Stephen J. Thomas is Associate Professor and Chair of the Exercise Science Department at Thomas Jefferson University. His research focuses on anatomic and biomechanical adaptations to stress, particularly in the shoulder and elbow. He is a consultant for the Philadelphia Phillies at the Penn Throwing Clinic and is a Past President of the American Society of Shoulder and Elbow Therapists.

Joseph A. Zeni is Associate Professor at Rutgers University, where he teaches graduate level courses and conducts research within the Rutgers Motion Analysis Laboratory. His current work is focused on using biomechanical feedback to restore normal movement patterns after knee replacement surgery.

David A. Winter (1930-2012) was a Distinguished Professor Emeritus at the University of Waterloo and a Founding Member of the Canadian Society of Biomechanics. He pioneered many important methods and concepts in the study of human movement and balance.

List of Contributors xv Preface xvii Acknowledgments xix About the Companion Website xxi 1 Biomechanics as an Interdiscipline 1Stephen J. Thomas Joseph A. Zeni and David A. Winters 1.0 Introduction 1 1.0.1 Importance of Human Movement Analysis 1 1.0.2 The Interprofessional Team 2 1.1 Measurement Description Analysis and Assessment 2 1.1.1 Measurement Description and Monitoring 3 1.1.2 Analysis 4 1.1.3 Assessment and Interpretation 5 1.2 Biomechanics and its Relationship with Physiology and Anatomy 6 1.3 References 7 2 Signal Processing 8Joseph A. Zeni Stephen J. Thomas and David A. Winters 2.0 Introduction 8 2.1 Auto- and Cross-Correlation Analyses 8 2.1.1 Similarity to the Pearson Correlation 9 2.1.2 Formulae for Auto- and Cross-Correlation Coefficients 10 2.1.3 Four Properties of the Autocorrelation Function 11 2.1.4 Three Properties of the Cross-Correlation Function 14 2.1.5 Importance in Removing the Mean Bias from the Signal 15 2.1.6 Digital Implementation of Auto- and Cross-Correlation Functions 15 2.1.7 Application of Autocorrelations 16 2.1.8 Applications of Cross-Correlations 17 2.2 Frequency Analysis 19 2.2.1 Introduction - Time Domain vs. Frequency Domain 19 2.2.2 Discrete Fourier (Harmonic) Analysis 19 2.2.3 Fast Fourier Transform (FFT) 21 2.2.4 Applications of Spectrum Analyses 22 2.3 Ensemble Averaging of Repetitive Waveforms 29 2.3.1 Examples of Ensemble-Averaged Profiles 31 2.3.2 Normalization of Time Bases to 100% 31 2.3.3 Measure of Average Variability about the Mean Waveform 32 2.4 References 32 3 Kinematics 34Amy L. Lenz 3.0 Historical Development and Complexity of Problem 34 3.1 Kinematic Conventions 35 3.1.1 Absolute Spatial Reference System 35 3.1.2 Total Description of a Body Segment in Space 36 3.2 Direct Measurement Techniques 36 3.2.1 Goniometers 36 3.2.2 Accelerometers 38 3.2.3 Inertial Sensors 39 3.2.4 Special Joint Angle Measuring Systems 40 3.2.5 Electromagnetic Systems 41 3.3 Imaging Measurement Techniques 42 3.3.1 Review of Basic Lens Optics 42 3.3.2 f-Stop Setting and Field of Focus 43 3.3.3 Television Imaging Camera Historical Development 43 3.3.4 Optical Motion Capture 44 3.3.5 Optoelectric Techniques 47 3.3.6 Biplane Fluoroscopy 48 3.3.7 Markerless Systems 51 3.3.8 Summary of Various Kinematic Systems 51 3.4 Clinical Measures of Kinematics 52 3.4.1 2-D Kinematic Apps/Sensors 52 3.4.2 Sensor-Based Systems 52 3.5 Processing of Raw Kinematic Data 52 3.5.1 Nature of Unprocessed Image Data 52 3.5.2 Signal Versus Noise in Kinematic Data 53 3.5.3 Problems of Calculating Velocities and Accelerations 54 3.5.4 Smoothing and Curve Fitting of Data 54 3.5.5 Comparison of Some Smoothing Techniques 60 3.6 Calculation of Other Kinematic