【正文】 ?? ? ? ? ?????? ? ? ? ? ?? ? ? ????? (5) where 0≤θ＜ 2pi And ф2 is the independent parameter of the cam motion. Referring to theory of envelopes for surfaces represented in parametric form (see equations 1and 2), we proceed with the solving process by finding ? ? ? ?? ? ? ?2222ta n c os c os sin ta nc os sin c os ta n sinrr rijk? ? ? ? ? ???? ? ? ? ???? ? ? ???????? ? ? ????? (6) There are no singular points on the family of surfaces, since(r +δtanα) ＞ 0 in actual applications. The profile equation satisfies equation 5 and the following equation: ? ?? ? ? ?? ?239。 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。然而還有重要的一點(diǎn)要指出，方程 和方程 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。如果曲面不包含奇點(diǎn)，那么該曲線就在包絡(luò)線上。 圖 a 表示的是帶有平移圓錐傳動件的圓柱凸輪機(jī)構(gòu)。傳動件反方向繞凸輪軸線旋轉(zhuǎn)。輪廓方程滿足 方程 .5 和下面的方程： ? ?? ? ? ?? ?239。如上面所述， hakraborty,Dhande通過這種相關(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，對這一結(jié)果進(jìn)行了畢較。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。 代入所得結(jié)果，可以得到壓力角方程如下： c os c os si nnp? ? ?? ? ? 錯誤 !未找到引用源。刀具的前部是一個圓錐形，最小半徑是 R。刀軸平行于 y 軸，標(biāo)記那兩個條件： ??? 錯誤 !未找到引用源。上升和下降部分是擺線。 該項(xiàng)成果即 將應(yīng)用于數(shù)控銑床上，簡化加工圓柱凸輪時刀具路徑生。由圖可知二者壓力角變化相同。 帶有平移圓錐傳動件的圓柱凸輪的輪廓由 方程 來確定代入得到角 ? ： ? ? ? ?? ?? ? ? ?2 2 2 222c osc os c os si n t a n c os si n c os t a nc ossi nsi n c osxnaijxkij?? ? ? ? ? ? ? ??????? ? ? ???? ???????????錯誤 !未找到引用源。39。加工過程中，圓柱凸輪固定在 4 軸銑床的旋轉(zhuǎn)工作臺上，隨著工作臺旋轉(zhuǎn)，刀具按照從動件運(yùn)動規(guī)律，平行于圓柱輪廓軸線運(yùn)動。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。凸輪方程向方程 一樣，那么，當(dāng) 2? 取具體值 20? 時，相交線方程為： ? ? ? ?20,cl cl cr r r? ? ??? 錯誤 !未找到引用源。 其中 ? ? ? ?39。 其中， 02??? ， 2? 是與凸輪運(yùn)動有關(guān)的獨(dú)立參數(shù)。 圖 b 表示傳動件移動時與凸輪二者的位置關(guān)系。 確定圓柱凸輪輪廓的包絡(luò)線理論。滿足下面方程的點(diǎn)即為異常點(diǎn)：120rr??????。 其中 ?是曲面族的參數(shù)， 12,??是曲面族中特定曲面的參 數(shù)。1 c osta n sin c ossinEsFrGa?? ? ? ? ? ???? ? ? ? ? ?? Substituting equation 8 into equation 5, and eliminating θ, we obtain the profile equation of the cylindrical cam with a translating conical follower, and denote it as ? ?2,ccrr??? (9) As shown in equation 8,θ is a function of the selected followermotion program and the dimensional parameters. As a consequence, the cylindrical profile can be controlled by the chosen followermotion curves and the dimensional parameters. Two values of θ correspond to the two groove walls of the cylindrical cam. Now the profile of the cylindrical cam with a translating conical follower is derived by the new proposed method. As stated above, Dhande et and Chakraborty and Dhande2 have derived the profile equation of the same type of cam by the method of contact points. A parison of the result is carried out here. Since the same fixed coordinate system and symbols are used, one can easily see that the profile equation is identical although the methods used are different. Moreover, we find that the process of finding the cam profile is significantly reduced by this method. CONTACT LINE At every moment, the cylindrical cam touches the follower along space lines. The contact lines between the cylindrical cam and its follower are discussed in this section. The concept of characteristic lines in the theory of envelopes for a 1parameter family of surfaces mentioned above could be applied to finding the contact lines in a cylindrical . The profile of a cylindrical cam with a translating conical follower is given by Equation9. Then, the contact line at a specific value of ф2, say ф20, is ? ? ? ?20,cl cl cr r r? ? ??? (10) Where, in Equation 10, the value of θ is a function of δ defined by Equation 8. The contact lines between the surfaces of the cam and the follower at each moment is determined by Equation 10. we see that the relationship between the two parameters θ and δ of the follower surface is given by Equation 8, a nonlinear function. Thus, one can easily find that the contact line is not always a straight line on the conical follower surface. PRESSURE ANGLE The angle that the mon normal vector of the cam and the follower makes with the path of the follower is called the pressure angle12. the pressure angle must be considered when designing a cam, and it is a measure of the instantaneous forcetransmission properties of the mechanism13. The magnitude of the pressure angle in such a camfollower system affects the efficiency of the cam. The smaller the pressure angle is, the higher its efficiency because14. In figure2, the unit normal vector which passes through the point of contact between the cylindrical cam and the translating conical follower in the inversion position, . point C, is denoted by n. The path of the follower labeled as the unit vector p is parallel to the axis of the follower. from the definition, the pressure angle Ψ is the angle between the unit vectors n and p. Since, at the point of contact, the envelope and the surface of the family possesses the same tangent plane, the unit normal of the cylindricalcam surface is the same as that of the follower surface. Referring to the family equation Equation5 and Figure2, we can obtain the unit vector as