Understanding Mammalian Locomotion

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