自輪子被發明以來，行的便利性便大大的提升。而自行車的問世，更使得人類得以不依賴外力而行遍天下。在能源日益枯竭的今日，自行車可說是日益重要。隨著工藝技術的發達，使得動力的運用更為有效率。其中藉由變速系統的運用，使得自行車的運用在各種不同狀況下，變得更為省力與便利。
行星齒輪系由於具有體積小、重量輕及多自由度的特性，廣泛的被運用於各種動力的傳遞系統中。而由於應用行星齒輪系所開發之自行車內變速系統，具有體積小、結構密實、可靠度高等原因，因此廣泛的被運用在高級自行車的變速系統。
本研究之目的，在於藉由行星齒輪系之特性，開發一套多範圍應用之自行車變速系統。並藉由CAE軟體的幫助，在設計過程中不斷的驗證與修正工程設計，最終完成一套包括變速操縱作系統、變速控制系統與內變速器本體所組成之完整的自行車內變速器系統。希望藉由此系統之開發，可以提供產業界一個嶄新的、性能較佳的、並實際可行的解決方案。

Since wheels are invented, the convenience of walking is highly improved for human beings. And, the appearance of the bicycles, furthermore make the mankind not rely on the external power but travel all over the world by oneself. Recently, the energy is exhausted day by day; it goes without saying that the importance of bicycle is increasing.
With the development of the technology of industry, the power can be applied more effectively. By using the changing-speed system, the application of the bicycle under all kinds of states become more convenient and save effort.
Planetary gear trains are commonly used in various transmissions due to the reasons of compact size, lightweight, and multi-degrees of freedom. Due to above reasons and higher reliability, the changing-speed gear hub system of bicycle is using the planetary gear train for quality bicycle.
The purpose of this paper is to design a general changing-speed gear hub system of bicycle with planetary gear train. In the same time, use the CAE programs to help verify and modify the engineering design in design process. Finally, finish a complete changing-speed gear hub system for bicycle including speed-operating system, speed-control device, and changing-speed gear box.
And we wish the development of this changing-speed gear hub system, can offer a brand-new, performance good, and feasible solution for industrial circle.

中文摘要 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ i
英文摘要 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ ii
誌謝 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ iii
目錄 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ iv
表目錄 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ viii
圖目錄 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ x
符號說明 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ xiv
第一章 前言∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 1
1.1 研究動機及目的∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 2
1.2 文獻回顧∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 3
1.3 論文架構∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 4
第二章 專利分析與回顧∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 5
2.1 專利分析∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 5
2.1.1 自行車內變速器本體∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 5
2.1.2 變速操控裝置專利∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 23
第三章 行星齒輪系分析與合成∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 28
3.1 行星齒輪系∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 28
3.2 相對速度法∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 29
3.3 輪系方程式∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 30
3.4 單一迴路行星齒輪系合成∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 32
3.5 雙迴路行星齒輪系合成∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 34
3.6 效率分析∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 36
第四章 內變速器本體運動設計∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 40
4.1 減速比計算∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 40
4.2 輪系耦合∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 41
4.3 耦合案例∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 44
4.3.1 Case I ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 44
4.3.2 Case II ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 45
4.3.3 Case III ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 47
4.3.4 Case IV ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 48
4.4 具增減速之案例∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 49
4.4.1 Case V ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 49
第五章 工程設計∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 51
5.1 設計需求與限制∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 51
5.2 強度分析∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 52
5.3 參考資料∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 52
5.3.1 驅動力公式∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 52
5.3.2 行星齒輪系扭矩公式∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 53
5.3.3 Load Share per Planet ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 54
5.3.4 各車種設定齒數比∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 54
5.4 Shimano 7 速內變速器資料分析∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 54
5.4.1 基本資料∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 55
5.4.2 運動分析∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 56
5.4.3 齒輪相關參數∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 59
5.5 第一代設計∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 60
5.5.1 第一代結構基本資料∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 60
5.5.2 第一代轉速計算∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 61
5.5.3 第一代效率分析∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 64
5.5.4 第一代扭力計算∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 66
5.5.5 第一代與同及品比較說明∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 67
5.5.6 第一代設計完成圖面∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 68
5.5.7 第一代設計成品相片∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 70
5.6 第二代設計∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 71
5.6.1 第二代結構基本資料∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 71
5.6.2 第二代轉速計算∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 72
5.6.3 第二代效率分析∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 74
5.6.4 第二代扭力計算∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 74
5.6.5 第二代電腦模擬∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 75
5.6.6 第二代設計完成圖面∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 77
5.6.7 第二代與第一代性能比較∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 79
第六章 結論及建議∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 81
參考文獻 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 82
簡歷 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 87

1.Johnson, R.C. and Towfigh, K., 1967, ”Creative Design of Epicyclic Gear Trains Using Number Synthesis”,ASME Transactions, Journal of Engineering for Industry , Vol.89, pp.309-314.
