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

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)計和加工有人提出了具有平移圓錐傳動件的圓柱凸輪的輪廓確定及其機(jī)加工的簡單方法.在單參數(shù)曲面族的包絡(luò)線理論的基礎(chǔ)上,給定從動件運(yùn)動規(guī)律的具有平移圓錐傳動件的圓柱凸輪的輪廓的設(shè)計是很簡單的.通過這種設(shè)計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)加工過程中,可以使用錐形端銑刀,它的尺寸小于等于圓錐傳動件的尺寸.很多實例證明該方法的實用性.關(guān)鍵詞:圓柱凸輪,包絡(luò)線,計算機(jī)輔助設(shè)計和計算機(jī)輔助制造.圓柱凸輪是利用其圓周上的溝槽來驅(qū)動傳動件的空間凸輪.傳動件是圓柱或者圓錐形狀的,可以做平行移動也可以做擺動.凸輪繞著它的縱向軸線旋轉(zhuǎn),同時將平移或擺動運(yùn)動傳遞給傳動件.這種機(jī)械原理長期廣泛應(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.這種方法是在一個前提下使用的,即認(rèn)為在主動輪和從動件交點處,凸輪的徑向矢量和速度矢量二者相互垂直.BROISOV提出了借助計算機(jī)輔助計算的方法來解決圓柱凸輪機(jī)構(gòu)設(shè)計上的問題.通過這種方法,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)計時就只需在實際圓柱上找到凸輪軌跡的中心和輪廓邊緣.瞬間螺旋運(yùn)動理論已經(jīng)應(yīng)用到凸輪機(jī)構(gòu)的設(shè)計中.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)用這個理論確定了球面擺動輥子凸輪機(jī)構(gòu)的幾何形狀.考慮到用與傳動件同樣尺寸的圓柱刀具加工圓柱凸輪,PAPAIOANNOU和KIRITSIS提出了通過解決最優(yōu)化受限問題來選擇刀具步距的程序.在這份研究報告提出了一個新的簡單的程序來確定圓柱凸輪的輪廓方程并提供機(jī)加工過程中所要求的刀具路徑.它是通過應(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)則曲面的傳動零件系統(tǒng)中，他們創(chuàng)建了普通凸輪偉動系統(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)時傳動件在不同位置，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對這個定理進(jìn)行了詳細(xì)的驗證。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要指出，方程1.1和方程1.2也能夠被曲面族外的異常點面非包絡(luò)線上的點所滿足，只有曲面族上有規(guī)律的，滿足方程的點才位于包絡(luò)線上。現(xiàn)在討論奇點出現(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)。滿足下面方程的點即為異常點：。如果一個奇點在曲面各種參數(shù)形式下都是奇點則稱該奇點為曲面的奇點。在一種曲面參數(shù)形式下為奇點，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，這些曲面對應(yīng)于參數(shù)的值。如果曲面不包含奇點，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)動過程中，傳動件曲面在圓柱凸輪表面與傳動件之間的位置時的傳動件曲面的包絡(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)，因為圓柱或圓錐傳動件曲面可以很容易地以參數(shù)形式表示出來，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，傳動件曲面上奇點的檢驗總是必要的。圖a表示的是帶有平移圓錐傳動件的圓柱凸輪機(jī)構(gòu)。傳動件移動軌跡的軸線與圓柱凸輪軸線重合，a是凸傳動件縱向軸線間距離的偏移值。Ｒ和Ｌ是凸輪的半徑和長度，是繞軸旋轉(zhuǎn)的角度，傳動行程，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表示傳動件移動時與凸輪二者的位置關(guān)系。傳動件是圓錐截體圓錐頂角一半為，最小半徑為，是高，是從面到圓錐頂點的距離。以凸輪旋轉(zhuǎn)軸線為ｚ軸，y軸平行于圓錐傳動件軸線建立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)來得到圓柱凸輪輪廓。傳動件反方向繞凸輪軸線旋轉(zhuǎn)。傳動件繞ｚ軸轉(zhuǎn)過角。同時，傳動件距凸輪線性偏移s，如圖b所示。因此，應(yīng)用這種理論，如果我們引進(jìn)和兩個參數(shù)，傳動件曲面族可以用下面公式來描述： 其中，，是與凸輪運(yùn)動有關(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)線理論通過下面這個方程我們繼續(xù)解決這個問題。 實際應(yīng)用中，如果，在這些曲面族中就不會出現(xiàn)奇點。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，的功能是用來選定傳動件運(yùn)動過程和作為尺寸參數(shù)，結(jié)果，圓柱凸輪輪廓可以通過選擇傳動件運(yùn)動曲線和尺寸參數(shù)來控制，的兩個值同圓柱凸輪的兩個螺旋角一樣?，F(xiàn)在，帶有平移圓錐傳動件的圓錐傳動件的圓柱凸輪的輪廓可以利用這種新的方法設(shè)計出來。如上面所述，Dhandeetal.和Ｃhakraborty,Dhande通過這種相關(guān)聯(lián)通點的方法推導(dǎo)出了同類型凸輪輪廓的方程，在這，對這一結(jié)果進(jìn)行了畢較。自從這種方法應(yīng)用以來，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)使用這種方法來確定輪廓方程的過程大簡化了。相交線：任何時候，圓柱凸輪與它的傳動件相交線為空間曲線時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可以應(yīng)用到這里來確定相交線。凸輪方程向方程1.9一樣，那么，當(dāng)取具體值時，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。凸輪和傳動件在任意時刻的表面交線是同方程1.10來確定的。我們知道傳動件表面參數(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)圓錐傳動件表面的交線并不總是一條直線。壓力角凸輪和其傳動件的公法線與傳動件的軌跡所成的角叫壓力角。設(shè)計時必須考慮壓力角，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件的單位法向量通過二者的交線上的一點，例如Ｃ點，以n來表示。傳動件的路徑用單位向量p表示，p平行于傳動件的軸線，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，傳動件的單位速度矢量為： MACROBUTTONMTPlaceRefSEQMTEqn\h(SEQMTSec\c