滾齒凸輪機構(Roller-gear cam mechanisms, RGCMs)因其易於產生兼具有暫停(Dwell)和分度(Index)的運動，故常被用於產生間歇運動(Intermittent motion)的機構。此外，其亦具有諸多優異的特性，故被廣泛地應用於各類自動化機械中，例如綜合加工機之自動換刀(Automatic tool changers)機構。
滾齒凸輪機構藉由桶形凸輪(Barrel cam)之肋曲面(Rib surfaces)與轉塔(Turret)上之滾子間的共軛接觸(Conjugate contact)，將運動和動力傳遞至轉塔上。因此，為得到良好的特性，優良的肋曲面設計是很重要的。但是，若其幾何參數選取不當，則一肋之兩側曲面可能會接觸，甚至相互交截(Intersection)。這樣的肋可能強度不足，嚴重時甚至會喪失其傳動的功能。然而在現有的文獻中，卻尚未發現肋曲面交截之相關問題的探討。故本文提出判斷一肋之兩側曲面是否接觸之檢測模式，並針對幾個幾何參數分別建立其避免肋面交截範圍之決定數學模式。隨後以一個實例介紹這些模式的使用方式，並據以驗證其正確性。而同時能避免肋面交截及避免曲面過切(Undercutting)等要求之幾何參數的可行範圍也於實例中顯示之。
在某些綜合加工機之自動換刀裝置中，其滾齒凸輪機構必須藉助其桶形凸輪的一側所切削出之溝槽面凸輪(Groove cam)，而驅動五連桿組(Five-bar linkage)，以達到拔刀及插刀所需之平移運動。因此為了簡化此類裝置的構造，本文提出一轉塔可同時兼具旋轉及線性平移輸出之新型滾齒凸輪機構。除了建立該新型機構之曲面設計及曲率分析的模式外，本文也分別建立其幾個幾何參數的避免肋面交截及過切範圍的決定模式。其中，針對嚙合件為圓柱滾子的情況，推導出決定其滾子半徑之避免過切範圍的閉合解。文中也利用兩個實例顯示該機構之特性並驗證所提模式之正確性，其中之一的轉塔之平移與旋轉同向；另一例中，其方向則相異。而該機構之同時能避免肋面交截與避免曲面過切等要求之幾何參數的可行範圍，也分別於兩實例中加以探討。
總結本文所得的結果，除了提出一新型之滾齒凸輪機構外，亦提出決定其幾何參數避免肋面交截及過切的範圍之理論模式。此對於設計該類機構應該會有所助益。故相信本文之研究成果，在學術及應用上均應有其參考價值。

Dwell and indexing motions are quite easy be given by using roller-gear cam mechanisms (RGCMs), so they are often used as intermittent motion mechanisms. Besides, they also have many good characteristics, so as to be used in various automatic machines, such as the automatic tool changers in machining centers.
For RGCMs, the barrel cam transmits motion and power to the turret via the conjugate contact between the rib surfaces and rollers. Thus to design the rib surfaces well is very important to get good characteristics. Whereas if the geometric parameters are selected inappropriately, two side-surfaces of a rib could contact to or even intersect each other, such that the rib has not enough strength or even lose its transmitting function. Yet, relevant studies on rib-surface intersection have not been found in existing literatures. A model, for the judgment of whether two side-surfaces of a rib contact or not, is proposed. Consequently, mathematical models for the determination of the ranges of several geometric parameters to avoid rib-surface-intersection are developed. An example is given to demonstrate the usages of the proposed models and to exam their correctness. Feasible regions of geometric parameters, to avoid rib-surface-intersection and undercutting, are also given.
For some existing automatic tool changers in machining centers, the RGCM has to be integrated with a five-bar linkage driven by the groove cam, which is cut on one side of the barrel cam, to provides translational motions of disengaging and inserting tools. A RGCM, whose turret can rotate and translate simultaneously, is proposed, such that the structure of such machines can be simplified. Except the models of surface design and curvature analysis been developed, those for determining the ranges of several geometric parameters to avoid rib-surface-intersection and undercutting, respectively, are also developed. Among them, a close-form solution, to determine the range of the roller radius for avoiding undercutting, is derived, if the rollers are cylindrical ones. Two examples are included to show the characteristics of the mechanism and to exam the correctness of the proposed models. In one of which, the translating direction of the turret is the same as its rotational axis; however, they are different in the other example. Feasible regions of geometric parameters, to avoid rib-surface-intersection and undercutting, are also given.
In summary, except an innovative roller-gear cam mechanism is proposed, the proposed models for the determination of the ranges of the geometric parameters to avoid rib-surface-intersection and undercutting of RGCMs should be helpful in the design of these mechanisms. It is believed that these results are valuable in both of the academic field and industrial applications.

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