超環面行星蝸桿減速器(Toroidal drive)為一行星齒輪系，相較於其他的齒輪傳動裝置如齒輪對及一般行星齒輪系等，其具有高馬力對重量比(High horsepower-to-weight ratio)、共軸結構、較高的減速比、低噪音及高輸入速度等等特色。為了對其特性能有進一步地瞭解，故本文針對其幾何特性，以曲面設計、曲率分析、過切研究與干涉研究等部分作一探討。
本文先利用共軛曲面理論建立其曲面設計與曲率分析模式，並據以建立該減速器決定設計變數避免過切範圍的理論模式；另外，也建立決定其各設計變數避免肋面干涉範圍的模式。文中並針對所建立的各模式與方法進行實例分析，以觀察其曲面與曲率之特性，以及驗證決定設計變數避免過切範圍與避免肋面干涉範圍之方法的正確性與可行性。
根據本文所得的結果可知，相對於過切，超環面行星蝸桿減速器較容易發生肋面干涉的現象。而由設計變數避免肋面干涉範圍的驗證結果可知，本文所建立之決定設計變數避免肋面干涉範圍的可行性，其可供作設計者選定參數值時之重要參考。因此，本文所得成果於學術及應用上均有其參考價值。

Toroidal drives are one type of planetary gear trains. Compared with other ordinary gear mechanisms, they have a number of advantages, such as higher horsepower-to-weight ratio, coaxial configuration, higher speed ratio, lower noise, and higher input speed, etc. The main purpose of this study is to investigate their geometric characteristics, thus their surface design, curvature analysis, and the avoidance of the undercutting and interference are studied.
Models for the surface design and curvature analysis are developed based on conjugate surface theory. Consequently, they are applied to evolve the models for the determination of the ranges of design variables for avoiding undercutting and avoiding rib-surface-interfering. Examples are included to verify the correctness of the models developed and to demonstrate the characteristics of the drives. For the drives, it is found that rib-surface-interfering occurs before undercutting happens.
The feasibility of the model to determine the ranges of design variables for avoiding rib-surface-interfering is verified. It is believed that the results are valuable in both of the academic field and industrial applications.

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