Understanding Mammalian Locomotion

John E.A. Bertram is a Professor in the Department of Cell Biology and Anatomy, Cumming School of Medicine, and adjunct Professor in the Department of Comparative Biology and Experimental Medicine, Faculty of Veterinary Medicine, at the University of Calgary in Calgary, AB, Canada

• List of Contributors xvPreface xviiChapter 1 Concepts Through Time: Historical Perspectives on Mammalian Locomotion 1John E. A. Bertram1.1 Introduction 11.2 The ancients and the contemplation of motion 21.3 The European Renaissance and foundations of the age of discovery 31.4 The era of technological observation 51.5 Physiology and mechanics of terrestrial locomotion – cost and consequences 71.6 Comparative studies of gait 101.6 Re]interpreting the mechanics: a fork in the road, or simply seeing the other side of the coin? 131.7 The biological source of cost 131.8 The physical source of cost (with biological consequences) – the road less traveled 141.9 Conclusions 21References 21Chapter 2 Considering Gaits: Descriptive Approaches 27John E. A. Bertram2.1 Introduction 272.2 Defining the fundamental gaits 282.3 Classifying and comparing the fundamental gaits 302.4 Symmetric gaits 322.5 A symmetric gaits 342.6 Beyond “Hildebrand plots” 402.7 Statistical classification 432.8 Neural regulation and emergent criteria 452.9 Mechanical measures as descriptions of gaits 472.10 Conclusion 47References 48Chapter 3 Muscles as Actuators 51Anne K. Gutmann and John E. A. Bertram3.1 Introduction 513.2 Basic muscle operation 523.2.1 Sliding filament theory – the basis for cross]bridge theory 523.2.2 Basic cross]bridge theory 523.2.3 Multi]state cross]bridge models 573.3 Some alternatives to cross]bridge theory 593.4 Force production 603.4.1 Isometric force production 603.4.2 Non]isometric force production 633.5 The Hill]type model 663.6 Optimizing work, power, and efficiency 683.7 Muscle architecture 703.7.1 The sarcomere as the fundamental contractile unit 703.7.2 Muscle geometry 703.7.3 Elastic energy storage and return 723.7.4 Damping/energy dissipation 723.8 Other factors that influence muscle performance 733.8.1 Fiber type 733.9 A ctivation and recruitment 753.10 What does muscle do best? 76References 76Chapter 4 Concepts in Locomotion: Levers, Struts, Pendula and Springs 79John E. A. Bertram4.1 Introduction 794.2 The limb: How details can obscure functional role 834.3 Limb function in stability and the concept of the “effective limb” 854.3.1 Considering the mechanisms of stability 854.3.2 The role of the effective limb 884.4 Levers and struts 894.5 Ground reaction force in gaits 924.5.1 Trot 944.5.2 Walk 964.5.3 Gallop 974.6 The consequence of applied force: CoM motion, pendula and springs 984.7 Energy exchange in locomotion – valuable or inevitable? 1024.8 Momentum and energy in locomotion: dynamic fundamentals 1034.9 Energy – lost unless recovered, or available unless lost? 104References 105Chapter 5 Concepts in Locomotion: Wheels, Spokes, Collisions and Insight from the Center of Mass 111John E. A. Bertram5.1 Introduction 1115.2 Understanding brachiation: an analogy for terrestrial locomotion 1125.3 Bipedal walking: inverted pendulum or inverted “collision]limiting brachiator analog”? 1175.4 Basic dynamics of the step]to]step transition in bipedal walking 1205.5 Subtle dynamics of the step]to]step transition in bipedal walking and running 1245.6 Pseudo]elastic motion and true elastic return in running gaits 1305.7 Managing CoM motion in quadrupedal gaits 1315.7.1 Walk 1325.7.2 Trot 1335.7.3 Gallop 1335.8 Conclusion 138References 139Chapter 6 Reductionist Models of Walking and Running 143James R. Usherwood6.1 Part 1: Bipedal locomotion and “the ultimate cost of legged locomotion?” 1436.1.1 Introduction 1436.1.2 Reductionist models of walking 1446.1.3 The benefit of considering locomotion as inelastic 1506.2 Part 2: quadrupedal locomotion 1586.2.1 Introduction 1586.2.2 Quadrupedal dynamic walking and collisions 1586.2.3 Higher speed quadrupedal gaits 1616.2.4 Further success of reductionist mechanics 162Appendix A: Analytical approximation for costs of transport including legs and “guts and gonads” losses 1666A.1 List of symbols 1666A.2 Period definitions for a symmetrically running biped 1666A.3 Ideal work for the leg 1676A.4 Vertical work calculations for leg 1686A.5 Horizontal work calculations for leg 1696A.6 Hysteresis costs of “guts and gonads” deflections 1696A.7 Cost of transport 170References 170Chapter 7 Whole]Body Mechanics: How Leg Compliance Shapes the Way We Move 173Andre Seyfarth, Hartmut Geyer, Susanne Lipfert, J. Rummel, Yvonne Blum, M. Maus and D. Maykranz7.1 Introduction 1737.2 Jumping for distance – a goal]directed movement 1757.3 Running for distance – what is the goal? 1777.4 Cyclic stability in running 1787.5 The wheel in the leg – how leg retraction enhances running stability 1797.6 Walking with compliant legs 1807.7 A dding an elastically coupled foot to the spring]mass model 1847.8 The segmented leg – how does joint function translate into leg function? 