【正文】 esearch1,2. Only one coordinate system is used in this approach. As a result, the process of derivation is simple. Work is currently under way to facilitate the implementation of the tool path for the machining of the cylindrical cam on a numerically controlled milling machine. 翻譯： 錯誤 !未找到引用源。1 2dss d?? or ? ?2 2 212 t a n E E F GGF? ???? ? ? ???? ??? (8) Where ? ? ? ?39。 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： ? ?12,rr? ? ?? 錯誤 !未找到引用源。 其中， 12,??是曲面的參數(shù)。利用它們可以找到圓柱凸輪曲面與傳動件的接觸線。 它們之間的替代關(guān)系通常是給定的。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： ? ?? ? ? ?? ? ? ?? ?22 2 22 2 2,c os si n t a n c os c ossi n c os t a n c os si n1 t a n si nrra r ia r js r k? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ?? ? ??? ? ? ? ?????? ? ? ? ? ?? ? ? ?????錯誤 !未找到引用源。1 2dss d?? 或 ? ?2 2 212 t a n E E F GGF? ???? ? ? ???? ???錯誤 !未找到引用源。 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)用到這里來確定相交線。 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(diǎn)，例如Ｃ點(diǎn)，以 n 來表示。 通常，考慮到尺寸精度和平面度，加工圓柱凸輪最方便的方法是使用和圓角半徑相同的刀具。o 的軌跡為： ? ?? ?39。刀軸單位矢量是 ? ? ? ?22sin c osax i j???? 錯誤 !未找到引用源。圖 6 中，有較小ｚ的表面為Ⅰ面 ,另一面是Ⅱ面，上升Ⅰ和下降Ⅱ部分的壓力角的變化分別如圖 7 和8 所示。 。圖 5 表示運(yùn)動軌跡。 rR? 錯誤 !未找到引用源。半頂角為 ? . 如果刀具沿著曲面 ? ?2,XX??? 上的曲線 0??? 移動，刀軸單位矢量 xa和在交點(diǎn)Ｃ處的單位公法線 n 所夾角 ? 由下式?jīng)Q定： cos xna? ?? 錯誤 !未找到引用源。 這里推導(dǎo)出的壓力角和 Chakraborty 和 Dhande以前工作中應(yīng)用的是一樣的。 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。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。1se c t a nc os si n t a n si n c os c os si n0r r r rs r a? ? ?? ? ?? ? ? ? ? ? ? ? ? ?? ? ?? ? ? ? ?? ? ?? ? ? ? ? ?????? 錯誤 !未找到引用源。傳動件繞ｚ軸轉(zhuǎn)過 2? 角。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。曲面和包絡(luò)線與這條曲線相切。 現(xiàn)在討論奇點(diǎn)出現(xiàn)的條件。 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。英文資料翻譯 英文原文： Design and machining of cylindrical cams with translating conical followers By DerMin Tsay and Hsien Min Wei A simple approach to the profile determination and machining of cylindrical cams with translating conical followers is presented .On the basis of the theory of envelopes for a 1parameter family of surfaces,a cam profile with a translating conical follower can be easily designed once the followermotion program has been given .In the investigation of geometric characteristics ,it enables the contact line and the pressure angle to be analysed using the obtained analytical profile expressions .In the process of machining ,the required cutter path is provided for a tapered endmill cutter ,whose size may be identical to or smaller than that of the conical follower .A numerical example is given to illustrate the application of the procedure . Keywords : cylindrical cams, envelopes , CAD/CAM A cylindrical cam is a 3D cam which drives its follower in a groove cut on the periphery of a cylinder .The follower, which is either cylindrical or conical, may translate or oscillate. The cam rotates about its longitudinal axis, and transmits a transmits a translation or oscillation displacement to the follower at the same time. Mechanisms of this type have long been used in many devices, such as elevators, knitting machines, packing machines, and indexing rotary tables. In deriving the profile of a 3Dcam, various methods have used. Dhande et and Chakraborty and dhande2 developed a method to find the profiles of planar and spatial cams. The method used is based on the concept that the mon normal vector and the relative velocity vector are orthogonal to each other at the point of contact between the cam and the follower surfaces. Borisov3 proposed an approach to the problem of designing cylindricalcam mechanisms by a puter algorithm. By this method, the contour of a cylindrical cam can be considered as a developed linear surface, and therefore the design problem reduces to one of finding the centre and side profiles of the cam track on a development of the effective cylinder. Instantaneous screwmotion theory4 has been applied to the design of cam mechanisms. GonzalezPalacios et used the theory to generate surfaces of planar, spherical, and spatial indexing cam mechanisms in a unified framework. GonzalezPalacios and Angeles5 again used the theory to determine the surface geometry of spherical camoscillating rollerfollower mechanisms. Considering machining for cylindrical cams by cylindrical cutters whose sizes are identical to those of the followers, Papaioannou and Kiritsis6 proposed a procedure for selecting the cutter step by solving a constrained optimization problem. The research presented in this paper shows q new, easy procedure for determining the cylindricalcam profile equations and providing the cutter path required in the machining process. This is acplished by the sue of the theory of envelopes for a 1parameter family of surfaces described in parametric form7 to define the cam profiles. Hanson and Churchill8 introduced the theory of envelopes for a 1parameter family of plane curves in implicit form to determine the equations of platecam profiles Chan and Pisano9 extended the envelope theory for the geometry of plate cams to irregularsurface follower systems. They derived an analytical description of cam prof