齒輪機構(Gear mechanisms)在工業上應用甚廣，如汽車變速箱、工具機、減速機及其他多種傳動系統上均可見。近年來，雖然齒輪之設計與製造技術已有長足的進展，但在某些應用場合，仍有背隙、邊緣接觸、及嚙合衝擊(Meshing impact)等問題存在，研發具有更好之特性的新型齒輪尚屬必要。
　　前人已提出具修整圓弧齒形(Modified circular-arc)之錐狀齒輪，其具有中央部位點接觸、背隙可調與加工容易等優點；但是，其卻仍存有嚙合衝擊的問題。本研究的主要目的在於提出一具雙向修整齒形之新型錐狀齒輪，以期能具有中央部位點接觸、背隙可調與加工容易等優點，又能避免嚙合衝擊的問題。
　　根據共軛曲面理論，本文先建立曲面設計與曲率分析的理論模式，進而據以建立設計參數避免過切範圍、齒印接觸分析、傳動誤差分析及接觸橢圓分析之模式。另外，文中並以實例顯示所提出之新型齒輪對的各種特性，並印證所提出之理論模式的正確性。
　　根據本文研究之成果，所得之具雙向修整齒形錐狀齒輪之參數避免過切範圍，可提供設計者選擇參數值時的重要參考，並由齒印接觸分析與傳動誤差分析之實例，可知其具有背隙可調、避免邊緣接觸、對裝配誤差不敏感與避免嚙合衝擊的特性。

　　Gear mechanisms have been used extensively in various industrial applications, such as gear boxes on vehicles, machine tools, speed-reducers and various transmission systems. Although 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 meshing impact are still exist. The researches on developing innovative gears with better characteristics are still necessary.
　　Among the results of previous researches, conical gears with curvilinear shaped teeth have the advantages of point contact in the middle parts of gear surfaces, adjustable backlash, easy manufacturing and lower sensitivity due to assembly errors. However, problems of meshing impact are still exist. The main purpose of this study is to propose an innovative conical gear with bi-directional modified teeth which has those good characteristics but without meshing impact.
　　Based on theory of conjugate surfaces, the models for the surface design and curvature analysis of the gear are developed; consequently, the methodology to determine the ranges of design parameters for avoiding undercutting of the gear is proposed. Design examples are included, and the models developed are applied to demonstrate various characteristics of the gears, and to verify the correctness of the models developed in this study.
　　Based on the results of this study, the ranges of design parameters for avoiding undercutting of the conical gears with bi-directional modified teeth can be determined, such that the spending-time for the design of the gear can be shorten. It is shown by the results of tooth contact analysis and transmission error analysis, that the proposed innovative conical gear pair is capable of avoiding edge contact and meshing impact, and they have the advantages of backlash can be adjusted and lower sensitivity due to assembly errors.

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