1857.9 Keeping the trunk upright during locomotion 1877.10 The challenge of setting up more complex models 188Notes 190References190Chapter 8 The Most Important Feature of an Organism’s Biology: Dimension, Similarity and Scale 193John E. A. Bertram8.1 Introduction 1938.2 The most basic principle: surface area to volume relations 1948.3 A ssessing scale effects 1978.4 Physiology and scaling 1988.5 The allometric equation: the power function of scaling 2038.6 The standard scaling models 2078.6.1 Geometric similarity 2088.6.2 Static stress similarity 2098.6.3 Elastic similarity 2098.7 Differential scaling – where the limit may change 2108.7.1 A ssessing the assumptions 2158.8 A fractal view of scaling 2158.9 Making valid comparisons: measurement, dimension and functional criteria 2178.9.1 Considering units 2178.9.2 Fundamental and derived units 2198.9.3 Froude number: a dimensionless example 222References 223Chapter 9 Accounting for the Influence of Animal Size on Biomechanical Variables: Concepts and Considerations 229Sharon Bullimore9.1 Introduction 2299.2 Commonly used approaches to accounting for size differences 2309.2.1 Dividing by body mass 2309.2.2 Dimensionless parameters 2329.3 Empirical scaling relationships 2379.4 Selected biomechanical parameters 2389.4.1 Ground reaction force 2389.4.2 Muscle force 2399.4.3 Muscle velocity 2429.4.4 Running speed 2429.4.5 Jump height 2449.4.6 Elastic energy storage 2469.5 Conclusions 247Acknowledgements 247References 247Chapter 10 Locomotion in Small Tetrapods: Size]Based Limitations to “Universal Rules” in Locomotion 251Audrone R. Biknevicius, Stephen M. Reilly and Elvedin Kljuno10.1 Introduction 25110.2 A ctive mechanisms contributing to the high cost of transport in small tetrapods 25410.3 Limited passive mechanisms for reducing cost of transport in small tetrapods 25510.4 Gait transitions from vaulting to bouncing mechanics 25710.5 The “unsteadiness” of most terrestrial locomotion 262Appendix – a model of non]steady speed walking 26510A.1 Spring]mass inverted pendulum model of walking 26510A.2 Recovery ratio calculation 269References 271Chapter 11 Non]Steady Locomotion 277Monica A. Daley11.1 Introduction 27711.1.1 Why study non]steady locomotion? 27811.2 A pproaches to studying non]steady locomotion 27911.2.1 Simple mechanical models 28011.2.2 Research approaches to non]steady locomotion 28111.3 Themes from recent studies of non]steady locomotion 28211.3.1 Limits to maximal acceleration 28211.3.2 Morphological and behavioral factors in turning mechanics 28311.4 The role of intrinsic mechanics for stability and robustness of locomotion 28811.4.1 Some definitions 28911.4.2 Measures of sensitivity and robustness 29011.4.3 What do we learn about stability from simple models of running? 29111.4.4 Limitations to stability analysis of simple models 29511.4.5 The relationship between ground contact conditions and leg mechanics on uneven terrain 29611.4.6 Compromises among economy, robustness and injury avoidance in uneven terrain 29811.5 Proximal]distal inter]joint coordination in non]steady locomotion 299References 302Chapter 12 The Evolution of Terrestrial Locomotion in Bats: the Bad, the Ugly, and the Good 307Daniel K. Riskin, John E. A. Bertram and John W. Hermanson12.1 Bats on the ground: like fish out of water? 30712.2 Species]level variation in walking ability 30812.3 How does anatomy influence crawling ability? 30912.4 Hindlimbs and the evolution of flight 31112.5 Moving a bat’s body on land: the kinematics of quadrupedal locomotion 31512.6 Evolutionary pressures leading to capable terrestrial locomotion 31812.7 Conclusions and future work 319Acknowledgements 320References 320Chapter 13 The Fight or Flight Dichotomy: Functional Trade]Off in Specialization for Aggression Versus Locomotion 325David R. Carrier13.1 Introduction32513.1.1 Why fighting is important 32713.1.2 Size sexual dimorphism as an indicator of male]male aggression 32813.2 Trade]offs in specialization for aggression versus locomotion 32913.2.1 The evolution of short legs – specialization for aggression? 32913.2.2 Muscle architecture of limbs specialized for running versus fighting 33113.2.3 Mechanical properties of limb bones that are specialized for running versus fighting 33413.2.4 The function of foot posture: aggression versus locomotor economy 33413.3 Discussion 338References 341Chapter 14 Design for Prodigious Size without Extreme Body Mass: Dwarf Elephants, Differential Scaling and Implications for Functional Adaptation 349John E. A. Bertram14.1 Introduction 34914.2 Elephant form, mammalian scaling and dwarfing 35114.2.1 Measurements 35614.2.2 Observations 35614.3 Interpretation 357Acknowledgements 364References 364Chapter 15 Basic Mechanisms of Bipedal Locomotion: Head]Supported Loads and Strategies to Reduce the Cost of Walking 369James R. Usherwood and John E. A. Bertram15.1 Introduction 36915.2 Head]supported loads in human]mediated transport 37015.2.1 Can the evidence be depended upon? 37115.3 Potential energy saving advantages 37315.4 A simple alternative model 37615.5 Conclusions 382References 382Chapter 16 Would a Horse on the Moon Gallop? Directions Available in Locomotion Research (and How Not to Spend Too Much Time Exploring Blind Alleys) 385John E. A. Bertram16.1 Introduction 385References 392Index 393