringmachiningforcylindricalcamsbycylindricalcutterswhosesizesareidenticaltothoseofthefollowers,PapaioannouandKiritsis6proposedaprocedureforselectingthecutterstepbysolvingaconstrainedoptimizationproblem.Theresearchpresentedinthispapershowsqnew,easyprocedurefordeterminingthecylindrical-camprofileequationsandprovidingthecutterpathrequiredinthemachiningprocess.Thisisaccomplishedbythesueofthetheoryofenvelopesfora1-parameterfamilyofsurfacesdescribedinparametricform7todefinethecamprofiles.HansonandChurchill8introducedthetheoryofenvelopesfora1-parameterfamilyofplanecurvesinimplicitformtodeterminetheequationsofplate-camprofilesChanandPisano9extendedtheenvelopetheoryforthegeometryofplatecamstoirregular-surfacefollowersystems.Theyderivedananalyticaldescriptionofcamprofilesforgeneralcam-followersystems,andgaveanexampletodemonstratethemethodinnumericalform.Usingthetheoryofenvelopesfora2-parameterfamilyofsurfacesinimplicitform,TsayandHwang10obtainedtheprofileequationsofcamoids.Accordingtothemethod,theprofileofacamisregardedasanenvelopeforthefamilyofthefollowershapesindifferentcam-followerpositionswhenthecamrotatesforacompletecycle.THEORYOFENVELPOESFOR1-PARAMETERFAMILYOFSURFACESINPARAMETRICFORMIn3DxyzCartesianspace,a1-parameterfamilyofsurfacescanbegiveninparametricformas(1)whereζistheparameterofthefamily,andu1,u2,aretheparametersforaparticularsurfaceofthefamily.Then,theenvelopeforthefamilydescribedinEquation1satisfiesequation1andthefollowingEquation:(2)wheretheright-handsideisaconstantzero7.Litvinshowedtheprovingprocessofthetheoremindetail.IfwecansolveEquation2andsubstituteintoequation1toeliminateoneofthethreeparametersu1,u2,andζ,wemayobtaintheenvelopeinparametricform.However,oneimportantthingshouldbepointedouthere.Equations1and2canalsobesatisfiedbythesingularpointsofsurfacesdescribedbelowIthefamily,eveniftheydonotbelongtotheenvelope.PointswhichareregularpointsofsurfacesofthefamilyandsatisfyEquation2lieontheenvelope.Theconditionforthesingularpointsofasurfaceisdiscussedhere..aparametricrepresentationofasurfaceis(3)whereu1andu2aretheparametersofthesurface.Apointofthesurfacethatcorrespondstoinagivenparameterizationiscalledasingularpointoftheparameterization.Apointofasurfaceiscalledsingularifitissingularforeveryparameterizationofthesurface7.Apointthatissingularinoneparameterizationofasurfacemaynotbesingularinotherparameterizations.Forafixedvalueofζ,equations1and2represent,ingeneral,acurveonthesurfacewhichcorrespondstothisvalueoftheparameter.Ifthisisnotalineofsingularpoints,thecurveslsoliesontheenvelope.Thesurfaceandtheenvelopearetangenttoeachotheralongthiscurve.Suchcurvesarecalledcharacteristiclinesofthefamily7.theycanbeusedtofindthecontactlinesbetweenthesurfacesofthecylindricalcamandthefollower.THEORYOFENVELOPESFORDETERMINATIONOFCYLINDRICAL-CAMPROFILESOnthebasisofthetheoryofenvelopes,theprofileofacylindricalcamcanberegardedastheenvelopeofthefamilyoffollowersurfacesinrelativepositionsbetweenthecylindricalcamandthefollowerwhilethemotionofcamproceeds.Insuchacondition,theinputparametersofthecylindricalcamserveasthefamilyparameters.Becausethecylindricalorconicalfollowersurfacecanbeexpressedinparametricformwithoutdifficulty,thetheoryofenvelopesfora1-parameterofsurfacesrepresentedinparametricform(seeequations1and2)isusedindeterminingtheanalyticalequationsofcylindrical-camprofiles.Asstatedinthelastsection,acheckforsingularpointsonthefollowersurfaceisalwaysneeded.Figure1ashowsacylindrical-cammechanismwithatranslatingconicalfollower.Theaxiswhichthefollowertranslatesalongisparalleltotheaxisofrotationofthecylindricalcam.aistheoffset,thatis,thenormaldistancebetweenthelongitudinalaxisofthecamandthatofthefollower.RandLaretheradiusandtheaxiallengthofthecam,respectively.TherotationangleofthecylindricalcamisФ2aboutitsaxis.Thedistancetraveledbythefolloweriss1,whichisafunctionofparameterФ2,asfollows:(4)Thedisplacementrelationship(seeequation4)forthetranslatingfollowerisassumedtobegiven.Infigure1b,therelativepositionofthefollowerwhenthefollowermovesisshown.Thefollowerisintheformofafrustumofacone.Thesemiconeangleisα,andthesmallestradiusisr.δ1istheheight,andμisthenormaldistancefromthexzplanetothebaseofthecone.ThefixedcoordinatesystemOxyzislocatedinsuchawaythatthezaxisisalongtherotationaxisofthecam,andtheyaxisisparalleltothelongitudinalaxisoftheconicalfollower.theunitvectorsofthexaxis,yaxisandzaxisarei,jandk,respectively.Bytheuseoftheenvelopetechniquetogeneratethecylindrical-camprofile,thecamisassumedtobestationary.Thefollowerrotatesaboutthedamaxisintheoppositedirection.ItisassumedthatthefollowerrotatesthroughanangleФ2abouttheaxis.Atthesametime,thefolloweristransmittedalineardisplacements1bythecam,asshowninFigure1b.Consequentlyusingthetechnique,ifweintroduceθandδastwoparametersforthefollowersurface,thefamilyofthefollowersurfacescanbedescribedas(5)where0≤θ＜2piAndф2istheindependentparameterofthecammotion.Referringtotheoryofenvelopesforsurfacesrepresentedinparametricform(seeequations1and2),weproceedwiththesolvingprocessbyfinding(6)Therearenosingularpointsonthefamilyofsurfaces,since(r+δtanα)＞0inactualapplications.Theprofileequationsatisfiesequation5andthefollowingequation:(7)Whereor(8)WhereSubstitutingequation8intoequation5,andeliminatingθ,weobtaintheprofileequationofthecylindricalcamwithatranslatingconicalfollower,anddenoteitas(9)Asshowninequation8,θisafunctionoftheselectedfollower-motionprogramandthedimensionalparameters.Asaconsequence,thecylindrical-comprofilecanbecontrolledbythechosenfollower-motioncurvesandthedimensionalparameters.Twovaluesofθcorrespondtothetwogroovewallsofthecylindricalcam.Nowtheprofileofthecylindricalcamwithatranslatingconicalfollowerisderivedbythenewproposedmethod.Asstatedabove,Dhandeetal.1andChakrabortyandDhande2havederivedtheprofileequationofthesametypeofcambythemethodofcontactpoints.Acomparisonoftheresultiscarriedouthere.Sincethesamefixedcoordinatesystemandsymbolsareused,onecaneasilyseethattheprofileequationisidenticalalthoughthemethodsusedaredifferent.Moreover,wefindthattheprocessoffindingthecamprofileissignificantlyreducedbythismethod.CONTACTLINEAteverymoment,thecylindricalcamtouchesthefolloweralongspacelines.Thecontactlinesbetweenthecylindricalcamanditsfollowerarediscussedinthissection.Theconceptofcharacteristiclinesinthetheoryofenvelopesfora1-parameterfamilyofsurfacesmentionedabovecouldbeappliedtofindingthecontactlinesinacylindricalcom.TheprofileofacylindricalcamwithatranslatingconicalfollowerisgivenbyEquation9.Then,thecontactlineataspecificvalueofф2,sayф20,is(10)Where,inEquation10,thevalueofθisafunctionofδdefinedbyEquation8.ThecontactlinesbetweenthesurfacesofthecamandthefollowerateachmomentisdeterminedbyEquation10.weseethattherelationshipbetweenthetwoparametersθandδofthefollowersurfaceisgivenbyEquation8,anonlinearfunction.Thus,onecaneasilyfindthatthecontactlineisnotalwaysastraightlineontheconicalfollowersurface.PRESSUREANGLETheanglethatthecommonnormalvectorofthecamandthefollowermakeswiththepathofthefolloweriscalledthepressureangle12.thepressureanglemustbeconsideredwhendesigningacam,anditisameasureoftheinstantaneousforce-transmissionpropertiesofthemechanism