Preface to the Fourth Edition

xiii

1

Biomechanics as an Interdisdpline

1

1.0

Introduction

1

1.1

Measurement, Description, Analysis, and Assessment

2

1.1.1

Measurement, Description, and Monitoring

3

1.1.2

Analysis

5

1.1.3

Assessment and Interpretation

6

1.2

Biomechanics and its Relationship with Physiology and Anatomy

7

1.3

Scope of the Textbook

9

1.3.1

Signal Processing

9

1.3.2

Kinematics

10

1.3.3

Kinetics

10

1.3.4

Anthropometry

11

1.3.5

Muscle and Joint Biomechanics

11

1.3.6

Electromyography

11

1.3.7

Synthesis of Human Movement

12

1.3.8

Biomechanical Motor Synergies

12

1.4

References

12

2

Signal Processing

14

2.0

Introduction

14

2.1

Auto- and Cross-Correlation Analyses

14

2.1.1

Similarity to the Pearson Correlation

15

2.1.2

Formulae for Auto- and Cross-Correlation Coefficients

16

2.1.3

Four Properties of the Autocorrelation Function

17

2.1.4

Three Properties of the Cross-Correlation Function

20

2.1.5

Importance in Removing the Mean Bias from the Signal

21

2.1.6

Digital Implementation of Auto- and Cross-Correlation Functions

22

2.1.7

Application of Autocorrelations

23

2.1.8

Applications of Cross-Correlations

23

2.2

Frequency Analysis

26

2.2.1

Introduction—Time Domain vs. Frequency Domain

26

2.2.2

Discrete Fourier (Harmonic) Analysis

27

2.2.3

Fast Fourier Transform (FFT)

30

2.2.4

Applications of Spectrum Analyses

30

2.3

Ensemble Averaging of Repetitive Waveforms

41

2.3.1

Examples of Ensemble-Averaged Profiles

41

2.3.2

Normalization of Time Bases to 100%

42

2.3.3

Measure of Average Variability About the Mean Waveform

43

2.4

References

43

3

Kinematics

45

3.0

Historical Development and Complexity of Problem

45

3.1

Kinematic Conventions

46

3.1.1

Absolute Spatial Reference System

46

3.1.2

Total Description of a Body Segment in Space

47

3.2

Direct Measurement Techniques

48

3.2.1

Goniometers

48

3.2.2

Special Joint Angle Measuring Systems

50

3.2.3

Accelerometers

50

3.3

Imaging Measurement Techniques

53

3.3.1

Review of Basic Lens Optics

54

3.3.2

f-Stop Setting and Field of Focus

54

3.3.3

Cinematography

55

3.3.4

Television

58

3.3.5

Optoelectric Techniques

61

3.3.6

Advantages and Disadvantages of Optical Systems

63

3.3.7

Summary of Various Kinematic Systems

64

3.4

Processing of Raw Kinematic Data

64

3.4.1

Nature of Unprocessed Image Data

64

3.4.2

Signal versus Noise in Kinematic Data

65

3.4.3

Problems of Calculating Velocities and Accelerations

66

3.4.4

Smoothing and Curve Fitting of Data

67

3.4.5

Comparison of Some Smoothing Techniques

74

3.5

Calculation of Other Kinematic Variables

75

3.5.1

Limb-Segment Angles

75

3.5.2

Joint Angles

77

3.5.3

Velocities—Linear and Angular

77

3.5.4

Accelerations—Linear and Angular

78

3.6

Problems Based on Kinematic Data

79

3.7

References

80

4

Anthropometry

82

4.0

Scope of Anthropometry in Movement Biomechanics

82

4.0.1

Segment Dimensions

82

4.1

Density, Mass, and Inertial Properties

83

4.1.1

Whole-Body Density

83

4.1.2

Segment Densities

84

4.1.3

Segment Mass and Center of Mass

85

4.1.4

Center of Mass of a Multisegment System

88

4.1.5

Mass Moment of Inertia and Radius of Gyration

89

4.1.6

Parallel-Axis Theorem

90

4.1.7

Use of Anthropometric Tables and Kinematic Data

91

4.2

Direct Experimental Measures

96

4.2.1

Location of the Anatomical Center of Mass of the Body

96

4.2.2

Calculation of the Mass of a Distal Segment

96

4.2.3

Moment of Inertia of a Distal Segment

97

4.2.4

Joint Axes of Rotation

98

4.3

Muscle Anthropometry

100

4.3.1

Cross-Sectional Area of Muscles

100

4.3.2

Change in Muscle Length during Movement

102

4.3.3

Force per Unit Cross-Sectional Area (Stress)

