臺灣博碩士論文加值系統

不同預蹲姿勢對跳躍表現之生物力學分析
指導教授：翁梓林 博士
研 究 生：古智文
摘要
本研究主要目的在探討不同預蹲姿勢（膝關節70、90、110、130、150度）對垂直跳表現之下肢段運動學、動力學及肌電參數的變化。受試對象為國立台北教育大學體育系男生十名，平均年齡、身高、體重分別為18.7 0.67歲，172.8 6.09cm， 65.4 3.89kg。實驗儀器以一部Mega speed高速攝影機（100hz）、AMTI測力板（1000hz）及Biovision 肌電系統（1000hz）及電子關節角度計（1000hz）同步擷取受試者執行不同膝關節角度垂直跳表現之下肢運動學、動力學及肌電參數。運動學參數透過高速攝影機拍攝，所得之影片以APAS軟體剪輯及直接線性轉換（DLT），得到關節角位移、角（加）速度及重心（加）速度等參數。動力學與肌電訊號參數以測力板及Biovision 肌電系統所得之訊號經放大器及低通率波（10hz）用DAZYLab6.0軟體進行量化分析得到地面反作用力量值、衝量值與IEMG。三者參數比較方面，採用SPSS 10.0統計軟體，以重複量數單因子變異數分析比較不同預蹲姿勢跳躍所得之參數是否達到顯著差異，若有顯著差異(P＜.05)，則以LSD法考驗其事後比較。本實驗顯著水準訂為α=.05。本研究結果發現：
一、 不同預蹲姿勢垂直跳表現以膝關節預蹲角度在130、150度時有最大的跳躍高度（p<.05）。
二、 當膝關節預蹲角度為90度時髖關節有最大角速度表現（p<.05）；膝與踝關節的最大角速度表現在預蹲角度為130度時最大（p<.05）。最大角加速度方面髖膝踝關節角加速度隨預蹲角度的增加有增加之趨勢。
三、 重心初速度與最大加速度皆隨預蹲角度的增加而增加，在膝關節預蹲150度時最大（p<.05）。
四、 最大地面反作用力隨預蹲角度增加而增加並在預蹲角度為150度時最大（p<.05）；衝量亦隨預蹲角度增加而增加在130度時最大（p<.05）；勁度則隨角度的增加而減小，70度時有最佳表現（p<.05）。
五、 不同預蹲姿勢垂直跳其作用肌群IEMG皆大於拮抗肌群（p<.05）；股直肌IEMG在預蹲130度有最佳表現；脛骨前肌IEMG在預蹲90度時有最佳表現（p<.05）。
將以上結果於討論後得到以下結論：膝關節預蹲角度在130、150度時會有最佳垂直跳躍高度，因在此角度具有最佳的重心初速度與最大重心加速度表現，並有最大地反作用力及衝量值以及最好的肌肉徴募動員與利用效率。

The Biomechanics Analysis of Different Postures in Prepared-Squatting to Jumping Performances

Adviser: Wong Tzi-Lin Ph.D.
Graduate Student: Gu Chi-Wen

Abstract
The purpose of this study was primarily investigated different prepared-squatting postures (knee joint, 70, 90, 110, 130, 150 degrees), towards to the vertical jump performances of lower limb kinematics, dynamics, myoelectric parameters changes. The testees of this study were ten male students from the Department of Physical Education of National Taipei Education University with the average age of 18.7 0.67yr, height of 172.8 6.09cm and weight of 65.4 3.89kg. A Mega speed video camera (100hz), AMTI force plate (1000hz), and Biovision myoelectric system (1000hz), and the electric knee joint meter (1000hz) were used as the experiement equipment of this study which could simulataneously gather data from all the testees with different joint knee angles, the lower limb kinematics, dynamics, myoelectric parameters changes. The kinematics parameters were photographed from high-speed video camera, and then the file received has being edited and rearranged by the APAS software, and being directly linear transformed (DLT), in order to get parameters of the joint angle displacement, angle (acceleration) velocity and the velocity (acceleration) of gravity. Dynamics and myoelectric signal parameters were obtained from the force plate and Biovision myoelectric system signals through the amplifier and low-pass filter (10hz), with conducting the quantitative analysis with using the DASYLab 6.0 software to get the ground reaction force value , impulse vlaue, and IEMG. In comparison with the three types of parameters, the SPSS 10.0 statistic software were used in this study together with the analytic method of the Repeated Measures of ANOVA, hence to compare different parameters that obtained from the prepared-squatting postures before jumping, to see if they reached the significant difference or not. If there were significant differences (P<0.05) between them, which should be applied the LSD (least significant difference) to test their post-hoc comparison. The significant level of this study was set at α=0.05. In addition, the results of this study were shown as belows:

