齒輪之設計與製造技術發展已有多年的歷史，但在某些應用上，仍有背隙、邊緣接觸及應力過大等問題存在，所以仍有許多專家學者嘗試設計新型齒輪，以期能有更佳的特性。其中，曲線齒形具有點接觸的特性；而錐狀齒輪(Conical gear)具有背隙可調、對組裝誤差敏感度較低，並可應用於平行軸、相交軸及歪斜軸齒輪對的特性。
　　本文主要參考前人所設計之一組平行軸曲線齒形錐狀齒輪與直齒錐狀齒輪，其可結合上述曲線齒形與錐狀齒輪兩者之優點，而兼具點接觸及背隙可調之特性。針對此兩種齒輪分別使用其曲率分析模式，推導出參數避免過切範圍，並延伸前人所建立之齒印接觸分析模式，分別作其齒印接觸分析及誤差分析，以顯示其具點接觸且背隙可調之特性，另外並探討其於相交軸時之接觸分析及誤差分析。
　　根據本文研究的成果，所得之曲線齒形錐狀齒輪及直齒錐狀齒輪之參數避免過切範圍，可提供設計者於設計此類型齒輪時，選定參數值的參考。並作齒印接觸分析及誤差分析實例，顯示其具有點接觸及背隙可調之特性，且能保持定速比傳動。因此本文於學術及應用上均有其參考價值。

　　The technologies for the design and manufacturing of gears have been improved quite a lot in these few decades, however for some applications, the problems of backlash, edge contact and over-stress are still exist. Thus, researches on developing innovative gears with better characteristics are necessary. Among the results of these researches, cylindrical gears with curvilinear shaped teeth have the advantages of point contact in the middle parts of gear surfaces and lower sensitivity due to errors; and conical gears have the advantages of adjustable backlash, ease machining, lower sensitivity due to errors, usability in cases of parallel shafts, intersecting shafts, and skew shafts.
　　In order to have the advantages of both of the above two gear-types, a conical gear pair on parallel shafts, one with curvilinear shaped teeth and the other one with straight teeth, was proposed and investigated in a previous study. This study is its extension. Based on the developed models for the surface design and curvature analysis of both types of gears, ranges of design parameters for avoiding undercutting are determined. Furthermore, the models of tooth contact analysis and error analysis of the gear pair are used, and design examples are included to show the advantages of point-contact and anti-backlash of the gear pair. Besides, tooth contact analysis and error analysis of the gear pair on intersecting shafts are also investigated.
　　Based on the results of this study, the ranges of design parameters for avoiding undercutting of the conical gears with curvilinear shaped teeth or with straight teeth can be determined, such that the spending-time for the design of gears can be shorten. It is shown by the results of tooth contact analysis and error analysis, that the proposed innovative conical gear pair is capable of avoiding edge contact and backlash, and they have the advantages of using involute tooth profiles. Thus, qualified academic papers can be expected to be published, and the proposed gear pair has great potential for various industrial applications.

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