因凸輪機構具有容易設計、容易獲得動平衡以及可作高速傳動等之優點，故在工業上之應用甚廣，其基本功用在於將旋轉運動與往復直線運動或往復搖擺運動作相互之變換。在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。本文針對各類具特殊幾何尺寸之擺動型或直動型滾子從動件空間凸輪機構，探討其設計參數之避免過切範圍，並藉由傳動性能指標驗證各特殊化幾何尺寸組合之凸輪類型的可行性。
本文以齊次坐標轉換矩陣作為坐標系轉換的工具，以共軛理論作為創成凸輪曲面的依據，建立其曲面設計、曲率分析、傳動性能評估以及避免過切條件等之數學模式。針對各種類型之幾何設計參數特殊化組合，利用避免過切條件決定其不過切之參數範圍以得到無干涉或過切現象之設計，並利用傳動性能指標評估其傳動之特性。最後再分別針對擺動型與直動型滾子從動件空間凸輪機構各舉一設計實例，說明該法的使用並進行其結果之驗證。
根據本文所得的結果可知，並非所有特殊化幾何設計參數之組合皆能使用。而針對所有可行之幾何設計參數特殊化組合，本文提出不過切條件具解析解之參數的數學模式，可提供使用者在設計這些機構時之參考。

Cam mechanisms are used in various automatic machinery due to the advantages of providing the simplest means of achieving almost any desired follower motion, better dynamic balance, and allowing high-speed applications. Their fundamental function is to transfer a rotating motion into a translating motion or an oscillating motion. When designing spatial cam mechanisms, except cam surface design for satisfying the required motion characteristics, the curvature analysis is needed to avoid undercutting. These make the design process time-consuming and perplexity. For each kind of spatial cam mechanisms with an oscillating or translating roller follower having special geometrical dimensions, to determine the ranges of design parameters for avoiding undercutting is the main subject of this study.
Models of surface design, curvature analysis, indices of transmission performance and the condition of avoiding undercutting are developed in this study, based on homogeneous coordinate transformation and theory of conjugate surfaces. For each spatial cam mechanism having special geometrical dimensions, the analytical expressions (if they exist) of the ranges of design variables to avoid undercutting are derived. Furthermore, the indices of transmission performance are used to verify the usability of these mechanisms. A design example is given for each of spatial cam mechanisms with an oscillating or translating roller follower having special geometrical dimensions, to explain the usage of the propose methodology and also to verify its correctness.
According to the results of this study, not every kind of combinations of special geometrical dimensions of the mechanism can be used. For those usable 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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