2.Buchsbaum, F. and Freudensteine. F., 1970, “Synthesis of Kinematic Structure of Geared Kinematic Chains and other Mechanisms” , Journal of Mechanism, Vol.5, pp.357-393.
3.Freudenatein, F., 1971, ”An Application of Boolean Algebra to the Motion of Planetary Drives”,ASME Transactions, Journal of Engineering for Industry, Vol.93, pp.176-182.
4.Freudenatein, F and Yang A.T., 1972, “kinematic and Statics of a Coupled Epicyclic Spur-Gear Trains”,Mechanism and Machine Theory, Vol., pp.263-275.
5.Freudenatein, F and Longman, R.W. and Chen C.K., 1984,” kinematic Analysis of Robotic Bevel-Gear Trains”, ASME Transcations, Journal of Mechanisms, Transmissions, and Automation in Design, Vol.106, pp.371-375.
6.Tsai, L.W., 1985, “An algorithm for the kinematic analysis of epicyclic gear trains”, Proc. 9th Applied Mechanisms Conf., Kansas City, Missouri, Vol. 1, pp 1-5.
7.Tsai, L.W., 1988, “The Kinematics of Spatial Robotic Bevel-Gear Trains”, IEEE, Journal of Robotic and Automation, Vol.4, No.2, pp.150-156.

8.Hsieh, L.C., Yan, H.S. and Wu, L.I., 1989, “An algorithm for the Automotive kinematic Analysis of Planetary Gear Trains by Fundamental Circuit Method”, Journal of Chinese Socity of Mechanical Engineers, Vol.10, No.2, pp.153-158.
9.Hsu, C.H. and Lam, K.T., 1989,”A New Graph Representation for Automatic Kinematic Analysis of Spur-planetary Gear Trains”,Proceedings of ASME 1989 Design Automation Conference, Montreal September Vol.17-20, pp. 403-408.
10.Tai, L.W., 1987. ”An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Planetary Gear Trains”,ASME Trainsactions, Journal of Mechanisms, Trainsmissions, and Automation in Design. Vol.109, pp.329-336.
11.Tai, L.W. and Lin, C.C., 1989, “ The Creation of Nonfractionated Two-degree-of-freedom Planetary Gear Trains” , ASME Trainsactions, Journal of Mechanisms, Trainsmissions, and Automation in Design. Vol.111, pp.524-529
12.Ravisankar, R. and Mruthyunjaya, T.S., 1985, “Computerized Synthesis of the Structure of Geared Kinematic Chains” ,Mechanism and Machine Theory, Vol.20, pp.367-387.
13.謝龍昌, 2003, 正齒輪限滑差速器之系統化設計, 機械月刊 2003年 9 月, pp 36-64.
14.Macmillan, R.H., 1949, “Epicyclic Gear Efficiencies”,The Engineers, pp.727-728.
15.Macmillan, R.H., 1961,”Power Flow and Loss in Differential Mechanisms”,Journal of Mechanical Engineering Science, Vol.3, No.1, pp.37-41.
16.Yu, D. and Beachley, N., 1985, “On the Mechanical Efficiency of Differential Gearing”,ASME Transactions, Journal of Mechanisms, Transmissions, and Automation in Design, Vol.107, pp.61-67.
17.Mashford, K.J. and Molian, S., 1986, “Efficiency of Compound Gear Trains”, ASME Paper No.86-DET-189.
18.Krstich, A.M., 1987, “Determination of General Equation of Gear Efficiency of Planetary Gear Trains”, International Journal of Vehicle Design, Vol.8, No.3, pp.365-374.
19.Pennestri, E. and Freudenstein, F., 1990,”The Mechanical Efficiency of Planetary Gear Trains”,Proceedings of 1990 ASME Design Technical Conference, DE-Vol-26, pp.71-79.
20.W.E.Harrison., 1918, Combined Variable Speed Gear And Brake Mechanism For Velocipedes., US. Pantent No.1277070.
21.Fichtel & Sachs AG., 1985, Multi-Speed Gear Hub for a Bicycle., US. Patent 4651853.
22.Masashi Nagano., 1991, Self-Contained Change Speed Apparatus for Use on a Bicycle and Having a Planetary Gear Mechanism., US. Patent No. 5273500.
23.Masashi Nagano., 1994, Self-Contained Change Speed Apparatus with Shaped Pawls to Equalize a Shifting Spring Force for a Bicycle., US. Patent No. 5322487.
24.Fichtel & Sachs AG., 1993, Multi-Speed Drive Hub with a Separate Mounting Ring for the Planetary Gearset for a Bicycle., US. Patent No. 5399128.
