Biomechanical Principles and Applications in Sports (eBook)

Foreword 6
Contents 8
Contributors 10
Part I Equipment Design and Manufacturing 12
1 Ergonomics and Biomechanics: Racquet Sensors for Monitoring Volume of Training and Competition in Tennis 13
1.1 Tennis Overuse Injuries 13
1.2 Loading and Monitoring Training/Competition Volume 14
1.2.1 Upper Extremity Loading in Tennis Strokes 14
1.2.2 Monitoring Training/Competition Volume 17
1.3 Racquet Sensors for Monitoring Training/Competition Volume 18
1.4 The Acute: Chronic Workload Ratio 20
1.4.1 Managing Data with the ACWR 21
1.4.2 Interpretation of the ACWR Data 21
1.5 Future Research 22
References 23
2 Facility Design: “Smart” Facilities Contribute to Advancement of Knowledge and Facilitate Learning 27
2.1 Introduction 27
2.2 An Approach for the Development of Evidence-Based Practices Using “Smart” Facilities 28
2.3 Measurements of Value and Validation of Technology to Support Decision Making 29
2.4 Data Management and Ethical Considerations 29
2.5 Improvements in Human Performance Involves Multiple Factors 31
2.6 Identifying Cause-Effect Principles Affecting Performance 34
2.7 “Smart” Training Environments that Facilitate the Use of Reaction Force as Augmented Feedback 37
2.8 Knowledge of Kinematics During Reaction Force Generation Provides Context Regarding Mechanical Demand During Task Performance 39
2.9 Embedding Force Plates into Indoor and Outdoor Training Environments 40
2.10 Understanding the Control and Dynamics of Task Performance in “Smart” Training Environments 42
2.10.1 Clarifying Cause-Effect Relationships in Horizontal Jumps in a “Smart” Training Environment 43
2.10.2 Testing Hypotheses About Volleyball Block Jump Performance in a “Smart” Training Environment 45
2.11 Considerations When Introducing Augmented Feedback in “Smart” Training Environments 48
2.12 Summary 50
References 50
3 Performance Tracking: A Multimedia Informatics System to Improve Decision Support in Movement Analysis 53
3.1 Introduction 53
3.1.1 The Medical Imaging Informatics Infrastructure 54
3.1.2 The Electronic Patient Record (ePR) Concept 56
3.2 Methodology for Designing and Developing the Multimedia Informatics System 56
3.2.1 Workflow Analysis 57
3.2.2 Data Objects Analysis and Data Model Development 58
3.2.3 Multimedia Informatics System Architecture 59
3.3 Application-Specific Use Case with Results 61
3.3.1 Volleyball Skills Development 61
3.4 Summary and Conclusion 64
References 64
Part II Quantitative Evaluation Methods 65
4 Wind Tunnels: Design Considerations in Wind Tunnel Testing of Cyclists 66
4.1 Introduction 66
4.2 Aerodynamic Drag 68
4.3 Bluff Body Aerodynamics 69
4.4 The Relationship Between Drag Coefficient, Reynolds Number, and the Boundary Layer 70
4.5 Effect of Surface Roughness on Drag 74
4.6 Wind Tunnels 76
4.7 Wind Tunnel Test Goals and Expected Outcomes 77
4.8 The Bike Mount 77
4.9 The Wind Tunnel Balance 80
4.10 Harmonic Oscillation Damping 80
4.11 Yaw Function 80
4.12 Measurement Precision and Control 82
4.13 Balance Shielding 82
4.14 Live Subjects and Mannequins 83
4.15 Wind Speed and Temperature 84
4.16 Wind Tunnel Data Acquisition and Test Protocol 84
4.17 Q Sweep, Linear Regression Analysis, 95% Confidence Intervals, and Sample Size 86
4.18 Frontal Area Measurements 89
4.19 Flow Visualization 89
4.20 Cyclist Communications System 90
4.21 Testing Bike Wheels in the Wind Tunnel 91
4.22 Wind-Averaged Drag Coefficient (“WAD”) 92
