Stephen J. Thomas is Associate Professor and Chair of the Exercise Science Department at Thomas Jefferson University. His research focuses on biomechanic 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 an 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. He has published over 50 peer-reviewed articles in the field of clinical biomechanics.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. The pioneer of many important methods and concepts in the study of human movement and balance, he received the Muybridge Medal of the International Society of Biomechanics and the Lifetime Achievement Award of the Gait and Clinical Movement Analysis Society.

• List of Contributors xvPreface xviiAcknowledgments xixAbout the Companion Website xxi1 Biomechanics as an Interdiscipline 1Stephen J. Thomas Joseph A. Zeni and David A. Winters1.0 Introduction 11.0.1 Importance of Human Movement Analysis 11.0.2 The Interprofessional Team 21.1 Measurement Description Analysis and Assessment 21.1.1 Measurement Description and Monitoring 31.1.2 Analysis 41.1.3 Assessment and Interpretation 51.2 Biomechanics and its Relationship with Physiology and Anatomy 61.3 References 72 Signal Processing 8Joseph A. Zeni Stephen J. Thomas and David A. Winters2.0 Introduction 82.1 Auto- and Cross-Correlation Analyses 82.1.1 Similarity to the Pearson Correlation 92.1.2 Formulae for Auto- and Cross-Correlation Coefficients 102.1.3 Four Properties of the Autocorrelation Function 112.1.4 Three Properties of the Cross-Correlation Function 142.1.5 Importance in Removing the Mean Bias from the Signal 152.1.6 Digital Implementation of Auto- and Cross-Correlation Functions 152.1.7 Application of Autocorrelations 162.1.8 Applications of Cross-Correlations 172.2 Frequency Analysis 192.2.1 Introduction – Time Domain vs. Frequency Domain 192.2.2 Discrete Fourier (Harmonic) Analysis 192.2.3 Fast Fourier Transform (FFT) 212.2.4 Applications of Spectrum Analyses 222.3 Ensemble Averaging of Repetitive Waveforms 292.3.1 Examples of Ensemble-Averaged Profiles 312.3.2 Normalization of Time Bases to 100% 312.3.3 Measure of Average Variability about the Mean Waveform 322.4 References 323 Kinematics 34Amy L. Lenz3.0 Historical Development and Complexity of Problem 343.1 Kinematic Conventions 353.1.1 Absolute Spatial Reference System 353.1.2 Total Description of a Body Segment in Space 363.2 Direct Measurement Techniques 363.2.1 Goniometers 363.2.2 Accelerometers 383.2.3 Inertial Sensors 393.2.4 Special Joint Angle Measuring Systems 403.2.5 Electromagnetic Systems 413.3 Imaging Measurement Techniques 423.3.1 Review of Basic Lens Optics 423.3.2 f-Stop Setting and Field of Focus 433.3.3 Television Imaging Camera Historical Development 433.3.4 Optical Motion Capture 443.3.5 Optoelectric Techniques 473.3.6 Biplane Fluoroscopy 483.3.7 Markerless Systems 513.3.8 Summary of Various Kinematic Systems 513.4 Clinical Measures of Kinematics 523.4.1 2-D Kinematic Apps/Sensors 523.4.2 Sensor-Based Systems 523.5 Processing of Raw Kinematic Data 523.5.1 Nature of Unprocessed Image Data 523.5.2 Signal Versus Noise in Kinematic Data 533.5.3 Problems of Calculating Velocities and Accelerations 543.5.4 Smoothing and Curve Fitting of Data 543.5.5 Comparison of Some Smoothing Techniques 603.6 Calculation of Other Kinematic Variables 623.6.1 Limb-Segment Angles 623.6.2 Joint