13.Themagnitudeofthepressureangleinsuchacam-followersystemaffectstheefficiencyofthecam.Thesmallerthepressureangleis,thehigheritsefficiencybecause14.Infigure2,theunitnormalvectorwhichpassesthroughthepointofcontactbetweenthecylindricalcamandthetranslatingconicalfollowerintheinversionposition,i.e.pointC,isdenotedbyn.Thepathofthefollowerlabeledastheunitvectorpisparalleltotheaxisofthefollower.fromthedefinition,thepressureangleΨistheanglebetweentheunitvectorsnandp.Since,atthepointofcontact,theenvelopeandthesurfaceofthefamilypossessesthesametangentplane,theunitnormalofthecylindrical-camsurfaceisthesameasthatofthefollowersurface.ReferringtothefamilyequationEquation5andFigure2,wecanobtaintheunitvectoras(11)wherethevalueofθisgivenbyequation8,andtheunitvectorofthefollowerpathis(12)Bytheuseoftheirinnerproduct,thepressureangleΨcanbeobtainedbythefollowingequation:(13)ThepressureanglederivedhereisidenticaltothatusedintheearlyworkcarriedoutbyChakrabortyandDhande2.CUTTERPATHInthissection,thecutterpathrequiredformachiningthecylindricalcamwithatranslatingconicalfollowerisfoundbyapplyingtheproceduredescribedbelow.Usually,withtheconsiderationsofdimensionalaccuracyandsurfacefinish,themostconvenientwaytomachineacylindricalcamistouseacutterwhosesizeisidenticaltothatoftheconicalroller.Intheprocessofmachining,thecylindricalblankisheldonarotarytableofa4-axismillingmachine.Asthetablerotates,thecutter,simulatingthegivenfollower-motionprogram,movesparalleltotheaxisofthecylindricalblank.Thusthecuttermovesalongtheruledsurfacegeneratedbythefolloweraxis,andthecamsurfaceisthenmachinedalongthecontactlinesstepbystep.Ifwehavenocutterofthesameshape,anavailablecutterofasmallersizecouldalsobesuedtogeneratethecamsurface.Underthecircumstances,thecutterpathmustbefoundforageneralendmillcutter.Figure3showsataperedendmillcuttermachiningacurvedsurface.Thefrontportionofthetoolisintheformofacone.ThesmallestradiusisR,andthesemiconeangleisβ.Ifthecuttermovesalongacurveδ=δ0onthesurfaceX=X（δ，ф2），theangleσbetweentheunitvectorofthecutteraxisaxandtheunitcommonnormalvectornatcontactpointCisdeterminedby(14)Thusthepathofthepoint?onthecutteraxisthatthevectornpassesthroughis(15)andthetipcentreTfollowsthepath(16)Figure4showsataperedendmillcuttermachiningthegroovewallofacylindricalcam.Theaxisofthetaperedendmillisparalleltotheyaxis.Notethatthetwoconditions （17）(18)forthegeometricparametersofthecutterandtherollerfollowermusthold,orotherwisethecutterwouldnotfitthegroove.Theunitvectorofthecutteraxisis(19)Fortheprofileofthecylindricalcamwithatranslatingconicalfollowergivenbyequation9,theangleσisdeterminedbytheinnerproduct:(20)Thus,byusingtheresultsobtainedearlier,thepositionofthetipcentreofthecuttercanbederivedas(21)whereNUMERICALEXAMPLETheproceduresdevelopedareappliedinthissectiontodeterminethecylindrical-camprofile,andtoanalyseitscharacteristics.Themotionprogramofthefollowerforthecylindricalcamwithatranslatingcylindricalcamisgivenas(22)wherehandλaretwoconstants.Andh=20unitsandλ=60℃.Themotionprogramisadwell-rise-dwell-return-dwellcurve,andtheriseandreturnportionsarecycloidalcurves15.Figure5showsthemotionprogram.Thedimensionalparametersusedforthecylindricalcamandthefollowerareasfollows:semiconeangleoffollowerα=0℃heightoffollowerδ1=15unitsdistancefrombottomoffollowertoxzplaneμ=55unitssmallestradiusoffollowerr=7.5unitsoffseta=20unitsradiusofcamR=73unitsaxiallengthofcamL=100unitsTheprofileofthecylindricalcamobtainedbyapplyingEquation9isshowninFigure6.InFigure6,thegroovewallwiththesmallerzcoordinatesissideⅠ,andtheotherissideⅡ.ThevariationsofthepressureanglesfortheriseandreturnportionsareshowninFigures7and8forsideⅠandⅡ,respectively.Itcanbeseenthatthepressureanglesforbothsideshappentobeidentical.CONCLUSIONSAshasbeenshownabove,theapplicationofthetheoryofenvelopesaffordsaconvenientandversatiletoolfordeterminingthecylinder-camprofileswithtranslatingconicalfollowers.Bymeansoftheanalyticalcamprofileequations,itcanbeeasilyextendedtoaccomplishthetaskfortheanalysisofthecontactlineandthepressureangle.Further,thecutterpathrequiredintheprocessofmachiningisgeneratedfortaperedendmillcutters.Sincethesamefixedcoordinatesystemandsymbolsareusedinthisstudy,onecanseethattheresultsforcamprofilesandpressureanglesareidenticaltothoseobtainedinpreviousresearch1,2.Onlyonecoordinatesystemisusedinthisapproach.Asaresult,theprocessofderivationissimple.Workiscurrentlyunderwaytofacilitatetheimplementationofthetoolpathforthemachiningofthecylindricalcamonanumericallycontrolledmillingmachine.翻譯：MACROBUTTONMTEditEquationSection2SEQMTEqn\r\hSEQMTSec\r1\hSEQMTChap\r1\h圓柱凸輪的設(shè)計(jì)和加工有人提出了具有平移圓錐傳動(dòng)件的圓柱凸輪的輪廓確定及其機(jī)加工的簡(jiǎn)單方法.在單參數(shù)曲面族的包絡(luò)線理論的基礎(chǔ)上,給定從動(dòng)件運(yùn)動(dòng)規(guī)律的具有平移圓錐傳動(dòng)件的圓柱凸輪的輪廓的設(shè)計(jì)是很簡(jiǎn)單的.