凸輪機構在自動機械中受到廣泛的應用，其中滾齒凸輪機構因其優良的運動和動力特性在研究和應用領域受到廣泛的關注。

本研究根據球面嚙合件藉由齊次座標轉換與共軛曲面原理，推導滾齒凸輪曲面方程式及嚙合方程式，並利用包絡法驗證嚙合方程式。在加工方面，利用轉標轉換原理推導了其刀具位置方程式，並在弦高誤差的限制下得到理想的刀具位置控制點。最後利用Visual Basic開發其設計及加工模組，透過模組的運算產生曲面點資料及加工位置點資料，利用Unigraphics完成曲面建構及後處理轉檔，驗證其曲面方程式，為驗證其加工路徑，本研究利用實體切削模擬軟體Vericut模擬刀具運動，完成滾齒凸輪之模擬切削，證實本研究方法之正確性。

Cam mechanism is widely applied in automatic, and in which, roller-gear cam mechanism is widely studied and used for their excellent performance in kinematics and dynamics.

The study derived the surface profile equations and the meshing equations of the spherical meshing elements from the homogeneous coordinate transformation matrix and the conjugate surface theory proved by the envelope theory. In the tool path generation aspect, we demonstrated the position equation of cam profile using the coordinate transformation theory and obtained the perfected controlling position point of the tool path under the limitation of the chord errors. Finally, the design and the machining module developed via Visual Basic that generates the cam profile points and the tool path points. Constructing the cam surface from Unigraphics to test and verify the cam profile equation. In order to examine the tool path, we use the hypostatized cutting simulation software, Vericut, to simulate the motion of the tool path of the roller-gear cam and to verify the correctness of the method proposed in this study.

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