List of Contributors xv
Preface xvii
Chapter 1 Concepts Through Time: Historical Perspectives on Mammalian Locomotion 1
John E. A. Bertram
1.1 Introduction 1
1.2 The ancients and the contemplation of motion 2
1.3 The European Renaissance and foundations of the age of discovery 3
1.4 The era of technological observation 5
1.5 Physiology and mechanics of terrestrial locomotion – cost and consequences 7
1.6 Comparative studies of gait 10
1.6 Re]interpreting the mechanics: a fork in the road, or simply seeing the other side of the coin? 13
1.7 The biological source of cost 13
1.8 The physical source of cost (with biological consequences) – the road less traveled 14
1.9 Conclusions 21
References 21
Chapter 2 Considering Gaits: Descriptive Approaches 27
John E. A. Bertram
2.1 Introduction 27
2.2 Defining the fundamental gaits 28
2.3 Classifying and comparing the fundamental gaits 30
2.4 Symmetric gaits 32
2.5 A symmetric gaits 34
2.6 Beyond “Hildebrand plots” 40
2.7 Statistical classification 43
2.8 Neural regulation and emergent criteria 45
2.9 Mechanical measures as descriptions of gaits 47
2.10 Conclusion 47
References 48
Chapter 3 Muscles as Actuators 51
Anne K. Gutmann and John E. A. Bertram
3.1 Introduction 51
3.2 Basic muscle operation 52
3.2.1 Sliding filament theory – the basis for cross]bridge theory 52
3.2.2 Basic cross]bridge theory 52
3.2.3 Multi]state cross]bridge models 57
3.3 Some alternatives to cross]bridge theory 59
3.4 Force production 60
3.4.1 Isometric force production 60
3.4.2 Non]isometric force production 63
3.5 The Hill]type model 66
3.6 Optimizing work, power, and efficiency 68
3.7 Muscle architecture 70
3.7.1 The sarcomere as the fundamental contractile unit 70
3.7.2 Muscle geometry 70
3.7.3 Elastic energy storage and return 72
3.7.4 Damping/energy dissipation 72
3.8 Other factors that influence muscle performance 73
3.8.1 Fiber type 73
3.9 A ctivation and recruitment 75
3.10 What does muscle do best? 76
References 76
Chapter 4 Concepts in Locomotion: Levers, Struts, Pendula and Springs 79
John E. A. Bertram
4.1 Introduction 79
4.2 The limb: How details can obscure functional role 83
4.3 Limb function in stability and the concept of the “effective limb” 85
4.3.1 Considering the mechanisms of stability 85
4.3.2 The role of the effective limb 88
4.4 Levers and struts 89
4.5 Ground reaction force in gaits 92
4.5.1 Trot 94
4.5.2 Walk 96
4.5.3 Gallop 97
4.6 The consequence of applied force: CoM motion, pendula and springs 98
4.7 Energy exchange in locomotion – valuable or inevitable? 102
4.8 Momentum and energy in locomotion: dynamic fundamentals 103
4.9 Energy – lost unless recovered, or available unless lost? 104
References 105
Chapter 5 Concepts in Locomotion: Wheels, Spokes, Collisions and Insight from the Center of Mass 111
John E. A. Bertram
5.1 Introduction 111
5.2 Understanding brachiation: an analogy for terrestrial locomotion 112
5.3 Bipedal walking: inverted pendulum or inverted “collision]limiting brachiator analog”? 117
5.4 Basic dynamics of the step]to]step transition in bipedal walking 120
5.5 Subtle dynamics of the step]to]step transition in bipedal walking and running 124
5.6 Pseudo]elastic motion and true elastic return in running gaits 130
5.7 Managing CoM motion in quadrupedal gaits 131
5.7.1 Walk 132
5.7.2 Trot 133
5.7.3 Gallop 133
5.8 Conclusion 138
References 139
Chapter 6 Reductionist Models of Walking and Running 143
James R. Usherwood
6.1 Part 1: Bipedal locomotion and “the ultimate cost of legged locomotion?” 143
6.1.1 Introduction 143
6.1.2 Reductionist models of walking 144
6.1.3 The benefit of considering locomotion as inelastic 150
6.2 Part 2: quadrupedal locomotion 158
6.2.1 Introduction 158
6.2.2 Quadrupedal dynamic walking and collisions 158
6.2.3 Higher speed quadrupedal gaits 161
6.2.4 Further success of reductionist mechanics 162
Appendix A: Analytical approximation for costs of transport including legs and “guts and gonads” losses 166
6A.1 List of symbols 166
6A.2 Period definitions for a symmetrically running biped 166
6A.3 Ideal work for the leg 167
6A.4 Vertical work calculations for leg 168
6A.5 Horizontal work calculations for leg 169
6A.6 Hysteresis costs of “guts and gonads” deflections 169
6A.7 Cost of transport 170
References 170
Chapter 7 Whole]Body Mechanics: How Leg Compliance Shapes the Way We Move 173
Andre Seyfarth, Hartmut Geyer, Susanne Lipfert, J. Rummel, Yvonne Blum, M. Maus and D. Maykranz
7.1 Introduction 173
7.2 Jumping for distance – a goal]directed movement 175
7.3 Running for distance – what is the goal? 177
7.4 Cyclic stability in running 178
7.5 The wheel in the leg – how leg retraction enhances running stability 179
7.6 Walking with compliant legs 180
7.7 A dding an elastically coupled foot to the spring]mass model 184
7.8 The segmented leg – how does joint function translate into leg function? 185
7.9 Keeping the trunk upright during locomotion 187
7.10 The challenge of setting up more complex models 188
Notes 190
References190
Chapter 8 The Most Important Feature of an Organism’s Biology: Dimension, Similarity and Scale 193
John E. A. Bertram
8.1 Introduction 193
