Transcript bio_walk_run

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:
o Bipedal:
o Walk
o Run
o Sprint
o Hop
o Quadipedal
o Walk
o Trot
o Gallop
•
How do we study something so complex?
Today we’ll discuss models
of locomotion for walking
and running/hopping
• Whole body level- mechanics
1. Ground reaction force
2. Movement and mechanical energy of CoM
3. Behavioral models of walking and running
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
Ground reaction force
• Force exerted by the ground on the feet
• Greatly affect energetics of motion
Ground reaction force in
walking
Running
Ground Reaction Force
Center of Mass
Motion
Center of mass- balance point of body
Center of Mass
Motion
Walking
Running
Velocity decreases
Height increases
Walk
Velocity increases
Height decreases
Velocity decreases
Height decreases
Run
Velocity increases
Height increases
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
Kinetic energy (Ek,t)
m
v
Ek,t = 0.5 mv2
m = mass
v = velocity
k = kinetic, t = translational
Gravitational potential energy
(Ep,g)
mg
ry
Ep,g = mgry
mg = weight of
object
ry = vertical position
of object
Elastic energy: energy stored
when a spring is stretched or
compressed
Spring
Rest length
(no energy stored)
Stretched
(Energy stored)
Compressed
(Energy stored)
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)
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
Mechanical Energy in
Walking
Mid-stance
KE minimized at mid-stance
and GPE maximized at mid-stance
Walking and Mechanical energy
• 1st half of stance: decrease Velocity &
increase Height
o KE converted to GPE
• 2nd half of stance: increase Velocity &
decrease Height
o GPE converted to KE
• KE and GPE are out
of phase
Walking as Inverted Pendulum
Alexander (1992)
Vertical motion allows
mechanical energy exchange
Perfect Inverted Pendulum
Single support phase
Total
energy
Kinetic
energy
Gravitational
Potential
Energy
Time (s)
60-70% of
mechanical
energy is
conserved
Work
Total
KE
0.2 J/kg
GPE
0.0
DS
(Ortega and Farley,
J. Applied Physiology, 2005)
0.2
SS
0.4
Time (s)
0.6
Mechanical energy exchange and
the cost of walking
200
70
60
160
Metabolic Cost
of Transport
(mlO2/kg/km)
50
Mechanical
Energy
40Exchange
(%)
120
30
80
0.5
1.0
1.5
Speed (m/s)
2.0
Effect of body
size on
mechanical
energy recovery
11-12 years
Cavagna, 1983
3-4 years
As increase size,
greatest
recovery at
faster speeds,
but similar
amount
Mechanical Energy in
Running
Mid-stance
KE and GPE minimized at mid-stance
KE (J)
Stance phase of
running
GPE (J)
Total
Energy
(J)
Time (s)
But what about EE?
Running: Spring mechanism
• Ek,t & Ep,g are in phase. Elastic
energy is stored in leg.
Leg stiffness
• Ratio of peak force
to maximum
displacement
Blickhan, 1989
Animals maintain same leg
stiffness across many speeds
Farley et al., 1993
How do we do it?
Effect of speed on leg spring
As speed increases….
-Peak force increases
-Compensate with greater angular excursion =  CoM disp.
Leg stiffness
and speed
in variety of
running animal
Farley et al., 1993
Stiffness
Speed (m/s)
Leg Angle
Speed (m/s)
Leg stiffness is
proportional to body
mass
Animals can adjust leg
stiffness for different
surface stiffnesses
Animal adjust leg stiffness
so CoM movement is same
Ferris & Farley, 1983
Running Robots ?
Using spring mass model to
improve performance
Alt video
Why is it so hard to walk
on the moon?
How did dinosaurs walk and
run?
Thank you