Angles 633.6.3 Velocities – Linear and Angular 633.6.4 Accelerations – Linear and Angular 633.7 Problems Based on Kinematic Data 643.8 References 654 Anthropometry 67Joseph A. Zeni Stephen J. Thomas and David A. Winters4.0 Scope of Anthropometry in Movement Biomechanics 674.0.1 Segment Dimensions 674.1 Density Mass and Inertial Properties 684.1.1 Whole-Body Density 684.1.2 Segment Densities 694.1.3 Segment Mass and Center of Mass 694.1.4 Center of Mass of a Multisegment System 724.1.5 Mass Moment of Inertia and Radius of Gyration 734.1.6 Parallel Axis Theorem 744.1.7 Use of Anthropometric Tables and Kinematic Data 754.2 Direct Experimental Measures 784.2.1 Location of the Anatomical Center of Mass of the Body 794.2.2 Calculation of the Mass of a Distal Segment 794.2.3 Moment of Inertia of a Distal Segment 804.2.4 Joint Axes of Rotation 814.3 Muscle Anthropometry 824.3.1 Cross-Sectional Area of Muscles 824.3.2 Change in Muscle Length During Movement 834.3.3 Force per Unit Cross-Sectional Area (Stress) 844.3.4 Mechanical Advantage of Muscle 844.3.5 Multijoint Muscles 854.4 Problems Based on Anthropometric Data 864.5 References 875 Kinetics: Forces and Moments of Force 89Stephen J. Thomas Joseph A. Zeni and David A. Winters5.0 Biomechanical Models 895.0.1 Link-Segment Model Development 895.0.2 Forces Acting on the Link-Segment Model 905.0.3 Joint Reaction Forces and Bone-on-Bone Forces 915.1 Basic Link-Segment Equations – The Free-Body Diagram 935.2 Force Transducers and Force Plates 985.2.1 Multidirectional Force Transducers 985.2.2 Force Plates 995.2.3 Combined Force Plate and Kinematic Data 1045.2.4 Interpretation of Moment-of-Force Curves 1055.2.5 Differences Between Center of Mass and Center of Pressure 1075.2.6 Kinematics and Kinetics of the Inverted Pendulum Model 1085.3 Bone-on-bone Forces During Dynamic Conditions 1105.3.1 Indeterminacy in Muscle Force Estimates 1105.3.2 Example Problem 1115.4 References 1146 Mechanical Work Energy and Power 115Joseph A. Zeni Stephen J. Thomas and David A. Winters6.0 Introduction 1156.0.1 Mechanical Energy and Work 1156.0.2 Law of Conservation of Energy 1166.0.3 Internal Versus External Work 1166.0.4 Positive Work of Muscles 1186.0.5 Negative Work of Muscles 1186.0.6 Muscle Mechanical Power 1196.0.7 Mechanical Work of Muscles 1196.0.8 Mechanical Work Done on an External Load 1206.0.9 Mechanical Energy Transfer Between Segments 1226.1 Efficiency 1236.1.1 Causes of Inefficient Movement 1246.1.2 Summary of Energy Flows 1276.2 Forms of Energy Storage 1286.2.1 Energy of a Body Segment and Exchanges of Energy Within the Segment 1296.2.2 Total Energy of a Multisegment System 1326.3 Calculation of Internal and External Work 1336.3.1 Internal Work Calculation 1336.3.2 External Work Calculation 1366.4 Power Balances at Joints and Within Segments 1366.4.1 Energy Transfer via Muscles 1376.4.2 Power Balance Within Segments 1386.5 Problems Based on Kinetic and Kinematic Data 1416.6 References 1437 Understanding 3D Kinematic and Kinetic Variables 145Thomas Hulcher7.0 Introduction 1457.1 Axes Systems 1457.1.1 Global Reference System 1457.1.2 Local Reference Systems and Rotation of Axes 1467.1.3 Other Possible Rotation Sequences 1477.1.4 Dot and Cross Products 1487.2 Marker and Anatomical Axes Systems 1487.2.1 Markerset Design 1507.2.2 Event Detection Methods for Gait 1527.2.3 Event