25.SRAM Deutschland GmbH., 2000, Shifting Device for a Multi-Speed Hub for a Bicycle., US. Patent No. 6478710 B1.
26.Kun Teng Industry Co., Ltd.(Taiwan)., 1999, Multi-Speed Hub for a Bicycle., US. Patent No. 6478710 B1.
27.Fichtel & Sachs AG., 1994, Multi-Speed Hub for a Bicycle., US. Patent No. 5527230.
28.財團法人工業技術研究院., 1997, 自行車內變速機構., 中華民國專利No.330544.
29.財團法人工業技術研究院., 1997, 自行車之變速輪轂., 中華民國專利No.331284.
30.日馳企業股份有限公司., 2003, 內變速器之改良., 中華民國專利No.584128.
31.川飛工業股份有限公司., 1998, 自行車內變速器之變速主體., 中華民國專利 No.392661.
32.川飛工業股份有限公司., 1998, 自行車內變速器之變速控制機構., 中華民國專利 No.360185.
33.劉仁熾., 2000, 自行車內變速器., 中華民國專利 No.360185.
34.Shimano,Inc., 2005, 自行車用內裝變速輪轂, 公開編號 No. 200537044.
35.斯蘭姆公司., 1994, 供腳踏車變速器所用之可轉動的把手式拉線系統, 中華民國專利 No.573662.
36.行政院國家科學委員會., 2000, 一種握把式自行車變速裝置, 中華民國專利 No.448900.
37.行政院國家科學委員會., 1999, 一種握把式自行車變速裝置, 中華民國專利 No.3999594.
38.島野 SHIMANO., 1999, 自行車的扭轉握把換檔控制裝置, 中華民國專利 No.580473.
39.島野 SHIMANO., 換檔控制裝置, 中華民國專利申請中.
40.勁準股份有限公司., 腳踏車用的握把式變速桿, 專利公告編號 No. 274270.
41.L.W. Tsai, & C.C. Lin, 1989, “The Creation of Non-Fractionated Two-Degree-of-Freedom Planetary Gear Trains”, ASME Transactions, Journal of Mechanisms, Transmission, and Transaction in Design, Vol.3, pp 524-529.
42.H.S. Yan, & L.C. Hsieh, 1994, “Conceptual design of gear differentials for automotive vehicles”, ASME Transactions, Journal of Mechanical Design, Vol.116, pp 565-570.
43.G.H. Martin & Mcgraw-Hill., 1982, “Kinematics and Dynamics of Machines”, New York.
44.C.E. Wilson, J.P. Sadler, and W.J., 1983, “Kinematics and Dynamics of Machinery”, Harper & Row Publishers, New York.
45.M.A. Townsed., 1972, “Extension of A Method of Analysis of Planetary Gear Trains,” Mechanism and Machine Theory, Vol.7, pp 21-426.
46.R.J. Willis Jr., 1982, “On the kinematics of the Closed Epicyclic Differential Gears,” ASME Transactions, Journal of Mechanical Design, Vol 104, pp 721-723.
47.H.H. Mabie and C.F.Reinholtz, John Wiley and Sons,., 1987, Mechanisms and Dynamics of Machinery, new York.
48.J.H. Keer and R.J. Ferguson., 1985, “Incremental Transmission Logic: Kinematics of the Quadriratio Stage,” Mechanism and Machine Theory, Vol.20, pp 1-6.
49.F. Freudenstein, 1971, “An application of boolean algebra to the motion of planetary drives”, ASME Transactions, Journal of Engineering for Industry, Vol.93, pp 176-182.
50.F. Freudenstein, & A.T. Yang, 1972, “Kinematics and statics of a coupled epicyclic spur gear train”, Mechanism and Machine Theory, Vol.7, pp 263-275.
51.L.C. Hsieh, H.S. Yan, & L.I. Wu., 1989, “An algorithm for the automotive kinematic analysis of planetary gear trains by fundamental circuit method”, Journal of the Chinese Society of Mechanical Engineers, Vol.10(2), pp 153-158.
52.C.H. Hsu, & K.T. Lam, 1989, “A new graph representation for automatic kinematic analysis of spur-planetary gear trains”, Proc. ASME Design Automation Conf., Montreal, Canada, pp 403-408.
53.謝龍昌, 1993, 輪型車輛差速傳動機構之系統化設計, 國立成功大學機械工程研究所 博士論文。
54.漸開線齒輪行星傳動的設計與製造編委會著., 2004, 漸開線齒輪行星傳動的設計與製造，ISBN 7-111-09832-3.
55.工業技術研究院，自行車實用手冊。
56.齒輪手冊編委會編著, 2000, 齒輪手冊, ISBN 7-111-01624-6.
57.American Gear Manufacturers Association, April 1989, AGMA 908-B89.