通過(guò)這種設(shè)計(jì)方法得到的輪廓曲線可以進(jìn)行凸輪切線和壓力角等幾何特征的分析研究.在機(jī)加工過(guò)程中,可以使用錐形端銑刀,它的尺寸小于等于圓錐傳動(dòng)件的尺寸.很多實(shí)例證明該方法的實(shí)用性.關(guān)鍵詞:圓柱凸輪,包絡(luò)線,計(jì)算機(jī)輔助設(shè)計(jì)和計(jì)算機(jī)輔助制造.圓柱凸輪是利用其圓周上的溝槽來(lái)驅(qū)動(dòng)傳動(dòng)件的空間凸輪.傳動(dòng)件是圓柱或者圓錐形狀的,可以做平行移動(dòng)也可以做擺動(dòng).凸輪繞著它的縱向軸線旋轉(zhuǎn),同時(shí)將平移或擺動(dòng)運(yùn)動(dòng)傳遞給傳動(dòng)件.這種機(jī)械原理長(zhǎng)期廣泛應(yīng)用在各種設(shè)備中,比如,運(yùn)輸機(jī),紡織機(jī),包裝機(jī),旋轉(zhuǎn)分度盤等等.為獲得三維凸輪的輪廓曲線,曾用過(guò)各種方法.DHANDE和CHAKRABORTY和DHANDE發(fā)明了確定平面和立體凸輪輪廓的一種方法.這種方法是在一個(gè)前提下使用的,即認(rèn)為在主動(dòng)輪和從動(dòng)件交點(diǎn)處,凸輪的徑向矢量和速度矢量二者相互垂直.BROISOV提出了借助計(jì)算機(jī)輔助計(jì)算的方法來(lái)解決圓柱凸輪機(jī)構(gòu)設(shè)計(jì)上的問(wèn)題.通過(guò)這種方法,可以把圓柱凸輪的輪廓考慮成為展開的線性曲面.這樣,設(shè)計(jì)時(shí)就只需在實(shí)際圓柱上找到凸輪軌跡的中心和輪廓邊緣.瞬間螺旋運(yùn)動(dòng)理論已經(jīng)應(yīng)用到凸輪機(jī)構(gòu)的設(shè)計(jì)中.GONZALEZ-PALACIOS在統(tǒng)一標(biāo)準(zhǔn)下應(yīng)用這種理論得到了平面,球面和柱面凸輪機(jī)構(gòu).GONZALEZ-PALACIOS和ANGLES又應(yīng)用這個(gè)理論確定了球面擺動(dòng)輥?zhàn)油馆啓C(jī)構(gòu)的幾何形狀.考慮到用與傳動(dòng)件同樣尺寸的圓柱刀具加工圓柱凸輪,PAPAIOANNOU和KIRITSIS提出了通過(guò)解決最優(yōu)化受限問(wèn)題來(lái)選擇刀具步距的程序.在這份研究報(bào)告提出了一個(gè)新的簡(jiǎn)單的程序來(lái)確定圓柱凸輪的輪廓方程并提供機(jī)加工過(guò)程中所要求的刀具路徑.它是通過(guò)應(yīng)用以參數(shù)形式描述的單參數(shù)曲面族的包絡(luò)線理論來(lái)完成的.Hanson和Churchill引用隱函數(shù)形式的單參數(shù)平面曲線族包絡(luò)線理論確定盤形凸輪的輪廓曲線方程。Chan和Pisano將這種盤形凸輪幾何輪廓包絡(luò)線理論擴(kuò)展運(yùn)用到非規(guī)則曲面的傳動(dòng)零件系統(tǒng)中，他們創(chuàng)建了普通凸輪偉動(dòng)系統(tǒng)中凸輪輪廓的解析法描述，并舉例證明了該方法適用于數(shù)字形式。Tsay和Hwang將這種包絡(luò)線理論應(yīng)用到隱函數(shù)形式的雙參數(shù)曲面族上，建立了它們的輪廓線方程。根據(jù)這種方法，凸輪的輪廓曲線被看作是，當(dāng)凸輪作圓周回轉(zhuǎn)時(shí)傳動(dòng)件在不同位置，其輪廓的包絡(luò)線。單參數(shù)曲面族的包絡(luò)線理論在三維笛卡爾坐標(biāo)系中，單參數(shù)曲面族可以用下面的公式來(lái)表示： 其中是曲面族的參數(shù)，是曲面族中特定曲面的參數(shù)。這樣，方程(1.1)所描述的曲面族的包絡(luò)線即滿足方程１.1又滿足下面的方程： 其中，方程右邊是常數(shù)0，Litvin對(duì)這個(gè)定理進(jìn)行了詳細(xì)的驗(yàn)證。如果我們能夠解出方程1.2，并把結(jié)果代入方程中就能消去，中的一個(gè)參數(shù)，我們就可以得到參數(shù)形式的包絡(luò)線方程。然而還有重要的一點(diǎn)要指出，方程1.1和方程1.2也能夠被曲面族外的異常點(diǎn)面非包絡(luò)線上的點(diǎn)所滿足，只有曲面族上有規(guī)律的，滿足方程的點(diǎn)才位于包絡(luò)線上?，F(xiàn)在討論奇點(diǎn)出現(xiàn)的條件。曲面的參數(shù)形式表達(dá)式為 其中，是曲面的參數(shù)。滿足下面方程的點(diǎn)即為異常點(diǎn)：。如果一個(gè)奇點(diǎn)在曲面各種參數(shù)形式下都是奇點(diǎn)則稱該奇點(diǎn)為曲面的奇點(diǎn)。在一種曲面參數(shù)形式下為奇點(diǎn)，在其它形式下卻不一定是。為了確定的值，一般地，方程1.1和方程1.2代表曲面上的一條曲線，這些曲面對(duì)應(yīng)于參數(shù)的值。如果曲面不包含奇點(diǎn)，那么該曲線就在包絡(luò)線上。曲面和包絡(luò)線與這條曲線相切。這些曲線稱為曲面族的特征線。利用它們可以找到圓柱凸輪曲面與傳動(dòng)件的接觸線。確定圓柱凸輪輪廓的包絡(luò)線理論。