Detection Methods for Other Activities 1537.2.4 Considerations for Applications with Implements 1537.2.5 Example of a Kinematic Data Set 1547.3 Determination of Segment Angular Velocities and Accelerations 1587.4 Kinetic Analysis of Reaction Forces and Moments 1627.4.1 Newtonian Three-Dimensional Equations of Motion for a Segment 1627.4.2 Euler’s Three-Dimensional Equations of Motion for a Segment 1637.4.3 Example of a Kinetic Data Set 1647.4.4 Joint Mechanical Powers 1677.4.5 Induced Acceleration Analysis 1677.4.6 Sample Moment and Power Curves 1687.5 Suggested Further Reading 1707.6 References 1708 Muscle Mechanics 171Stephen J. Thomas Joseph A. Zeni and David A. Winters8.0 Introduction 1718.0.1 The Motor Unit 1718.0.2 Recruitment of Motor Units 1728.0.3 Size Principle 1738.0.4 Types of Motor Units – Fast- and Slow-Twitch Classification 1748.0.5 The Muscle Twitch 1758.0.6 Shape of Graded Contractions 1768.1 Force–Length Characteristics of Muscles 1778.1.1 Force–Length Curve of the Contractile Element 1778.1.2 Influence of Parallel Connective Tissue 1788.1.3 Series Elastic Tissue 1788.1.4 In Vivo Force–Length Measures 1808.2 Force–Velocity Characteristics 1818.2.1 Concentric Contractions 1818.2.2 Eccentric Contractions 1838.2.3 Combination of Length and Velocity Versus Force 1838.2.4 Combining Muscle Characteristics with Load Characteristics: Equilibrium 1848.3 Technique to Measure in Vivo Tendon Mechanical Properties 1868.3.1 Ankle Joint Moment 1868.3.2 Tendon Mechanical Properties 1878.4 References 1879 Kinesiological Electromyography 189Joseph A. Zeni Stephen J. Thomas and David A. Winters9.0 Introduction 1899.1 Electrophysiology of Muscle Contraction 1899.1.1 Motor End Plate 1899.1.2 Sequence of Chemical Events Leading to a Twitch 1909.1.3 Generation of a Muscle Action Potential 1909.1.4 Duration of the Motor Unit Action Potential 1929.1.5 Detection of Motor Unit Action Potentials from Electromyogram During Graded Contractions 1949.2 Recording of the Electromyogram 1959.2.1 Amplifier Gain 1969.2.2 Input Impedance 1969.2.3 Frequency Response 1979.2.4 Common-Mode Rejection 1999.2.5 Cross-Talk in Surface Electromyograms 2029.2.6 Recommendations for Surface Electromyogram Reporting and Electrode Placement Procedures 2059.3 Processing of the Electromyogram 2059.3.1 Full-Wave Rectification 2069.3.2 Linear Envelope 2079.3.3 True Mathematical Integrators 2089.4 Relationship Between Electromyogram and Biomechanical Variables 2089.4.1 Electromyogram Versus Isometric Tension 2099.4.2 Electromyogram During Muscle Shortening and Lengthening 2109.4.3 Electromyogram Changes During Fatigue 2119.5 References 21210 Modeling of Human Movement 215Brian A. Knarr Todd J. Leutzinger and Namwoong Kim10.0 Introduction 21510.1 Review of Forward Solution Models 21610.1.1 Assumptions and Constraints of Forward Solution Models 21710.1.2 Potential of Forward Solution Simulations 21710.2 Muscle-Actuated Simulation of Movement 21810.2.1 Musculoskeletal Modeling 21810.2.2 Control 22110.2.3 OpenSim 22310.2.4 EMG-Driven Modeling 22710.3 Model Validation 23010.4 References 23111 Static and Dynamic Balance 235Stephen J. Thomas Joseph A. Zeni and David A. Winters11.0 Introduction 23511.1 The Support Moment Synergy 23611.1.1 Relationship Between Ms and the Vertical Ground Reaction Force 23711.2 Medial/Lateral and Anterior/Posterior Balance