1. In terms of the performance of different prepared-squatting vertical postures, which showed the maximum jumping height when the knee joint angle was at 130 and 150 degress (p<.05).
2. When the prepared-squatting knee joint angle was at 90 degrees, the hip joint reached its maximum angle velocity (p<.05); and when the prepared-squatting knee joint angle was at 130 degrees, the knee joint and ankle reached their maximum angle velocity (p<.05). In terms of the maximum angle acceleration, which showed the trend of increasing prepared-squatting angle would increase the angle acceleration in hip joint, knee joint and ankle.
3. Initial velocity of center-of-gravity and the maximum acceleration that all increased with the increasing prepared-squatting knee joint angle, which showed the maximum value when the prepared-squatting knee joint angle was at 150 degrees (p<.05).
4. The maximum ground reaction force increased with the increasing prepared-squatting knee joint angle and reached its maximum value when the prepared-squatting knee joint angle was at 150 degrees (p<0.05); Impulse was aslo increased with the increasing prepared-squatting knee joint angle too, which reached its maximum value when the prepared-squatting knee joint angle was at 130 degrees (p<0.05); and the stiffness decreased with the increasing prepared-squatting knee joint angle which showed its best performance when the prepared-squatting angle was at 70 degrees (p<0.05).
5. In terms of different prepared-squatting postures for vertical jump, the functioning muscle groups IEMG were all greater than the opposing muscle groups (p<0.05); Rectus Femoris IEMG showed the best performance when the prepared-squatting knee joint angle was at 130 degrees; and Tibialis Anterior Muscle IEMG showed the best performance when the prepared-squatting knee joint angle was at 90 degrees (p<0.05).

To conclude all the above results after discussions, the below conclusions were obtained: when the prepared-squatting knee joint angle was at 130 and 150 degrees that showed the best vertical jump height. Therefore, this angle would have the best performance of initial volecity of center-of-gravitity and the maximum acceleration of center-of-gravitity, as well as the best ground reaction force, impulse value and the best muscle collections and usage efficacy.

目 次
中文摘要 Ⅰ
英文摘要 Ⅲ
謝誌 Ⅴ
目次 Ⅵ
表次 Ⅷ
圖次 Ⅸ
壹、緒論
一、前言 1
二、研究背景 3
三、研究目的 6
四、研究範圍 7
五、名詞操作性定義 8
貳、文獻探討
一、垂直跳之運動學相關文獻 10
二、垂直跳之動力學相關文獻 21
三、垂直跳之肌電相關文獻 27
四、文獻總結 31
參、研究方法與步驟
一、研究對象 32
二、實驗時間與地點 32
三、實驗儀器與工具 33
四、實驗方法與步驟 37
五、資料收集與處理 46
六、統計方法 48

肆、結果與討論
一、運動學參數分析 49
二、動力學參數分析 60
三、肌電參數分析 66
四、綜合討論 69
伍、結論與建議
一、結論 71
二、建議 71
參考文獻
一、中文部分 72
二、英文部分 76
附錄
附錄一、受試者須知及同意書 82
附錄二、不同預蹲姿勢與跳躍高度事後比較表 83
附錄三、不同預蹲姿勢與髖膝踝關節最大角速度事後比較表 84
附錄四、不同預蹲姿勢與髖膝踝關節最大角加速度事後比較表 87
附錄五、不同預蹲姿勢與重心最大速度事後比較表 90
附錄六、不同預蹲姿勢與重心最大加速度事後比較表 91
附錄七、不同預蹲姿勢與最大地面反作用力事後比較表 92
附錄八、不同預蹲姿勢與衝量事後比較表 93
附錄九、不同預蹲姿勢與作用時間事後比較表 94
附錄十、不同預蹲姿勢與勁度事後比較表 95
附錄十一、不同預蹲角度離心末期力量事後比較表 96
附錄十二、不同預蹲姿勢之股直肌與脛骨前肌之IEMG事後比較表 97