4.23 Summary 93
References 93
5 Overview of Numerical Methods: Introduction to Analytical Methods in Sports 96
5.1 A Brief History of Analytics in Sports 96
5.2 Graphs 99
5.3 Probability 103
5.3.1 Applications of Probability in Strategy Development and Assessment 103
5.3.2 Applications of Probability in Game Outcomes 104
5.4 Regression Analysis 104
5.5 Mathematical Programming 110
5.6 Education 114
5.7 Conclusions 115
Exercises 115
Solutions to Exercises 118
References 125
6 Overview of Numerical Methods: Applications of Analytical Methods in Sports 128
6.1 Introduction 128
6.2 Graphs and Sports Problems 129
6.3 Probability and Sports Problems 129
6.3.1 Applications of Probability in Strategy Development and Assessment 130
6.3.2 Applications of Probability in Game Outcomes 131
6.3.3 Applications of Probability in Performance Evaluation 131
6.4 Regression and Sports Problems 132
6.4.1 Applications of Regression to Problems in Sports Economics 133
6.4.2 Applications of Regression to Problems in Performance Evaluation 136
6.4.3 Applications of Regression to Problems in Biomechanics 138
6.5 Mathematical Programming and Sports Problems 139
6.5.1 Applications of Mathematical Programming in Performance Evaluation 139
6.5.2 Applications of Mathematical Programming in Sports Scheduling 141
6.5.3 Applications of Mathematical Programming to Problems in Biomechanics 144
6.6 Conclusions 144
Exercises 145
Solutions to Exercises 149
References 156
7 3D Kinematics: Using Quaternions for Modeling Orientation and Rotations in Biomechanics 164
7.1 Introduction 164
7.2 Mathematical Preliminaries 166
7.2.1 Vectors in Real Three-Dimensional Space 166
7.2.1.1 Inner (Scalar) Product and Vector Norm (Length) 167
7.2.1.2 Vector Product 168
7.2.1.3 Standard Basis 169
7.2.2 Linear Operators and Matrices 172
7.2.2.1 Types of Matrices 173
7.2.3 The Algebraic Eigenvalue Problem 176
7.2.3.1 Characteristic Equation and Eigenvalues 176
7.2.3.2 Eigenvectors 176
7.2.3.3 Modal Matrix and Similarity Transformation 177
7.2.3.4 Complex Eigenvalues and Eigenvectors 177
7.2.4 Change of Coordinates 184
7.3 Modeling the Kinematics of Human Movement 185
7.4 Rotation Matrix 186
7.4.1 Orthogonal Transformations: Direction Cosine Matrix 186
7.4.1.1 Characteristics of Direction Cosine Matrix (DCM) 189
7.4.2 Direction Cosines Matrix Is a Rotation Operation 190
7.4.3 Interpretation of Rotation Matrix 190
7.4.3.1 Changing Description Between Rotated Frames 190
7.4.3.2 A Rotation Operator Acting on a Vector 192
7.4.3.3 Basic Rotations ? 193
7.4.3.4 Changing the Frame in Which Operation Is Defined 194
7.4.3.5 Inverse Transformation 194
7.4.3.6 Successive Rotations 195
7.5 Angle/Axis Parameterization of Rotation Matrix 196
7.5.1 Euler Axis/Angle Parameterization 199
7.5.1.1 Rotation Operation 199
7.5.1.2 Eigenvalue Analysis of RSO(3) 201
7.5.1.3 Euler's Theorem 202
7.5.1.4 Euler's Formula 205
7.5.1.5 Composition Rule for Axis/Angle Parameterization 206
7.6 Quaternion Parameterization 207
7.6.1 Quaternions and Quaternion Operations 207
7.6.1.1 Quaternion Addition 208
7.6.1.2 Quaternion Multiplication 208
7.6.1.3 Conjugate of a Quaternion 209
7.6.1.4 Norm (Absolute Value) of a Criterion 210
7.6.1.5 Inverse of a Quaternion 210
7.6.1.6 Unit Quaternions 212
7.6.2 Modeling Rotation Using Quaternions 214
7.6.2.1 Computation of Euler–Rodrigues Symmetric Parameters 216
7.6.2.2 Successive Rotations 217