Variables 62 3.6.1 Limb-Segment Angles 62 3.6.2 Joint Angles 63 3.6.3 Velocities - Linear and Angular 63 3.6.4 Accelerations - Linear and Angular 63 3.7 Problems Based on Kinematic Data 64 3.8 References 65 4 Anthropometry 67Joseph A. Zeni Stephen J. Thomas and David A. Winters 4.0 Scope of Anthropometry in Movement Biomechanics 67 4.0.1 Segment Dimensions 67 4.1 Density Mass and Inertial Properties 68 4.1.1 Whole-Body Density 68 4.1.2 Segment Densities 69 4.1.3 Segment Mass and Center of Mass 69 4.1.4 Center of Mass of a Multisegment System 72 4.1.5 Mass Moment of Inertia and Radius of Gyration 73 4.1.6 Parallel Axis Theorem 74 4.1.7 Use of Anthropometric Tables and Kinematic Data 75 4.2 Direct Experimental Measures 78 4.2.1 Location of the Anatomical Center of Mass of the Body 79 4.2.2 Calculation of the Mass of a Distal Segment 79 4.2.3 Moment of Inertia of a Distal Segment 80 4.2.4 Joint Axes of Rotation 81 4.3 Muscle Anthropometry 82 4.3.1 Cross-Sectional Area of Muscles 82 4.3.2 Change in Muscle Length During Movement 83 4.3.3 Force per Unit Cross-Sectional Area (Stress) 84 4.3.4 Mechanical Advantage of Muscle 84 4.3.5 Multijoint Muscles 85 4.4 Problems Based on Anthropometric Data 86 4.5 References 87 5 Kinetics: Forces and Moments of Force 89Stephen J. Thomas Joseph A. Zeni and David A. Winters 5.0 Biomechanical Models 89 5.0.1 Link-Segment Model Development 89 5.0.2 Forces Acting on the Link-Segment Model 90 5.0.3 Joint Reaction Forces and Bone-on-Bone Forces 91 5.1 Basic Link-Segment Equations - The Free-Body Diagram 93 5.2 Force Transducers and Force Plates 98 5.2.1 Multidirectional Force Transducers 98 5.2.2 Force Plates 99 5.2.3 Combined Force Plate and Kinematic Data 104 5.2.4 Interpretation of Moment-of-Force Curves 105 5.2.5 Differences Between Center of Mass and Center of Pressure 107 5.2.6 Kinematics and Kinetics of the Inverted Pendulum Model 108 5.3 Bone-on-bone Forces During Dynamic Conditions 110 5.3.1 Indeterminacy in Muscle Force Estimates 110 5.3.2 Example Problem 111 5.4 References 114 6 Mechanical Work Energy and Power 115Joseph A. Zeni Stephen J. Thomas and David A. Winters 6.0 Introduction 115 6.0.1 Mechanical Energy and Work 115 6.0.2 Law of Conservation of Energy 116 6.0.3 Internal Versus External Work 116 6.0.4 Positive Work of Muscles 118 6.0.5 Negative Work of Muscles 118 6.0.6 Muscle Mechanical Power 119 6.0.7 Mechanical Work of Muscles 119 6.0.8 Mechanical Work Done on an External Load 120 6.0.9 Mechanical Energy Transfer Between Segments 122 6.1 Efficiency 123 6.1.1 Causes of Inefficient Movement 124 6.1.2 Summary of Energy Flows 127 6.2 Forms of Energy Storage 128 6.2.1 Energy of a Body Segment and Exchanges of Energy Within the Segment 129 6.2.2 Total Energy of a Multisegment System 132 6.3 Calculation of Internal and External Work 133 6.3.1 Internal Work Calculation 133 6.3.2 External Work Calculation 136 6.4 Power Balances at Joints and Within Segments 136 6.4.1 Energy Transfer via Muscles 137 6.4.2 Power Balance Within Segments 138 6.5 Problems Based on Kinetic and Kinematic Data 141 6.6 References 143 7 Understanding 3D Kinematic and Kinetic Variables 145Thomas Hulcher 7.0 Introduction 145 7.1 Axes Systems 145 7.1.1 Global Reference System 145 7.1.2 Local Reference Systems and Rotation of Axes 146 7.1.3 Other Possible Rotation Sequences 147 7.1.4 Dot and Cross Products 148 7.2 Marker and Anatomical Axes Systems 148 7.2.1 Markerset Design 150 7.2.2 Event Detection Methods for Gait 152 7.2.3 Event Detection Methods for Other Activities 153 7.2.4 Considerations for Applications with Implements 153 7.2.5 Example of a Kinematic Data Set 154 