表 次
表一、受試者基本資料表 32
表二、測力板精確度誤差表 41
表三、表面肌電圖電極片黏貼的位置 43
表四、不同預蹲角度與重心離地高度變化統計摘要表 50
表五、不同預蹲角度與髖、膝、踝關節最大角速度變化統計摘要表 52
表六、不同預蹲角度與髖、膝、踝關節最大角加速度變化統計摘要表 55
表七、不同預蹲角度與重心初速度及最大速度變化統計摘要表 57
表八、不同預蹲角度與重心最大加速度變化統計摘要表 59
表九、不同預蹲角度與最大地面反作用力變化統計摘要表 60
表十、不同預蹲角度與衝量變化統計摘要表 62
表十一、不同預蹲角度離心末期力量與勁度變化統計摘要表 64
表十二、不同預蹲角度蹬伸期之標準化IEMG變化統計摘要表 66


圖 次
圖一、垂直跳動作分期示意圖 8
圖二、APAS影像動作分析軟體 34
圖三、電子關節角度計及相關器材 34
圖四、高速攝影機和同步器 35
圖五、測力板及相關器材 35
圖六、表面肌電及相關器材 36
圖七、實驗場地與儀器布置圖 39
圖八、參考架 42
圖九、四條肌群黏貼位置圖 44
圖十、實驗流程圖 45
圖十一、不同預蹲角度重心位置變化圖 50
圖十二、預蹲角度130度時之髖、膝、踝關節角速度變化圖 53
圖十三、不同預蹲角度的膝關節角速度變化圖 54
圖十四、不同預蹲角度髖關節角加速度變化圖 56
圖十五、不同預蹲角度膝關節角加速度變化圖 56
圖十六、不同預蹲角度重心速度變化圖 58
圖十七、不同預蹲角度重心加速度變化圖 59
圖十八、不同預蹲角度地面反作用力作用情形 61
圖十九、不同預蹲角度蹬伸期作用時間變化 63
圖廿、膝關節預蹲130度時各肌群肌電訊號變化圖 68

參考文獻
中文部分
王令儀（2003）。不同型態蹲踞垂直跳下肢生物力學研究。未出版博士論文，國立台灣師範大學，台北市。
王金成、蘇榮基（1991）。垂直跳地面反作用力的探討。國立體育學院論叢，1（3），51-58。
王順正（1992）。垂直跳動力測驗的探討。中華民國大專院校體育總會81年度體育學術研討會專刊，339-347 。
王斌、何智美、虞重干（1998）。排球運動中滯空技術的生物力學分析。上海體育學報，22(1)，25-29。
王興林（1997）。跳躍運動員起跳過程的肌肉工作方式與專項力量訓練。中國體育科技，33（4），60-62。
史世民（2004）。應用類神經網路以地面反作用力參數推估兩種垂直跳之下肢關節力矩。未出版碩士論文，國立體育學院，桃園。
朱國生（2000）。不同膝角靜態蹲跳的生物力學研究。浙江體育科學，22（6），44-46。
呂香珠（1991）。垂直跳-簡而易行的爆發力測驗。國教輔導，30（6），20-25 。
李毅均(1993)。男排三種扣球技術的運動學比較分析。西安體育學報，10（4），38-42。
孟站領、張慶來（2004）。膝關節屈伸肌力矩、關節角度對下蹲跳高度影響程度的實驗研究。浙江體育科學，3（26），100-103。
林正常（1996）。運動生理學實驗指引（增訂三版）。台北：師大書苑。
林政東（2000）。兩種不同牽張幅度深跳動作的生物力學要素與肌電現象之分析。未出版碩士論文，國立體育學院，桃園。
林順萍、陳俊忠（1993）。田徑訓練對國小六年級學生神經傳導速度、動作時間、敏捷性及瞬發力之影響。國立體育學院論叢，3（2），171-189。
林嘉鴻（2005）。不同膝關節預蹲角度魚躍起跳動作之下肢段生物力學特徵探討。未出版碩士論文，國立台北師院，台北市。
林輝雄(1990)。台灣省中小學生球類體能訓練手冊。台灣省政府主編，71。
洪彰岑、莊榮仁、劉宇（1997）。直膝與屈膝垂直跳的生物力學分析比較。大專體育，29，105-111。
崔治平、劉宇（1998）。測力板之垂直跳實驗分析與應用。文化體育，14，97-106 。
張恩崇（2001）。我國優秀三級男子排球選手四號位強攻扣球運動學分析。未出版碩士論文，國立體育學院，桃園。
張華(1997)。排球強攻扣球的新特點。成都體育學院學報，23（3），33-36。
張資榮（1980）。排球正面攻擊之起跳動力研究。未出版碩士論文，國立台灣師範大學，台北市。
許樹淵（1987）。4~20歲男女生瞬發力相關發展研究。體育學報，9，71-79。
陳太正（1977）。垂直跳的力學分析。國立台灣師範大學體育研究所集刊，4。
陳定雄（1989）。足球運動訓練處方。台中：林家。
陳重佑（2004）。以獲取運動速度的最大衝量原理探討垂直跳動作的擺臂作用效果。國立臺灣體育學院學報，14（15），1-15
程峻（2003）。穿鞋與赤足在沙地及硬地上垂直跳之生物力學分析。未出版碩士論文，國立體育學院，桃園。
覃素莉（1993）。垂直跳技術動力學分析。中華排球，60，96-100。
黃志剛、王煜（2000）。不同膝角半蹲跳的生物力學實驗研究。酉安体育學院學報，17（1），89-91。
詹清泉（1978）。排球扣球跳躍動作之分析。中華排球，5（4），97-99。
趙國斌、黃長福（1994）。排球前後排扣球之運動學分析。體育學報，17，243-254。
鄭道隆（1993）。南榮工商專校足球隊員在不同位置的人體測量及基本能力之比較研究。台南：漢明。
蕭乃升（1994）。垂直跳起跳期膝、踝關節聯合運動之研究。未出版碩士論文，國立台灣師範大學，台北市。
賴永成、洪得明、吳福明（1997）。排球長攻及快攻扣球之運動學分析。國立體育學院論叢，8（1），243-255。
謝伸裕譯（1994）。Joseph E. D.著。活體解剖學。台北：力大。
鍾寶弘（2000a）。垂直跳之肌電圖分析。2000年運動生物力學應用與展望研討會論文集，54- 55。
鍾寶弘（2000b）。垂直跳與跨步跳之生物力學分析比較。未出版碩士論文，國立體育學院，桃園。
鍾寶弘、相子元（2000）。垂直跳表現好壞之力學因素分析。國立體育學院論叢，11(1)，163-181。
羅宏仁（1997）。垂直跳擺臂動作之生物力學分析。未出版碩士論文，文化大學，台北。
蘇耿賦（1995）。敏捷性與爆發力間相關之探討。台灣體育，79，48-54。


英文部分
Aragon- Vargas, L. F. & Gross, M. M. (1997). Kinesiological Factorsin Vertical Jump Performance: Differences Within Individuals. Journal of Applied Biomechanics, 13 (1), 45-65.
Aragon- Vargas, L. F. (2000). Evaluation of four vertical jump tests: methodology, reliability, validity, and accuracy. Measurement in physical education and exercise science, 4 (4), 215-228.
Arampatzis, A., Schade, F., Walsh, M., & Brüggemann, G. P. (2001). Influence of leg stiffness and its effect on myodynamic jumping performance. Journal of Electromyography and Kinesiology, 11, 355-364.
Bishop, E. J., & Perez, C. M. (2004). Segmental and Kinetic Contributions in Vertical Jumps Performed With and Without an Arm Swing. Research Quarterly for Exercise & Sport, 75(3), 216-231.
Bobbert, M. F., & Casius, L. J. (2005). Is the effect of a countermovement on jump height due to active state development? Medicine and science in sports and exercise, 37 (3), 440-446.
Bobbert, M. F., & van Ingen Schenau, G. J. (1988). Coordination in vertical jumping. Journal of Biomechanics, 21(3), 249-262.
Bobbert, M. F., Gerritsen, K.G. M., Litjens, M.C.A., & van Soest, A. J. (1996). Why is countermovement jump height greater than squat jump height? Medicine and science in sports and exercise , 28 (11), 1402-1412.
Bobbert, M. F., & van Soest, A. J. (1994). Effects of muscle strengthening on vertical jump height: a simulation study. Medicine and science in sports and exercise, 26 (8), 1012-1020.
Bosco, C., Belli, A., Astrua, M., Tihanyi, J., Pozzo, R., & Tranquili, C. (1995). A dynamometer for evaluation of dynamic muscle work. European Journ of Applied Physiology .70 (5), 379-386.
Davies, B. N., & Jones, K. G. (1993). An analysis of the performance of male student in vertical and standing long jump tests and the contribution of arm swinging. Journal of Human Movement Studies, 24, 25-38.
de Graaf, J. B., Bobbert, M. F., Tetteroo,W. E., & van Ingen Schenau, G. J. (1987). Mechanical out put about the ankle in countermovement jump and jumps with extended knee. Human Movement Science , 6, 333-347.
de Luca, C. J. (1997). The Use of Surface Electromyography in Biomechanics. Journal of Applied Biomechanics, 13, 135-163.
Elvira, J. L. L., Rodriguez, I. G., Riera, M. M., & Jodar, X. A. (2001). Comparative study of the reliability of three jump tests with two measurement systems. Journal of Human Movement Studies, 41(5), 369-383.
Feltner, M.E., Fraschetti, D.J., & Crisp, R.J. (1999). Upper extremity augmentation of lower extremity kinetics during countermovement vertical jumps. Journal of Sports Sciences, 17(6), 449-467.
Gallahue, D. L., & Ozmun, J. C. (1998). Understanding motor development: Infants, children, adolescent, adults (4th ed.). Boston : WCB/McGraw-Hill.
Gollhofer, A., Schmidtbleicher, D., & Dietz, V. (1984). Regulation of musclestiffness in human locomotion. International Journal of Sportsmedicine. 5, 156-159.
Harman, E. A., Rosenstein, M. T., Frykman, P. N., & Rosenstein, R. M. (1990). The effects of arms and countermovement to vertical jumping. Medicine and Science in Sports and Exercise, 22, 825-833.
Henry, C. (1984). Mechanical analysis of the initial velocity in the standing board jump and in the sergeant jump. master thesis, University of Iowa.
Horita T., Komi, P. V., Nicol, C., & Kyröläinen, H. (2002). Interaction between pre-landing activities and stiffness regulation of the knee joint musculoskeletal system in the drop jump: implications to performance. European journal of applied physiology, 88 (1-2), 76-84.