102

4.3.4

Mechanical Advantage of Muscle

102

4.3.5

Multijoint Muscles

102

4.4

Problems Based on Anthropometric Data

104

4.5

References

106

5

Kinetics: Forces and Moments of Force

107

5.0

Biomechanical Models

107

5.0.1

Link-Segment Model Development

108

5.0.2

Forces Acting on the Link-Segment Model

109

5.0.3

Joint Reaction Forces and Bone-on-Bone Forces

110

5.1

Basic Link-Segment Equations—The Free-Body Diagram

112

5.2

Force Transducers and Force Plates

117

5.2.1

Multidirectional Force Transducers

117

5.2.2

Force Plates

117

5.2.3

Special Pressure-Measuring Sensory Systems

121

5.2.4

Synchronization of Force Plate and Kinematic Data

122

5.2.5

Combined Force Plate and Kinematic Data

123

5.2.6

Interpretation of Moment-of-Force Curves

124

5.2.7

A Note About the Wrong Way to Analyze Moments of Force

126

5.2.8

Differences Between Center of Mass and Center of Pressure

127

5.2.9

Kinematics and Kinetics of the Inverted Pendulum Model

130

5.3

Bone-on-Bone Forces during Dynamic Conditions

131

5.3.1

Indeterminacy in Muscle Force Estimates

131

5.3.2

Example Problem (Scott and Winter, 1990)

132

5.4

Problems Based on Kinetic and Kinematic Data

136

5.5

References

137

6

Mechanical Work, Energy, and Power

139

6.0

Introduction

139

6.0.1

Mechanical Energy and Work

139

6.0.2

Law of Conservation of Energy

140

6.0.3

Internal versus External Work

141

6.0.4

Positive Work of Muscles

143

6.0.5

Negative Work of Muscles

144

6.0.6

Muscle Mechanical Power

144

6.0.7

Mechanical Work of Muscles

145

6.0.8

Mechanical Work Done on an External Load

146

6.0.9

Mechanical Energy Transfer Between Segments

148

6.1

Efficiency

149

6.1.1

Causes of Inefficient Movement

151

6.1.2

Summary of Energy Flows

154

6.2

Forms of Energy Storage

155

6.2.1

Energy of a Body Segment and Exchanges of Energy within the Segment

157

6.2.2

Total Energy of a Multisegment System

160

6.3

Calculation of Internal and External Work

162

6.3.1

Internal Work Calculation

162

6.3.2

External Work Calculation

167

6.4

Power Balances at Joints and within Segments

167

6.4.1

Energy Transfer via Muscles

167

6.4.2

Power Balance within Segments

168

6.5

Problems Based on Kinetic and Kinematic Data

173

6.6

References

174

7

Three-Dimensional Kinematics and Kinetics

176

7.0

Introduction

176

7.1

Axes Systems

176

7.1.1

Global Reference System

177

7.1.2

Local Reference Systems and Rotation of Axes

177

7.1.3

Other Possible Rotation Sequences

179

7.1.4

Dot and Cross Products

179

7.2

Marker and Anatomical Axes Systems

180

7.2.1

Example of a Kinematic Data Set

183

7.3

Determination of Segment Angular Velocities and Accelerations

187

7.4

Kinetic Analysis of Reaction Forces and Moments

188

7.4.1

Newtonian Three-Dimensional Equations of Motion for a Segment

189

7.4.2

Euler’s Three-Dimensional Equations of Motion for a Segment

189

7.4.3

Example of a Kinetic Data Set

191

7.4.4

Joint Mechanical Powers

194

7.4.5

Sample Moment and Power Curves

195

7.5

Suggested Further Reading

198

7.6

References

198

8

Synthesis of Human Movement—Forward Solutions

200

8.0

Introduction

200

8.0.1

Assumptions and Constraints of Forward Solution Models

201

8.0.2

Potential of Forward Solution Simulations

201

8.1

Review of Forward Solution Models

202

8.2

Mathematical Formulation

203

8.2.1

Lagrange’s Equations of Motion

205

8.2.2

The Generalized Coordinates and Degrees of Freedom

205

8.2.3

The Lagrangian Function L

207

8.2.4

Generalized Forces [Q]

