一直以來，在對投手的訓練過程中，教練大部分只能透過肉眼或是自身經
驗來教導球員。本論文提出透過將投手的數據科學化，利用演算法計算出量化
的數據與分析幫助投手訓練。我們希望能提供投擲過程中的投球參數，作為對
於投手健康保護的關鍵。
在這篇論文中，透過應用於慣性測量單元的演算法，能提供投手許多投球
參數包括手臂加速時間、揮臂速度、手臂加速過程的三維軌跡、出手最大球速
和平均球速。
在驗證的實驗中，我們是與國立清華大學運動科學系合作完成，會利用高
速攝影機並透過影像分析軟體，將得到的結果作為標準數據，也會利用測速槍
來進行球速的驗證。對於手臂加速時間，透過影像分析軟體與計算結果進行比
較，此結果的誤差約為百分之3.56，根據相關研究，手臂加速時間所提供的資
訊，能為投手達到提升球速和手肘健康保護的作用。對於揮臂速度而言，誤差
約為百分之8.14，揮臂速度的資訊能提供投手觀測投球過程的各位置手臂揮動
速度。關於手臂加速過程中的三維軌跡，此結果的均方根誤差約為0.094 公
尺，誤差為百分之10.09，實驗之下的平均互相關係數約為0.801，重建手臂加
速過程的三維軌跡可以幫助投手在訓練過程中改善投球動作。對於出手最大球
速而言，誤差為百分之3.98，出手最大球速可以最直觀的衡量投手能力。對於
平均球速而言，誤差為百分之4.82，平均球速能夠提供投手出手與捕手接球瞬
間的速度變化。
在本論文中，我們提供了投擲過程的參數，這些參數能夠帶給投手與教練
更直觀的數據，並且透過這些量化的數據可以幫助投手在各方面自我提升和避
免投手受傷。

For a long time, most coaches only train the players through their eyes or own experience
in the training process of pitchers. This thesis proposes to design algorithms to calculate
quantitative data during pitching and analysis to train through scientific data. We hope to
provide parameters during pitching as the key to the health protection of pitchers.
In this thesis, algorithms based on inertial measurement unit (IMU) sensors can provide
many pitchers’ pitching parameters, including the time of arm acceleration phase, swing velocity,
3D trajectory during arm swing, maximum ball velocity, and average ball velocity.
We cooperated with the Department of Kinesiology of National Tsing Hua University for
the verification experiments. The calculated results of high-speed cameras and image analysis
software are regarded as the ground truth. For the time of arm acceleration phase, the error of
this result is about 3.56%. According to the related researches, the time of arm acceleration
phase can improve the maximum ball velocity and protect the health of the pitcher’s elbow.
For swing velocity, the error is about 8.14%. The information of the swing velocity can
provide the pitcher to observe the swing velocity at each position during the pitching process.
For the 3D trajectory during arm swing, the root-mean-square error (RMSE) position error
of the result is about 0.094 meters, the error is 10.09%, and the average cross-correlation
coefficient is about 0.801. Reconstructing 3D trajectory during arm swing can help the pitcher
improve the pitching posture during the training process. For the maximum ball velocity, the
error is 3.98%. The maximum ball velocity can be the most intuitive measure of pitching
ability. For the average ball velocity, the error is 4.82%. The average ball velocity can provide
the pitcher with the velocity change between the moment of release and catch.
In this thesis, we provide the parameters of the pitching process. It can help the pitchers
improve themselves in all aspects and avoid injuries by these quantitative data.

Abstract i
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Related Products and Works 7
2.1 Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 High-Speed Camera . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Rapsodo Pitching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 SKLZ Bullet Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.4 Strike Smart Baseball . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Discussion and Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Algorithms of Pitching Parameters 19
3.1 Functions Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Time of Arm Acceleration Phase . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Swing Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Linear Regression Correction . . . . . . . . . . . . . . . . . . . . . 27
3.4 Trajectory During Arm Swing . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.1 Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.2 Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5 Maximum Ball Velocity Calculation . . . . . . . . . . . . . . . . . . . . . . 31
3.5.1 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.2 Motion Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.6 Average Velocity Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Experiments and Evaluation Results 35
4.1 Experiment Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Experiment Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Error Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.1 RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.2 Percentage Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.3 Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Time of Arm Acceleration Phase . . . . . . . . . . . . . . . . . . . . . . . . 42
4.5 Swing Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.6 Trajectory During Arm Swing . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6.1 Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.6.2 Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6.3 Verification and Implement Results . . . . . . . . . . . . . . . . . . 67
4.7 Maximum Ball Velocity Measurement . . . . . . . . . . . . . . . . . . . . . 93
4.8 Average Ball Velocity Measurement . . . . . . . . . . . . . . . . . . . . . . 95
4.9 Comparison and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5 Conclusions and Future Works 105
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Bibliography 109

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