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Models of Terrestrial Locomotion: From Mice to Men… to Elephants?

Models of Terrestrial Locomotion: From Mice to Men… to Elephants?. Justus D. Ortega Dept. of Kinesiology Humboldt State University. What do all these animals have in common?. Locomotion. Complex interaction of the neuromuscular and musculoskeletal systems Comes in many forms: Bipedal:

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Models of Terrestrial Locomotion: From Mice to Men… to Elephants?

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  1. Models of Terrestrial Locomotion:From Mice to Men…to Elephants? Justus D. Ortega Dept. of Kinesiology Humboldt State University

  2. What do all these animals have in common?

  3. Locomotion • Complex interaction of the neuromuscular and musculoskeletal systems • Comes in many forms: • Bipedal: • Walk • Run • Sprint • Hop • Quadipedal • Walk • Trot • Gallop • How do we study something so complex?

  4. Today we’ll discuss models of locomotion for walking and running/hopping • Whole body level- mechanics • Ground reaction force • Movement and mechanical energy of CoM • Behavioral models of walking and running

  5. Basic patterns in walking and running • Walking • Double support: two feet on ground • Single support: One foot on ground • Running • Stance phase: one foot on ground • Aerial phase: no ground contact

  6. Ground reaction force • Force exerted by the ground on the feet • Greatly affect energetics of motion

  7. Ground reaction force in walking

  8. Running Ground Reaction Force

  9. Center of MassMotion Center of mass- balance point of body

  10. Center of MassMotion Walking Running

  11. Walk Velocity decreases Height increases Velocity increases Height decreases

  12. Run Velocity increases Height increases Velocity decreases Height decreases

  13. Mechanical Energy of Center of Mass Mechanical Energy- Energy of an object related to its motion Two primary forms: Kinetic: energy in motion Potential: stored energy -Gravitational - elastic

  14. Kinetic energy (Ek,t) m = mass v = velocity k = kinetic, t = translational v m Ek,t = 0.5 mv2

  15. Gravitational potential energy (Ep,g) mg Ep,g = mgry mg = weight of object ry= vertical position of object ry

  16. Elastic energy:energy stored when a spring is stretched or compressed Spring Rest length (no energy stored) Stretched (Energy stored) Compressed (Energy stored)

  17. Mechanical energy in walking Some kinetic energy Some gravitational potential energy Little work done against aerodynamic drag Unless slipping, no work done against friction Not much bouncing (elastic energy)

  18. Mechanical energy fluctuations in level walking Average Ek,t constant (average vx constant) Average Ep,g constant (average ry constant) HOWEVER Ek,t and Ep,g fluctuate within each stance

  19. Mechanical Energy in Walking Mid-stance KE minimized at mid-stance and GPE maximized at mid-stance

  20. Walking and Mechanical energy • 1st half of stance: decrease Velocity & increase Height • KE converted to GPE • 2nd half of stance: increase Velocity & decrease Height • GPE converted to KE • KE and GPE are out of phase

  21. Walking as Inverted Pendulum Alexander (1992) Vertical motion allows mechanical energy exchange

  22. Perfect Inverted Pendulum Single support phase Total energy Kinetic energy Gravitational Potential Energy Time (s)

  23. 60-70% of mechanical energy is conserved Work Total KE GPE 0.0 0.2 0.4 0.6 0.2 J/kg DS SS Time (s) (Ortega and Farley, J. Applied Physiology, 2005)

  24. 200 160 120 80 0.5 1.0 1.5 2.0 Mechanical energy exchange and the cost of walking 70 60 Metabolic Cost of Transport (mlO2/kg/km) 50 Mechanical Energy Exchange (%) 40 30 Speed (m/s)

  25. 3-4 years Effect of body size on mechanical energy recovery 11-12 years As increase size, greatest recovery at faster speeds, but similar amount Cavagna, 1983

  26. Mechanical Energy in Running KE and GPE minimized at mid-stance Mid-stance

  27. KE (J) Stance phase of running GPE (J) Total Energy (J) Time (s) But what about EE?

  28. Running: Spring mechanism • Ek,t & Ep,g are in phase. Elastic energy is stored in leg.

  29. Leg stiffness • Ratio of peak force to maximum displacement Blickhan, 1989

  30. Animals maintain same leg stiffness across many speeds Farley et al., 1993 How do we do it?

  31. Effect of speed on leg spring • As speed increases…. • Peak force increases • Compensate with greater angular excursion =  CoM disp.

  32. Stiffness Leg Angle Leg stiffness and speed in variety of running animal Farley et al., 1993 Speed (m/s) Speed (m/s)

  33. Leg stiffness is proportional to body mass

  34. Animals can adjust leg stiffness for different surface stiffnesses

  35. Animal adjust leg stiffness so CoM movement is same Ferris & Farley, 1983

  36. Running Robots ?

  37. Using spring mass model to improve performance Alt video

  38. Why is it so hard to walk on the moon?

  39. How did dinosaurs walk and run?

  40. Thank you

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