諧波齒輪在減速機構中廣泛應用，替代從前笨重的減速裝置，且具有更高的減速比。這篇論文著重要剛性齒輪之齒形的研究，從固定的減速比中可以求得剛輪與柔輪的齒數，再從繪圖法來初步作圖，接著利用兩齒輪間做剛體運動的接觸條件，到齒輪運動的常微分方程式，最後使用數值法求解來求其接觸點座標，然後再使用MATLAB將整個齒形畫出來。

Widely used in harmonic gear reduction mechanism, instead of the previous heavy
deceleration devices, and has a higher reduction ratio. This paper studies the important
rigid tooth gear, the gear ratio from a fixed number of teeth can be obtained just round the
flexible wheel, and then to a preliminary drawing from the drawing method, and then use
the gear to do between two rigid motions contact conditions , to ordinary differential gear
movement, and finally to seek the use of numerical methods for solving the contact point
coordinates, then use MATLAB entire tooth drawn.

[1] 司光晨，諧波齒輪傳動，國防工業出版社，北京，1978.
[2] 羅驥韡，GeoGebra幾何與代數的美麗邂逅，五南，2013.
[3] 洪維恩，C語言教學手冊，第四版，旗標，2016.
[4] 洪維恩，Matlab程式設計，第二版，旗標，2015.
[5] 陳政逸，齒輪運動分析─使用常微分方程，國立成功大學應用數學所碩士論文，
2011.
[6] 諧波傳動責任有限公司，Harmonic Drive LLC：
http://www.harmonicdrive.net/
[7] 教育部，剛體之平面運動學，取自教育部高職教師進修教學網站：
http://elearning.stut.edu.tw/mechanical/Dynamics/ch16/main16-1.htm
[8] Nagle, R. Kent., Fundamentals of fidderential equations, Pearson Education, 8th, 2012.
[9] C.F., Gerald, P.O., Applied numerical analysis, Wheatly, 6th edition, 1999.