7.6.2.3 Rotation Operation of a Vector 218
7.7 Differential Kinematics of Rotational Motion 220
7.7.1 Differential Kinematics Using Rotation Matrix 221
7.7.1.1 Angular Velocity of Successively Rotated Frames 222
7.7.2 Differential Kinematics Using Axis and Angle of Rotation 222
7.7.3 Differential Kinematics Using Quaternions 223
7.7.4 Computation of the Instantaneous Axis of Rotation Between Links 227
7.8 Estimation of Rigid Body Orientation and Interpolation 228
7.8.1 Optimal Orientation: Wahba's Problem 228
7.8.2 The q-Method for the Solution of Wahba 230
7.8.3 Interpolation of Orientations 237
7.8.3.1 Linear Matrix Interpolation: LinMat 238
7.8.3.2 Linear Quaternion Interpolation (Lerp) 239
7.8.3.3 Spherical Linear Quaternion Interpolation (Slerp) 239
References 241
8 Inertial Sensors 243
8.1 Introduction 243
8.2 Sensor Selection 243
8.2.1 Dynamic Range 244
8.2.2 Bandwidth 244
8.2.3 Nonlinearity of the Scale Factor 246
8.2.4 Static Bias 247
8.2.5 Bias Time 247
8.2.6 Bias Instability 247
8.3 Reference Frames 247
8.4 Signal Analysis 248
8.4.1 Sensor Errors Models 248
8.4.2 Basic Analysis 249
8.4.3 Orientation Estimation 250
8.4.3.1 Quaternion Calculation 250
8.4.3.2 Orientation Correction 251
8.4.3.3 Process Definition 253
8.4.3.4 Observation Definition 254
8.4.3.5 The Kalman Loop 255
8.4.3.6 Quaternion Error Correction 256
8.4.3.7 The Feedback Loop 257
References 258
Part III Sports Medicine 259
9 Traumatic Brain Injury: Introduction to Anatomy of the Human Head and Basic Mechanical Principles 260
9.1 Introduction 260
9.1.1 Structure of the Chapter 262
9.2 Morphology, Anatomy, and Histology of the Human Head 262
9.3 Mechanical Properties of the Human Head 267
9.3.1 Qualitative Description 267
9.3.1.1 Elastic Materials 268
9.3.1.2 Newtonian Viscous Fluids 270
9.3.2 Viscoelastic Behavior: A Phenomenological Description 271
9.3.3 Mathematical Formulation of Linear Viscoelastic Theory: A Primer 275
9.3.3.1 Spring-Dashpot Mechanical Models for Linear Viscoelastic Modeling 276
9.3.3.2 Maxwell Element: Creep Response 277
9.3.3.3 Maxwell Element: Stress Relaxation Response 279
9.3.3.4 Voigt Element: Creep and Stress Relaxation Response 280
9.3.3.5 Standard Linear Solid Element: Creep and Stress Relaxation Response 281
9.3.3.6 Boltzmann's Superposition Principle 282
9.4 Dynamic Behavior of Materials 285
9.5 Conclusion 288
References 289
10 Traumatic Brain Injury: Models and Mechanisms of Traumatic Brain Injury 290
10.1 Introduction 291
10.1.1 Structure of the Chapter 292
10.2 Mechanical Properties of the Human Head Tissues: Experimental Data 292
10.2.1 Scalp 293
10.2.2 Skull 293
10.2.2.1 Skull Properties in Tension 294
10.2.2.2 Skull Properties in Compression 294
10.2.3 Meninges 296
10.2.4 Cerebrospinal Fluid 296
10.2.5 Brain 297
10.2.5.1 Brain Tissue Properties in Tension 297
10.2.5.2 Brain Tissue Properties in Compression 300
10.2.5.3 Brain Tissue Properties in Shear 304
10.2.5.4 Brain Tissue Properties Using Non-conventional Tests 306
10.3 Models of TBI 306
10.3.1 Analytical Models of TBI 306
10.3.1.1 Quantitative Information Drawn from “Natural Experiments”: Accidents 308
10.3.1.2 Brain Deformation Quantification: Experimental Efforts 309
10.3.1.3 Experimental Efforts: Physical, In-Silico, In-Vivo, and In-Vitro Models of TBI 310
10.4 Mechanisms of TBI 312
10.4.1 Pathology of TBIs 312
10.4.2 Mechanical Loading Causing TBIs 313
10.5 Conclusion: Discussion—Outlook 315
References 316
Index 321