Horita, T., Kitamura, K., & Kohno, N. (1991). Body configuration and joint moment analysis during standing long jump in 6-yr-old children and adult males. Medicine and science in sports and exercise, 23(9), 1068-1077.
Hubley, C. L., & Wells, R. P. (1983). A work-energy approach to determine individual joint contributions to vertical jump performance. European Journal of Applied Physiology, 50, 247-254.
Hudson, J.L. (1986). Coordination of segments in the vertical jump. Medicine and science in sports and exercise, 18 (2), 242-251.
Hunebelle, G., & Darmoiseau, J. (1973). Relation between performance in high-jump and graph of impulsion. Medicine and sports, 8(3), 417-425.
Jensen, J.L., & Phillips, S.J. (1991). Variations on The Vertical Jump: Individual Adaptations to Changing Task Demands. Journal of Motor Behavior, 23(1), 63-74.
Jocobs, R., & van Ingen Schenau, G.J. (1996). Intermuscular coordination inasports push-off. Journal of biomechanics, 29(4), 513-523.
Komi, P. V. (1973). Relationship between muscle tension, EMG and velocity of contraction under concentric and eccentric work. New developments in electromyography and clinical neurophysiology, 1, 596-606.
Komi, P. V., Kaneko, M., & Aura, O. (1987). EMG Active of The Leg Extensor Muscles with Special Reference to Mechanical Efficiencyin Concentricand Eccentric Exercise. International Journal of Sports Medicine, 8, 22-29.
Kubo K., Tsunoda N., Kanehisa H., & Fukunaga, T. (2004). Activation of agonist and antagonist muscles at different joint angles during maximal isometric efforts. European journal of applied physiolog, 91(2-3), 349-352.
Kyrolainen, H., Oksanen, P., Komi, P.V., & Aura, O. (1990). Estimation of errors in mechanical efficiency. European journal of applied physiology and occupational physiology , 61 (5), 473-478.
Lees, A., Vanrenterghem, J., & de Clercq, D. (2004). Understanding how an arm swing enhances performance in the vertical jump. Journal of Biomechanics, 37(12), 19-29.
Lees, A., Vanrenterghem, J., & de Clercq, D. (2006). The energetics and benefit of an arm swing in submaximal and maximal vertical jump performance. Journal of Sports Sciences, 24 (1), 51-57.
Li, L., Dennis, L., Janene, G., & Joseph, M. (2002). The function of gastrocnemius as a knee flexor at selected knee and ankle angles. Journal of Electromyography & Kinesiology, 12( 5), 385-391.
Luhtanen, P., & Komi, P.V. (1978). Segmental contribution to force in vertical jump. European Journal of Applied Physiology, 38, 181-188.
Lynn, S. M. (1996). Scientific rationale and physiological basis for the use of closed kinetic chain exercise in the lower extremity. Journal of Sport Rehabilitation, 5, 2-12.
Malliou, P., Ispirlidis, I., Beneka, A., Taxildaris, K., & Godolias, G. (2003). Vertical jump and knee extensors isokinetic performance in professional soccer players related to the phase of the training period. Isokinetics and exercise science, 11 (3), 165-169.
Marginson, V., & Eston, R. (2001). The relationship between torque and joint angle during knee extension in boys and men. Journal of sports sciences, 19 (11), 875-881.
Mc Coy, B. K. (1997). Role of the lower leg in determining vertical jump height. Eugene, Or. : Microform Publications, University of Oregon.
McHugh M.P., & Hogan D.E. (2004) . Effect of knee flexion angle on active joint stiffness. Acta Physiologica Scandinavica, 180(3), 249-255.
