models of terrestrial locomotion: from mice to men… to elephants? justus d. ortega dept. of...
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Models of Terrestrial Locomotion:Models of Terrestrial Locomotion:From Mice to Men…From Mice to Men…
to Elephants?to Elephants?
Justus D. Ortega
Dept. of KinesiologyHumboldt State University
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What do all these animals have in
common?
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Locomotion• Complex interaction of the neuromuscular and
musculoskeletal systems• Comes in many forms:
oBipedal: oWalkoRunoSprinto Hop
oQuadipedaloWalkoTrotoGallop
• How do we study something so complex?
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Today we’ll discuss models of locomotion
for walking and running/hopping
•Whole body level- mechanics1. Ground reaction force2. Movement and mechanical energy of
CoM3. Behavioral models of walking and
running
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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
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Ground reaction force
•Force exerted by the ground on the feet
•Greatly affect energetics of motion
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Ground reaction force in walking
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Running Ground Reaction Force
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Center of MassMotion
Center of mass- balance point of body
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Center of MassMotion
Walking Running
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WalkVelocity decreasesHeight increases
Velocity increasesHeight decreases
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RunVelocity decreases Height decreases
Velocity increasesHeight increases
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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
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Kinetic energy (Ek,t)
m = massv = velocityk = kinetic, t = translational
m
Ek,t = 0.5 mv2
v
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Gravitational potential energy (Ep,g)
mg = weight of object
ry = vertical position of object
Ep,g = mgry
ry
mg
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Elastic energy: energy stored when a spring is stretched or
compressed
Stretched(Energy stored)
Rest length(no energy stored)
Compressed(Energy stored)
Spring
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Mechanical energy in walking
Some kinetic energySome gravitational potential energyLittle work done against aerodynamic dragUnless slipping, no work done against friction
Not much bouncing (elastic energy)
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Mechanical energy fluctuations in level walking
Average Ek,t constant (average vx constant)
Average Ep,g constant (average ry constant)
HOWEVEREk,t and Ep,g fluctuate within each stance
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Mechanical Energy in Walking
Mid-stance
KE minimized at mid-stanceand GPE maximized at mid-
stance
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Walking and Mechanical energy
•1st half of stance: decrease Velocity & increase HeightoKE converted to GPE
•2nd half of stance: increase Velocity & decrease HeightoGPE converted to KE
•KE and GPE are out of phase
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Alexander (1992)
Vertical motion allows mechanical energy
exchange
Walking as Inverted Pendulum
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Kineticenergy
Gravitational Potential
Energy
Totalenergy
Time (s)
Single support phase
Perfect Inverted Pendulum
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Total
GPE
KE
Time (s)0.0 0.2 0.4 0.6
DS SS
0.2 J/kg
Work
(Ortega and Farley, J. Applied Physiology, 2005)
60-70% of mechanical energy is conserved
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Mechanical energy exchange and the cost of
walking
Metabolic Cost of Transport (mlO2/kg/km)
Speed (m/s)1.00.5 1.5 2.0
80
120
160
200
Mechanical Energy
Exchange (%)
70
60
40
50
30
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Effect of body size on mechanical
energy recovery
As increase size, greatest recovery at faster speeds, but similar amount
11-12 years
3-4 years
Cavagna, 1983
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Mechanical Energy in Running
KE and GPE minimized at mid-stance
Mid-stance
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KE (J)
GPE (J)
TotalEnergy (J)
Time (s)
Stance phase of running
But what about EE?
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Running: Spring mechanism
•Ek,t & Ep,g are in phase. Elastic energy is stored in leg.
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Leg stiffness
•Ratio of peak force to maximum displacement
Blickhan, 1989
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Animals maintain same leg stiffness across many
speeds
Farley et al., 1993
How do we do it?
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Effect of speed on leg spring
As speed increases….-Peak force increases-Compensate with greater angular excursion = CoM disp.
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Leg stiffness
and speed in variety of
running animal
Leg Angle Stiffness
Speed (m/s) Speed (m/s)Farley et al., 1993
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Leg stiffness is proportional to body mass
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Animals can adjust leg stiffness for different
surface stiffnesses
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Animal adjust leg stiffness so CoM
movement is same
Ferris & Farley, 1983
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Running Robots ?
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Using spring mass model to improve
performance
Alt video
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Why is it so hard to walk on the moon?
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How did dinosaurs walk and run?
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Thank you