【正文】 自從同樣的系統(tǒng)和符號在研究中使用以來，大家可看，使用這種方法得到的凸輪輪廓線結果與以前的研究所得結果是一致的。 其中 22s in c o sc o s 2 s in ta n c o s c o ss in ta n s inR R RA a r??? ? ? ? ? ? ? ?? ? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ?? ? ? ? 22s in c o sc o s 2 c o s ta n c o s ss in ta n s inR R RB a r in? ? ? ? ? ? ? ?? ? ?? ? ? ?? ? ? ? ? ? ? ? ?? ? ? ?? ? ? ? c o s1 ta n s ins inrC s r ?? ? ????? ? ? ? ????? 實際應用舉例： 在這部分中，應用高級程序來確定圓柱凸輪輪廓，分析它的特征，帶有平移圓錐傳動件的圓柱凸輪的從動件運動程序由下式給出： ? ?? ?1 1 2022 1 2 2sin2 2 220222221sin2hshh??? ? ?? ? ?? ? ???? ? ?? ? ???? ? ???????????????????????????????? 其中， h 和 ? 兩個常數(shù)， 20, 60h ???。 頂點處軌跡為 ? ?? ? 0202,11,sin ta nTTxXXX R n a???? ??????????? 錯誤 !未找到引用源。在這種情況下，刀具軌跡必須通過通用端銑刀來確定。參照方程 和圖 2，可以得到單位法矢量如下： ? ? ? ? ? ?2 2 2 2c o s c o s c o s sin ta n c o s sin c o s ta n sinrrni j k??? ? ? ? ? ? ? ? ? ???????? ? ? ? ? ????? 錯誤 !未找到引用源。 凸輪和傳動件在任意時刻的表面交線是同方程 來確定的。 如方程 所示， ? 的功能是用來選定傳動件運動過程和 作為尺寸參數(shù)，結果，圓柱凸輪輪廓可以通過選擇傳動件運動曲線和尺寸參數(shù)來控制， ? 的兩個值同圓柱凸輪的兩個螺旋角一樣。 ? ? ? ?? ? ? ?2222ta n c os c os sin ta nc os sin c os ta n sinrr rijk? ? ? ? ? ???? ? ? ? ???? ? ? ???????? ? ? ?????錯誤 !未找到引用源。以凸輪旋轉軸線為ｚ軸， y 軸平行于圓錐傳動件軸線建立 0xyz 坐標系。 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 和 ）的單參數(shù)曲面族的包絡線理論用來確定圓柱凸輪輪廓的解析方程。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。 其中，方程右邊是常數(shù) 0， Litvin 對這個定理 進行了詳細的驗證。0 0 0 202, sinXXRX???? ???? (15) and the tip centre T follows the path ? ?? ?0202,11,sin ta nTTxXXX R n a???? ??????????? (16) Figure 4 shows a tapered endmill cutter machining the groove wall of a cylindrical cam. The axis of the tapered endmill is parallel to the y axis. Note that the two conditions ??? （ 17） rR? (18) for the geometric parameters of the cutter and the roller follower must hold, or otherwise the cutter would not fit the groove. The unit vector of the cutter axis is ? ? ? ?22sin c osax i j???? (19) For the profile of the cylindrical cam with a translating conical follower given by equation 9, the angle σ is determined by the inner product: ? ? ? ?? ?? ? ? ?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?? ? ? ? ? ? ? ??????? ? ? ???? ??????????? (20) Thus, by using the results obtained earlier, the position of the tip centre of the cutter can be derived as ? ?2,11s i n t anTTxrrrc r n aA i B j C k???????? ? ?????? ? ? (21) where22s in c o sc o s 2 s in ta n c o s c o ss in ta n s inR R RA a r??? ? ? ? ? ? ? ?? ? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ?? ? ? ? 22s in c o sc o s 2 c o s ta n c o s ss in ta n s inR R RB a r in? ? ? ? ? ? ? ?? ? ?? ? ? ?? ? ? ? ? ? ? ? ?? ? ? ?? ? ? ? c o s1 ta n s ins inrC s r ?? ? ????? ? ? ? ????? NUMERICAL EXAMPLE The procedures developed are applied in this section to determine the cylindricalcam profile, and to analyse its characteristics. The motion program of the follower for the cylindrical cam with a translating cylindrical cam is given as ? ?? ?1 1 2022 1 2 2sin2 2 220222221sin2hshh??? ? ?? ? ?? ? ???? ? ?? ? ???? ? ???????????????????????????????? (22) where h and λ are two constants. And h=20 units and λ=60℃ . The motion program is a dwellrisedwellreturndwell curve, and the rise and return portions are cycloidal curves 15. Figure 5 shows the motion program. The dimensional parameters used for the cylindrical cam and the follower are as follows: semicone angle of follower α = 0℃ height of follower δ1 =15 units distance from bottom of follower to xz plane μ =55 units smallest radius of follower r = units offset a = 20 units radius of cam R = 73 units axial length of cam L = 100 units The profile of the cylindrical cam obtained by applying Equation 9 is shown in Figure 6. In Figure 6, the groove wall with the smaller z coordinates is side Ⅰ , and the other is side Ⅱ . The variations of the pressure angles for the rise and return portions are shown in Figures 7 and 8 for side Ⅰ and Ⅱ , respectively. It can be seen that the pressure angles for both sides happen to be identical. CONCLUSIONS As has been shown above , the application of the theory of envelopes affords a convenient and versatile tool for determining the cylindercam profiles with translating conical followers. By means of the analytical cam profile equations, it can be easily extended to acplish the task for the analysis of the contact line and the pressure angle. Further , the cutter path required in the process of machining is generated for tapered endmill cutters. Since the same fixed coordinate system and symbols are used in this study, one can see that the results for cam profiles and pressure angles are identical to those obtained in previous r