207

8.2.5

Lagrange’s Equations

208

8.2.6

Points and Reference Systems

208

8.2.7

Displacement and Velocity Vectors

210

8.3

System Energy

214

8.3.1

Segment Energy

215

8.3.2

Spring Potential Energy and Dissipative Energy

216

8.4

External Forces and Torques

216

8.5

Designation of Joints

217

8.6

Illustrative Example

217

8.7

Conclusions

222

8.8

References

222

9

Muscle Mechanics

224

9.0

Introduction

224

9.0.1

The Motor Unit

224

9.0.2

Recruitment of Motor Units

225

9.0.3

Size Principle

226

9.0.4

Types of Motor Units—Fast- and Slow-Twitch Classification

228

9.0.5

The Muscle Twitch

228

9.0.6

Shape of Graded Contractions

230

9.1

Force-Length Characteristics of Muscles

231

9.1.1

Force-Length Curve of the Contractile Element

231

9.1.2

Influence of Parallel Connective Tissue

232

9.1.3

Series Elastic Tissue

233

9.1.4

In Vivo Force-Length Measures

235

9.2

Force-Velocity Characteristics

236

9.2.1

Concentric Contractions

236

9.2.2

Eccentric Contractions

238

9.2.3

Combination of Length and Velocity versus Force

239

9.2.4

Combining Muscle Characteristics with Load Characteristics: Equilibrium

240

9.3

Muscle Modeling

243

9.3.1

Example of a Model—EMG Driven

244

9.4

References

247

10

Kinesiological Electromyography

250

10.0

Introduction

250

10.1

Electrophysiology of Muscle Contraction

250

10.1.1

Motor End Plate

251

10.1.2

Sequence of Chemical Events Leading to a Twitch

251

10.1.3

Generation of a Muscle Action Potential

251

10.1.4

Duration of the Motor Unit Action Potential

256

10.1.5

Detection of Motor Unit Action Potentials from Electromyogram during Graded Contractions

256

10.2

Recording of the Electromyogram

257

10.2.1

Amplifier Gain

258

10.2.2

Input Impedance

258

10.2.3

Frequency Response

260

10.2.4

Common-Mode Rejection

261

10.2.5

Cross-Talk in Surface Electromyograms

265

10.2.6

Recommendations for Surface Electromyogram Reporting and Electrode Placement Procedures

268

10.3

Processing of the Electromyogram

269

10.3.1

Full-Wave Rectification

270

10.3.2

Linear Envelope

271

10.3.3

True Mathematical Integrators

272

10.4

Relationship Between Electromyogram and Biomechanical Variables

273

10.4.1

Electromyogram versus Isometric Tension

273

10.4.2

Electromyogram during Muscle Shortening and Lengthening

275

10.4.3

Electromyogram Changes during Fatigue

276

10.5

References

277

11

Biomechanical Movement Synergies

281

11.0

Introduction

281

11.1

The Support Moment Synergy

282

11.1.1

Relationship Between M_s and the Vertical Ground Reaction Force

285

11.2

Medial/Lateral and Anterior/Posterior Balance in Standing

286

11.2.1

Quiet Standing

286

11.2.2

Medial Lateral Balance Control during Workplace Tasks

288

11.3

Dynamic Balance during Walking

289

11.3.1

The Human Inverted Pendulum in Steady State Walking

289

11.3.2

Initiation of Gait

290

11.3.3

Gait Termination

293

11.4

References

295

APPENDICES

A

Kinematic, Kinetic, and Energy Data

296

Figure A.1

Walking Trial—Marker Locations and Mass and Frame Rate Information

296

Table A.1

Raw Coordinate Data (cm)

297

Table A.2(a)

Filtered Marker Kinematics—Rib Cage and Greater Trochanter (Hip)

301

Table A.2(b)

Filtered Marker Kinematics—Femoral Lateral Epicondyle (Knee) and Head of Fibula

306

Table A.2(c)

Filtered Marker Kinematics—Lateral Malleolus (Ankle) and Heel

311

Table A.2(d)

Filtered Marker Kinematics—Fifth Metatarsal and Toe

316

Table A.3(a)

Linear and Angular Kinematics—Foot

321

Table A.3(b)

Linear and Angular Kinematics—Leg

326

Table A.3(c)

Linear and Angular Kinematics—Thigh

331

Table A.3(d)

Linear and Angular Kinematics— ½ HAT

336

Table A.4

Relative Joint Angular Kinematics—Ankle, Knee, and Hip

341

Table A.5(a)

Reaction Forces and Moments of Force—Ankle and Knee

346

Table A.5(b)

Reaction Forces and Moments of Force—Hip

350

Table A.6

Segment Potential, Kinetic, and Total Energies—Foot, Leg, Thigh, and ½ HAT

353

Table A.7

Power Generation/Absorption and Transfer—Ankle, Knee, and Hip

358

B

Units and Definitions Related to Biomechanical and Electromyographical Measurements

361

Table B.1

Base SI Units

361

Table B.2

Derived SI Units

361

Index

367