7.3 Determination of Segment Angular Velocities and Accelerations 158 7.4 Kinetic Analysis of Reaction Forces and Moments 162 7.4.1 Newtonian Three-Dimensional Equations of Motion for a Segment 162 7.4.2 Euler's Three-Dimensional Equations of Motion for a Segment 163 7.4.3 Example of a Kinetic Data Set 164 7.4.4 Joint Mechanical Powers 167 7.4.5 Induced Acceleration Analysis 167 7.4.6 Sample Moment and Power Curves 168 7.5 Suggested Further Reading 170 7.6 References 170 8 Muscle Mechanics 171Stephen J. Thomas Joseph A. Zeni and David A. Winters 8.0 Introduction 171 8.0.1 The Motor Unit 171 8.0.2 Recruitment of Motor Units 172 8.0.3 Size Principle 173 8.0.4 Types of Motor Units - Fast- and Slow-Twitch Classification 174 8.0.5 The Muscle Twitch 175 8.0.6 Shape of Graded Contractions 176 8.1 Force-Length Characteristics of Muscles 177 8.1.1 Force-Length Curve of the Contractile Element 177 8.1.2 Influence of Parallel Connective Tissue 178 8.1.3 Series Elastic Tissue 178 8.1.4 In Vivo Force-Length Measures 180 8.2 Force-Velocity Characteristics 181 8.2.1 Concentric Contractions 181 8.2.2 Eccentric Contractions 183 8.2.3 Combination of Length and Velocity Versus Force 183 8.2.4 Combining Muscle Characteristics with Load Characteristics: Equilibrium 184 8.3 Technique to Measure in Vivo Tendon Mechanical Properties 186 8.3.1 Ankle Joint Moment 186 8.3.2 Tendon Mechanical Properties 187 8.4 References 187 9 Kinesiological Electromyography 189Joseph A. Zeni Stephen J. Thomas and David A. Winters 9.0 Introduction 189 9.1 Electrophysiology of Muscle Contraction 189 9.1.1 Motor End Plate 189 9.1.2 Sequence of Chemical Events Leading to a Twitch 190 9.1.3 Generation of a Muscle Action Potential 190 9.1.4 Duration of the Motor Unit Action Potential 192 9.1.5 Detection of Motor Unit Action Potentials from Electromyogram During Graded Contractions 194 9.2 Recording of the Electromyogram 195 9.2.1 Amplifier Gain 196 9.2.2 Input Impedance 196 9.2.3 Frequency Response 197 9.2.4 Common-Mode Rejection 199 9.2.5 Cross-Talk in Surface Electromyograms 202 9.2.6 Recommendations for Surface Electromyogram Reporting and Electrode Placement Procedures 205 9.3 Processing of the Electromyogram 205 9.3.1 Full-Wave Rectification 206 9.3.2 Linear Envelope 207 9.3.3 True Mathematical Integrators 208 9.4 Relationship Between Electromyogram and Biomechanical Variables 208 9.4.1 Electromyogram Versus Isometric Tension 209 9.4.2 Electromyogram During Muscle Shortening and Lengthening 210 9.4.3 Electromyogram Changes During Fatigue 211 9.5 References 212 10 Modeling of Human Movement 215Brian A. Knarr Todd J. Leutzinger and Namwoong Kim 10.0 Introduction 215 10.1 Review of Forward Solution Models 216 10.1.1 Assumptions and Constraints of Forward Solution Models 217 10.1.2 Potential of Forward Solution Simulations 217 10.2 Muscle-Actuated Simulation of Movement 218 10.2.1 Musculoskeletal Modeling 218 10.2.2 Control 221 10.2.3 OpenSim 223 10.2.4 EMG-Driven Modeling 227 10.3 Model Validation 230 10.4 References 231 11 Static and Dynamic Balance 235Stephen J. Thomas Joseph A. Zeni and David A. Winters 11.0 Introduction 235 11.1 The Support Moment Synergy 236 11.1.1 Relationship Between Ms and the Vertical Ground Reaction Force 237 11.2 Medial/Lateral and Anterior/Posterior Balance in Standing 239 11.2.1 Quiet Standing 239 11.2.2 Medial Lateral Balance Control During Workplace Tasks 240 11.3 Dynamic Balance During Walking 241 11.3.1 The Human Inverted Pendulum in Steady State Walking 241 11.3.2 Initiation of Gait 242 11.3.3 Gait Termination 244 11.4 References 246 12 Central Nervous System's Role in Biomechanics 247Alan...