McMahon, T. A. & Cheng, G. C. (1990). The mechanics of running: how does stiffness couple with speed? Journal Biomechanics, 23, Suppl.1:65-78.
Miller, D. I., & Nelson, R. C. (1973). The biomechanics of sport. Philadelphia : Lea and Febiger.
Moritani, T., Muramatsu, S., & Muro, M. (1988 ). Activity of motor units during concentric and eccentric contractions. Journal of Physiology Medicine, 66, 338-350.
Muraki, Y. A., Michiyoshi, Y. T., & Koyama, H. (2005). Mechanical properties of the take-off leg as a support mechanism in the long jump. Sports Biomechanics, 1(4), 1-15.
Nagano, A., & Fukashiro, S. (2000b). Biomechanical comparison of the role of bi-articular rectus femoris in standing broad jump and vertical jump. Japanese journal of biomechanics in sports and exercise, 4 (1), 8-15.
Nagano, A., & Fukashiro, S. (2000a). Relationships between mechanical output from individual joints and jump height in sub-maximal to maximal effort vertical jumps. Japanese journal of biomechanics in sports and exercise, 4 (1), 16-20.
Nigg, B. M., & Herzog, W. (1994). Biomechanics of the Musculo-Skeletal System, New York, John Wiley & Sons, 308-336.
Rack, P. M. H., & Westbury, D. R. (1974). The short range stiffness of active mammalian muscle and its effect on mechanical properties. Journal of Physiology, 240 , 331-350.
Ridderikhoff, A., Batelaan, J. H., & Borrert, M. F. (1999). Jumping for distance: control of the external force in squat jumps. Medicine and science in sports and exercise , 31(8), 1196-1204.
Rodacki, A. L, Fowler, N. E., and Bennett, S. J. (2002). Vertical jump coordination: Fatigue effect. Medicine & Science in Sports & Exercise, 34(1), 105-116.
Rodacki, A. L. F. (2002). The specificity of two training programmes on vertical jump coordination. Revista Brasileira de biomecanics, 3 (4), 27-35.
Rodger, K. L., & Berger, R. A. (1974). Motor-unitinvolvement and tension during maximun, voluntary concentric, eccentric and isometric contractions of the elbow flexors. Medicine Science and Sports , 6, 253-259.
Stefanyshyn, D. J., & Nigg, B. M. (1998). Contribution of the lower extremity joints to mechanical energy in running vertical jumps and running long jumps. Journal of sports sciences (London), 16 (2). 177-186.
Tomioka, M., Owings, T. M., & Grabiner, M. D. (2001). Lower extremity strength & coordination are independent contributors to maximum vertical jump height. Journal of applied biomechanics, 17 (3), 181-187.
van Ingen Schenau, G. J. (1989). From rotation to translation: Constraints of muti-joint movements and the unique action bi-articular muscles. Human Movement Science, 8(4), 301-337.
van Soest, A. J., Roebroeck, M. E., Bobbert, M .F., Huijing, P. A., & van Ingen Schenau, G. J. (1985). A comparison of one-legged and two-legged countermovement jumps. Medicine and Science in Sports and Exercise, 17(6), 635-639.
Vanrenterghem, J., Lees, A., Lenoir, M., Aerts, P., & de Clercq, D. (2004). Performing the vertical jump: Movement adaptations for submaximal jumping. Human Movement Science, 22 (6) , 713-728.
Viitasalo, J. T., & Bosco, C. (1982). Electromechanical behavior of human muscles in vertical jumps. European journal of applied physiology and occupational physiology, 48 (2) , 253-261.
Wang, L. I., Lin, D. C., & Huang, C. (2004). Age effect on jumping techniques and lower limb stiffness during vertical jump. Research in Sports Medicine, 12(3), 1-23.
Winter, D. A. (1979). Biomechanics of Human Movement. John Wiely & Sons, Inc.　Zatsiorsky, V. M. (1995). Science and Practice of Strength Training.