凸輪機構在工業上應用甚廣，如紡織機械、食品生產機械、內燃機、拉線機械及其他自動化機械等。但設計空間凸輪機構時，除了設計其曲面以達到所需之運動特性外，尚須進行其曲率分析以避免過切現象的發生，以致增加了設計所需的時間以及繁雜度。

　　本文所探討之凸輪機構乃針對凸輪作往復平移運動，而從動件則分別為作往復平移運動、作搖擺運動之從動件、以及作兼具往復平移及搖擺運動之圓錐滾子從動件。利用齊次坐標轉換矩陣且配合共軛曲面理論與包絡理論，推導其曲面方程式。並使用共軛曲面理論推導曲率分析模式，且利用其結果建立兩嚙合曲面避免過切的條件，並據以推得部份設計參數不過切範圍的解析解型式。文中並分別針對作往復平移、搖擺及兼具兩者之圓錐滾子從動件凸輪機構各舉一到二個實例，進行設計分析及其結果之驗證。

　　根據所得之結果可知，僅部分設計參數之不過切範圍具有解析解，而本文所建立之曲面設計、曲率分析及設計參數之不過切範圍具解析解型式的數學模式，可作為設計此類型之凸輪機構時的參考。

　　Cam mechanisms are used in various automatic machinery. When designing spatial cam mechanisms, except cam surface design for satisfying the required motion characteristics, the curvature analysis is need to avoid undercutting, and these make the design process time-consuming and perplexing.

　　For spatial cam mechanisms with a translating cam and a conical roller follower, the follower moving in a translation, or in an oscillation, or in both translation and oscillation simultaneously, models of surface design, curvature analysis, and the condition of avoiding undercutting are developed in this study, based on homogenous coordinate transformation and theory of conjugate surface. According to the condition of avoiding undercutting, the analytical expressions (if they exist) of the ranges of design variables to avoid undercutting are derived. Some examples are given for each of spatial cam mechanisms to explain the usage of propose models and also to verify their correctness.

　　According to the results of this study, some design parameters for avoiding undercutting have analytical-form solutions. For the spatial cam mechanisms, the analytical expressions for determining the ranges of design parameters to avoid undercutting are given in this study, and they are believed to be valuable for the research and development of these mechanisms.

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