旋轉球體轉軸與轉速測量方法之研究

The Measuring Method for the Spin Axis and the Rate of the Rotational Ball

10.5297/ser.200609_8(3).0012

邱永興(Yung-Hsing Chiu)；涂瑞洪(Jui-Hung Tu)

旋轉 ； 轉軸 ； 轉速 ； 垂直平分面 ； rotation ； spin axis ； spin rate ； perpendicular bisecting plane

大專體育學刊

8卷3期（2006 / 09 / 30）

139 - 147

繁體中文;英文

目前為止，國內外極少有相關文獻能夠提出計算自由旋轉球體運動學參數的具體方法，一般僅提及其影響空氣動力學升力甚鉅，或估計或目測觀察，一直缺乏有效實際測量的研究方法。本研究主要目的是藉由拍攝模擬球體表面在空中旋轉的變化情形，應用垂直平分面的數學原理於測量3D旋轉球體的旋轉軸上，發展出一種能夠有效測量出空中自由球體轉速與轉軸的方法，並推估其精確性。藉由使用2台JVC數位攝影機，以120Hz同步進行拍攝，並以APAS動作分析系統將影片3D數位化，計算出球體瞬時旋轉軸與其轉速。研究所得結果如下：本研究利用3D攝影分析配合垂直平分面數學原理，藉由球體表面上任意兩標誌點的位移變化，發展出一種實際量測出空中自由旋轉球體瞬時轉速與轉軸的方法，其精確度之誤差，整體平均SEE%分別為5.2%與1.8%。本研究所提供之方法與結果可做為空氣動力學相關研究測量旋轉轉軸與轉速之重要參考。

Up to the present, there have been few documents providing the actual measuring methods that could calculate the kinematics parameters (KPs) of the free rotational ball. Most studies just mentioned the KPs' influence on aerodynamic lift force, but there was no valid and actual measuring method for research. This study was to develop an effective method for measuring the spin rate and the axis of the free rotational ball, and estimate the accuracy of this method. The variation of the simulated spherical surface that rotated in the sky was taken and the mathematical principle of perpendicular bisecting plane in measuring the spin axis of the three-dimensional rotational ball was applied. The study employed 2 JVC digital cameras with 120 Hz in the course of shooting. Furthermore, the films were digitized with APAS software (Ariel Performance Analysis System) to determine the instantaneous axis of rotation and the spin rate of the ball. The results of the study showed that this study utilized 3-D cinematography analysis and connected with the mathematical principle of perpendicular bisecting plane to develop a kind of method to effectively and actually measure the spin rate and the axis of the free rotational ball in the sky by the displacement changes of any two markers that marked the point on the surface of the sphere. The overall accuracy for SEE% was 5.2% and 1.8% respectively. This study provided the important rotation measurement bases for some relevant studies such as aerodynamics.

1. 邱永興(2006)。碩士論文(碩士論文)。屏東市，國立屏東教育大學體育研究所。
   連結：
2. Asai, T.,Carre, M. J.,Akatsuka, T.,Haake, S. J.(2002).The curve kick of a football I: impact with the foot.Sports Engineering,5,183-192.
3. Bearman, P. W.,Harvey, J. K.(1976).Golf ball aerodynamics.Aeronaut Q,27,112-122.
4. Bray, K.,Kerwin, D. G.(2003).Modeling the flight of a soccer ball in a direct free kick.Journal of Sports Science,21,75-85.
5. Carre, M. J.,Asai, T.,Akatsuka, T.,Haake, S. J.(2002).The curve kick of a football II: Flight though the air.Sports Engineering,5,193-200.
6. Dapena, J.,Harman, E., Miller, A.(1982).Three-dimensional cinematography with control object of unknown shape.Journal of Biomechanics,15(1),11-19.
7. Frohlich, C.(1984).Aerodynamic drag crisis and its possible effect on the flight of baseballs.American Journal of Physics,52(4),325-334.
8. Grant, A. G.,Williams, A. M.,Reilly, T.(1999).Analysis of goals scored in the 1998 World Cup.Journal of Sports Sciences,17,826-827.
9. Haake, S. J.,Chadwick, S. G.,Dignall, R. J.,Goodwill, S.,Rose, P.(2000).Engineering tennis slowing the game down.Sports Engineering,3,131-144.
10. Kreighbaum, E.,Barthels, K. M.(1996).Biomechanics: A qualitative approach for studying human movement.Needham Heights, MA:Simon & Schuster.
11. Lee, A.,Nolan, L.(1998).The biomechanics of soccer: A review.Journal of Sports Science,16,211-234.
12. Levendusky, T. A.,Armstrong, C. W.,Eck, J. S.,Spryropoulous, P.,Jeziorowski, J.,Kugler, L.,T. Reilly(Eds.),A. Lees(Eds.),K. Davids(Eds.),W. J. Murphy(Eds.)(1988).Science and football.London:E & FN Spon.
13. Mehta, R. D.(1985).Aerodynamics of sports balls.Annual Review of Fluid Mechanics,17,151-189.
14. Mehta, R. D.,Pallis, J. M.(2001).Sports ball aerodynamics: Effects of velocity, spin and surface roughness.Proceedings of TMS conference:Materials and Science in Sports,San Diego, CA:
15. Panjabi, M. M.,Goel, V. K.,Walter, S. D.(1982).Errors in kinematic parameters of a planar joint: Guidelines for optimal experimental design.Journal of Biomechanics,15(7),537-544.
16. Shapiro, R.(1978).Direct linear transformation method for three-dimensional cinematography.Research Quarterly,49,197-205.
17. Soudan, K.,Audekercke, R. V.,Martens, M.(1979).Methods, difficulties and inaccuracies in the study of human joint kinematics and pathokinematics by the instant axis concept.12(1),27-33.
18. Watts, R. G.,Ferrer, R.(1987).The lateral force on a spinning sphere: Aerodynamics of a curveball.American Journal of Physics,55,40-44.
19. Winter, D. A.(1990).Biomechanics and motor control of human novement.New York, NY:John Wiley & Sons.
20. Winter, D. A.(1990).Biomechanics and motor control of human movement.New York, NY:John Wiley & Sons.
21. Woltring, H. J.,Huiskes, R.(1983).A statistically motivated approach to instantaneous helical axis estimation from noisy, sampled landmark corrdinates.Biomechanics,9B,274-279.
22. Zernicke, R.,Roberts, E.(1978).Lower extremity forces and torques during systematic variation of non-weight bearing motion.Medicine and Science in Sports,10,21-26.
23. 松本光弘、石井信義、掘田哲爾、山成宣彥、宇野勝(2000)。實戰足球。台北市:聯廣圖書公司。
24. 邱靖華(2000)。足球踢遠與射門分析。中華體育，14(3)，118-128。
25. 劉鎮國(1997)。論足球運動停、踢、傳、基本技術。成大體育研究集刊，3，19-30。

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