一次完整的纖毛運動包含兩種划動運動，一為提供推進力的有效划動運動，另一為復歸纖毛位置的恢復划動運動。根據生物學的描述，使纖毛產生此兩種不相同划動的機制是相同的，卻能產生兩種的運動模式，而這就是引發本研究想要探究的問題。
本研究藉由功能分析法及觀察纖毛特殊的運動形式與機制發展一種仿生纖毛運動機構，其利用拉伸彈簧有彎曲彈性且不會壓縮長度的特性作為仿生纖毛元件，以四連桿機構驅動使拉伸彈簧做預期範圍的擺動運動，同時以繩控制拉伸彈簧頂端至拉伸彈簧底端的距離，使拉伸彈簧做出不對稱的擺動運動，以別有傳統機械方法設計出纖毛的不對稱運動機構。

A complete cilium motion contains two paddling sports; one is effective stroke for providing propelling, the other is recovery stroke for restoring the cilium initial position. According to the description of biology, the mechanisms of the two strokes are the same. That’s the reason why we want to research this phenomenon.
In this thesis, we designed a bionic mechanism with function analysis method and cilium motion. We used extensional spring which has characteristic with bending elasticity and constant length to be our component of mechanism. In processing, we used four-bar linkage to make the extensional spring do anticipatory swing. At the same time, we used rope to limit distance from the top to the bottom of the spring to make it do asymmetric motions unlike traditional designs.

摘要 ................................................................................................................................... i
Abstract ............................................................................................................................. ii
目 錄 ............................................................................................................................. iii
圖 目 錄 .......................................................................................................................... v
表 目 錄 ......................................................................................................................... ix
第一章 緒論 .............................................................................................................. 1
1-1 研究動機與方向 ................................................................................................... 1
1-2 纖毛簡介 ............................................................................................................... 2
1-3 文獻回顧 ............................................................................................................... 7
1-4 論文架構 ............................................................................................................... 8
第二章 現有曲線運動機構 ...................................................................................... 9
2-1 平面連桿機構 ....................................................................................................... 9
2-2 凸輪機構 ............................................................................................................. 12
2-3 齒輪連桿組合機構[16] ...................................................................................... 17
2-4 伺服機構 ............................................................................................................. 19
2-5 小結 ..................................................................................................................... 22
第三章 纖毛運動機構之研究 ................................................................................ 23
3-1 功能分析法[20] .................................................................................................. 23
3-2 纖毛模型 ............................................................................................................. 25
3-3 分解纖毛運動 ..................................................................................................... 26
3-3-1 擺動運動 ..................................................................................................... 26
3-3-2 彎曲運動 ..................................................................................................... 27
3-4 纖毛仿生 ............................................................................................................. 28
3-5 纖毛彎曲控制機制 ............................................................................................. 31
3-6 纖毛運動機構 ..................................................................................................... 33
第四章 纖毛運動機構之設計 ................................................................................ 35
4-1 擺動運動 ............................................................................................................. 36
4-1-1 二分離(限制)位置尺寸設計[13] ................................................................ 36
4-1-2 四桿機構Freudenstein 方程[21] ................................................................ 38
4-2 彎曲運動 ............................................................................................................. 44
4-3 纖毛運動機構 ..................................................................................................... 50
4-4 纖毛運動機構應用 ............................................................................................. 58
4-4-1 水面上機器人 ............................................................................................. 58
4-4-2 水面下機器人 ............................................................................................. 60
第五章 討論與結論 ................................................................................................ 62
5-1 討論 ..................................................................................................................... 62
5-2 結論 ..................................................................................................................... 62
參考文獻 ........................................................................................................................ 64

[1] Scanning electron microscope image of lung trachea epithelium
(http://remf.dartmouth.edu/images/mammalianLungSEM/source/9.html)。
[2] Neil A. Campbell (1990). Biology (2nd ed.)., 141-145. Redwood City, California:
Benjamin/Cummings.
[3] 翟中和（1996）。細胞生物學。北京：高等教育出版社。
[4] Knowles, J. R. (1980). Enzyme-catalyzed phosphoryl transfer reactions. Annual
review of biochemistry, 49(1), 877-919.
[5] Sugino, K., & Naitoh, Y. (1982). Simulated cross-bridge patterns corresponding to
ciliary beating in Paramecium. Nature, 295, 609-611.
[6] Rikmenspoel, R., & Rudd, W. G. (1973). The contractile mechanism in cilia.
Biophysical journal, 13(9), 955-993.
[7] Sugino, K., & Naitoh, Y. (1982). Simulated cross-bridge patterns corresponding to
ciliary beating in Paramecium. Nature, 295, 609-611.
[8] Gueron, S., & Liron, N. (1992). Ciliary motion modeling, and dynamic multicilia
interactions. Biophysical journal, 63(4), 1045-1058.
[9] Gueron, S., & Levit-Gurevich, K. (2001). A three–dimensional model for ciliary
motion based on the internal 9+2 structure. Proceedings of the Royal Society of London.
Series B: Biological Sciences, 268(1467), 599-607.
[10] Dillon, R. H., Fauci, L. J., & Yang, X. (2006). Sperm motility and multiciliary
beating: an integrative mechanical model. Computers and mathematics with
applications, 52(5), 749-758.
[11] 高德祐（2006）。纖毛不對稱運動的模擬。中央大學物理學系學位論文，桃
園縣。
[12] Mitran, S. M. (2007). Metachronal wave formation in a model of pulmonary cilia.
Computers & structures, 85(11), 763-774.
[13] A.S. Hall Jr. (1986). Kinematics and Linkage Design. U.S.A.: Waveland Pr Inc.
[14] 李平雄（2007）。機件原理II。台北：華興書局。
[15] The most famous Japanese "Karakuri" automata that have made 200 years ago.
(http://www.youtube.com/watch?v=i5zYK9FxORI&list=LLnxhTdsu3ZtnAb2wPZcV9
VQ&feature=share&index=50)
[16] 徐錦康（1995）。機械原理。北京：機械工業出版社。
[17] 孫桓、陳作模（1996）機械原理(5 版)。北京：高等教育出版社。
[18] Coros, S., Thomaszewski, B., Noris, G., Sueda, S., Forberg, M., Sumner, R. W., ...
& Bickel, B. (2013). Computational design of mechanical characters. ACM
Transactions on Graphics (TOG), 32(4), 83.
[19] 莊政義（1984）。線性控制系統。台北：中央圖書供應社。
[20] Cross, N. (2008). Engineering design methods: strategies for product design. John
Wiley & Sons.
[21] A. H. Soni (1974). Mechanism Synthesis and Analysis. New York: McGraw-Hill.