在包絡(luò)線理論的基礎(chǔ)上，圓柱凸輪的輪廓可以被看作是在凸輪運(yùn)動(dòng)過(guò)程中，傳動(dòng)件曲面在圓柱凸輪表面與傳動(dòng)件之間的位置時(shí)的傳動(dòng)件曲面的包絡(luò)線。在這種條件下，輸入的圓柱凸輪參數(shù)作為曲面族的參數(shù)，因?yàn)閳A柱或圓錐傳動(dòng)件曲面可以很容易地以參數(shù)形式表示出來(lái)，以參數(shù)形式表示（見方程1.1和1.2）的單參數(shù)曲面族的包絡(luò)線理論用來(lái)確定圓柱凸輪輪廓的解析方程。正如上面最后一部分所述，傳動(dòng)件曲面上奇點(diǎn)的檢驗(yàn)總是必要的。圖a表示的是帶有平移圓錐傳動(dòng)件的圓柱凸輪機(jī)構(gòu)。傳動(dòng)件移動(dòng)軌跡的軸線與圓柱凸輪軸線重合，a是凸傳動(dòng)件縱向軸線間距離的偏移值。Ｒ和Ｌ是凸輪的半徑和長(zhǎng)度，是繞軸旋轉(zhuǎn)的角度，傳動(dòng)行程，是的函數(shù)，它們之間關(guān)系為 它們之間的替代關(guān)系通常是給定的。圖b表示傳動(dòng)件移動(dòng)時(shí)與凸輪二者的位置關(guān)系。傳動(dòng)件是圓錐截體圓錐頂角一半為，最小半徑為，是高，是從面到圓錐頂點(diǎn)的距離。以凸輪旋轉(zhuǎn)軸線為ｚ軸，y軸平行于圓錐傳動(dòng)件軸線建立0xyz坐標(biāo)系。Xyz軸的單位方向矢量分別為i,j,k.通常在靜止?fàn)顟B(tài)下，利用包絡(luò)線技術(shù)來(lái)得到圓柱凸輪輪廓。傳動(dòng)件反方向繞凸輪軸線旋轉(zhuǎn)。傳動(dòng)件繞ｚ軸轉(zhuǎn)過(guò)角。同時(shí)，傳動(dòng)件距凸輪線性偏移s，如圖b所示。因此，應(yīng)用這種理論，如果我們引進(jìn)和兩個(gè)參數(shù)，傳動(dòng)件曲面族可以用下面公式來(lái)描述： 其中，，是與凸輪運(yùn)動(dòng)有關(guān)的獨(dú)立參數(shù)。參考如方程1.1和1.2所描述的參數(shù)形式的曲面的包絡(luò)線理論通過(guò)下面這個(gè)方程我們繼續(xù)解決這個(gè)問(wèn)題。 實(shí)際應(yīng)用中，如果，在這些曲面族中就不會(huì)出現(xiàn)奇點(diǎn)。輪廓方程滿足方程.5和下面的方程： 其中，或 其中將方程1.8代入方程1.5中，消去，我們得到帶有平移圓錐凸輪的圓柱凸輪的輪廓方程， 如方程1.8所示，的功能是用來(lái)選定傳動(dòng)件運(yùn)動(dòng)過(guò)程和作為尺寸參數(shù)，結(jié)果，圓柱凸輪輪廓可以通過(guò)選擇傳動(dòng)件運(yùn)動(dòng)曲線和尺寸參數(shù)來(lái)控制，的兩個(gè)值同圓柱凸輪的兩個(gè)螺旋角一樣?，F(xiàn)在，帶有平移圓錐傳動(dòng)件的圓錐傳動(dòng)件的圓柱凸輪的輪廓可以利用這種新的方法設(shè)計(jì)出來(lái)。如上面所述，Dhandeetal.和Ｃhakraborty,Dhande通過(guò)這種相關(guān)聯(lián)通點(diǎn)的方法推導(dǎo)出了同類型凸輪輪廓的方程，在這，對(duì)這一結(jié)果進(jìn)行了畢較。自從這種方法應(yīng)用以來(lái)，盡管方法不同，但大家卻可以很容易得到同樣的輪廓方程，而且，我們發(fā)現(xiàn)使用這種方法來(lái)確定輪廓方程的過(guò)程大簡(jiǎn)化了。相交線：任何時(shí)候，圓柱凸輪與它的傳動(dòng)件相交線為空間曲線時(shí)它們之間的相交線是必需要討論的。上文提到的單參數(shù)曲面族的包絡(luò)線理論中的特征線觀點(diǎn)可以應(yīng)用到這里來(lái)確定相交線。凸輪方程向方程1.9一樣，那么，當(dāng)取具體值時(shí)，相交線方程為： 其中，方程1.10中，的值和方程1.8中定義的的功能是一樣的。凸輪和傳動(dòng)件在任意時(shí)刻的表面交線是同方程1.10來(lái)確定的。我們知道傳動(dòng)件表面參數(shù)和之間的關(guān)系是由非線性方程1.8給出的。因此，大家可以很容易的發(fā)現(xiàn)圓錐傳動(dòng)件表面的交線并不總是一條直線。壓力角凸輪和其傳動(dòng)件的公法線與傳動(dòng)件的軌跡所成的角叫壓力角。設(shè)計(jì)時(shí)必須考慮壓力角，它們衡量機(jī)構(gòu)是否恰當(dāng)進(jìn)行連續(xù)力傳遞的參數(shù)，在這種凸輪傳動(dòng)系統(tǒng)中壓力角的大小影響系統(tǒng)的效率，壓力角越小，效率越高。如圖2，圓柱凸輪和它的圓錐傳動(dòng)件的單位法向量通過(guò)二者的交線上的一點(diǎn)，例如Ｃ點(diǎn)，以n來(lái)表示。傳動(dòng)件的路徑用單位向量p表示，p平行于傳動(dòng)件的軸線，從壓力角定義可知，矢量n和p所夾的角就是壓力角。在交線處，既然系包絡(luò)線和曲面有共切面，那么，圓柱凸輪表面的法線和傳動(dòng)件表面法線是共線的。參照方程1.5和圖2，可以得到單位法矢量如下： 其中，的值由方程1.8給定，傳動(dòng)件的單位速度矢量為： MACROBUTTONMTPlaceRefSEQMTEqn\h(SEQMTSec\c