in Standing 23911.2.1 Quiet Standing 23911.2.2 Medial Lateral Balance Control During Workplace Tasks 24011.3 Dynamic Balance During Walking 24111.3.1 The Human Inverted Pendulum in Steady State Walking 24111.3.2 Initiation of Gait 24211.3.3 Gait Termination 24411.4 References 24612 Central Nervous System’s Role in Biomechanics 247Alan R. Needle and Christopher J. Burcal12.0 Introduction 24712.1 Central Nervous System and Volitional Control of Movement 24712.1.1 Key Structures for Movement 24712.1.2 Synapses and Neurotransmitters 24912.1.3 CNS Adaptations 24912.2 Peripheral Nervous System and Reflexive Control of Movement 25012.2.1 Sensory Receptors and Motor Units 25212.3 Methodologies to Understand Central Nervous System Function 25312.3.1 Functional Magnetic Resonance Imaging (fMRI) 25312.3.2 Electroencephalography (EEG) 25712.3.3 Neural Excitability 26512.4 Peripheral Nervous System Measurement Techniques 26912.4.1 Nerve Conduction Studies 26912.4.2 Microneurography 27112.5 Methodologies to Understand Central Nervous System Behavior and Environmental Interactions 27112.5.1 Virtual Reality 27112.6 Nervous System Role in Muscle Synergies 27412.6.1 Measurement Techniques and Experimental Setup 27412.6.2 Analysis Techniques 27512.7 The Central Nervous System and Learning and Injury 27612.7.1 Translation of Synaptic Plasticity to Motor Learning 27612.7.2 Role of Pathology on the Central Nervous System 27612.8 References 27813 A Case-Based Approach to Interpreting Biomechanical Data 281Ankur Padhye John D. Willson Joseph A. Zeni Kristen F. Nicholson and Garrett S. Bullock13.0 Patellofemoral Pain 28113.0.1 Introduction 28113.0.2 Case Description 28113.0.3 Patient Examination 28213.0.4 Gait Analysis 28213.0.5 Interpretations and Intervention 28213.0.6 Patient Outcomes and Discussion 28313.0.7 Conclusion 28413.0.8 References 28413.1 Biomechanical Approach to Manage Knee Osteoarthritis 28413.1.1 Osteoarthritis and Biomechanics 28413.1.2 Patient History 28613.1.3 Biomechanical Assessment 28613.1.4 References 28813.2 Ulnar Collateral Ligament Reconstruction 28813.2.1 Player History 28913.2.2 References 293APPENDICESA. Kinematic Kinetic and Energy Data 295Figure A.1 Walking Trial – Marker Locations and Mass and Frame Rate Information 295Table A.1 Raw Coordinate Data (cm) 296Table A.2(a) Filtered Marker Kinematics – Rib Cage and Greater Trochanter (Hip) 300Table A.2(b) Filtered Marker Kinematics – Femoral Lateral Epicondyle (Knee) and Head of Fibula 304Table A.2(c) Filtered Marker Kinematics – Lateral Malleolus (Ankle) and Heel 308Table A.2(d) Filtered Marker Kinematics – Fifth Metatarsal and Toe 312Table A.3(a) Linear and Angular Kinematics – Foot 316Table A.3(b) Linear and Angular Kinematics – Leg 320Table A.3(c) Linear and Angular Kinematics – Thigh 324Table A.3(d) Linear and Angular Kinematics – ½ HAT 328Table A.4 Relative Joint Angular Kinematics – Ankle Knee and Hip 332Table A.5(a) Reaction Forces and Moments of Force – Ankle and Knee 336Table A.5(b) Reaction Forces and Moments of Force – Hip 340Table A.6 Segment Potential Kinetic and Total Energies – Foot Leg Thigh and ½ HAT 344Table A.7 Power Generation/Absorption and Transfer – Ankle Knee and Hip 348B. Units and Definitions Related to Biomechanical and Electromyographical Measurements 351Table B.1 Base SI Units 351Table B.2 Derived SI Units 352Index 355