8.2 The most basic principle: surface area to volume relations 194
8.3 A ssessing scale effects 197
8.4 Physiology and scaling 198
8.5 The allometric equation: the power function of scaling 203
8.6 The standard scaling models 207
8.6.1 Geometric similarity 208
8.6.2 Static stress similarity 209
8.6.3 Elastic similarity 209
8.7 Differential scaling – where the limit may change 210
8.7.1 A ssessing the assumptions 215
8.8 A fractal view of scaling 215
8.9 Making valid comparisons: measurement, dimension and functional criteria 217
8.9.1 Considering units 217
8.9.2 Fundamental and derived units 219
8.9.3 Froude number: a dimensionless example 222
References 223
Chapter 9 Accounting for the Influence of Animal Size on Biomechanical Variables: Concepts and Considerations 229
Sharon Bullimore
9.1 Introduction 229
9.2 Commonly used approaches to accounting for size differences 230
9.2.1 Dividing by body mass 230
9.2.2 Dimensionless parameters 232
9.3 Empirical scaling relationships 237
9.4 Selected biomechanical parameters 238
9.4.1 Ground reaction force 238
9.4.2 Muscle force 239
9.4.3 Muscle velocity 242
9.4.4 Running speed 242
9.4.5 Jump height 244
9.4.6 Elastic energy storage 246
9.5 Conclusions 247
Acknowledgements 247
References 247
Chapter 10 Locomotion in Small Tetrapods: Size]Based Limitations to “Universal Rules” in Locomotion 251
Audrone R. Biknevicius, Stephen M. Reilly and Elvedin Kljuno
10.1 Introduction 251
10.2 A ctive mechanisms contributing to the high cost of transport in small tetrapods 254
10.3 Limited passive mechanisms for reducing cost of transport in small tetrapods 255
10.4 Gait transitions from vaulting to bouncing mechanics 257
10.5 The “unsteadiness” of most terrestrial locomotion 262
Appendix – a model of non]steady speed walking 265
10A.1 Spring]mass inverted pendulum model of walking 265
10A.2 Recovery ratio calculation 269
References 271
Chapter 11 Non]Steady Locomotion 277
Monica A. Daley
11.1 Introduction 277
11.1.1 Why study non]steady locomotion? 278
11.2 A pproaches to studying non]steady locomotion 279
11.2.1 Simple mechanical models 280
11.2.2 Research approaches to non]steady locomotion 281
11.3 Themes from recent studies of non]steady locomotion 282
11.3.1 Limits to maximal acceleration 282
11.3.2 Morphological and behavioral factors in turning mechanics 283
11.4 The role of intrinsic mechanics for stability and robustness of locomotion 288
11.4.1 Some definitions 289
11.4.2 Measures of sensitivity and robustness 290
11.4.3 What do we learn about stability from simple models of running? 291
11.4.4 Limitations to stability analysis of simple models 295
11.4.5 The relationship between ground contact conditions and leg mechanics on uneven terrain 296
11.4.6 Compromises among economy, robustness and injury avoidance in uneven terrain 298
11.5 Proximal]distal inter]joint coordination in non]steady locomotion 299
References 302
Chapter 12 The Evolution of Terrestrial Locomotion in Bats: the Bad, the Ugly, and the Good 307
Daniel K. Riskin, John E. A. Bertram and John W. Hermanson
12.1 Bats on the ground: like fish out of water? 307
12.2 Species]level variation in walking ability 308
12.3 How does anatomy influence crawling ability? 309
12.4 Hindlimbs and the evolution of flight 311
12.5 Moving a bat’s body on land: the kinematics of quadrupedal locomotion 315
12.6 Evolutionary pressures leading to capable terrestrial locomotion 318
12.7 Conclusions and future work 319
Acknowledgements 320
References 320
Chapter 13 The Fight or Flight Dichotomy: Functional Trade]Off in Specialization for Aggression Versus Locomotion 325
David R. Carrier
13.1 Introduction325
13.1.1 Why fighting is important 327
13.1.2 Size sexual dimorphism as an indicator of male]male aggression 328
13.2 Trade]offs in specialization for aggression versus locomotion 329
13.2.1 The evolution of short legs – specialization for aggression? 329
13.2.2 Muscle architecture of limbs specialized for running versus fighting 331
13.2.3 Mechanical properties of limb bones that are specialized for running versus fighting 334
13.2.4 The function of foot posture: aggression versus locomotor economy 334
13.3 Discussion 338
References 341
Chapter 14 Design for Prodigious Size without Extreme Body Mass: Dwarf Elephants, Differential Scaling and Implications for Functional Adaptation 349
John E. A. Bertram
14.1 Introduction 349
14.2 Elephant form, mammalian scaling and dwarfing 351
14.2.1 Measurements 356
14.2.2 Observations 356
14.3 Interpretation 357
Acknowledgements 364
References 364
Chapter 15 Basic Mechanisms of Bipedal Locomotion: Head]Supported Loads and Strategies to Reduce the Cost of Walking 369
James R. Usherwood and John E. A. Bertram
15.1 Introduction 369
15.2 Head]supported loads in human]mediated transport 370
15.2.1 Can the evidence be depended upon? 371
15.3 Potential energy saving advantages 373
15.4 A simple alternative model 376
15.5 Conclusions 382
References 382
Chapter 16 Would a Horse on the Moon Gallop? Directions Available in Locomotion Research (and How Not to Spend Too Much Time Exploring Blind Alleys) 385
John E. A. Bertram
16.1 Introduction 385
References 392
Index 393
