Lecture 2: Terrestrial Locomotion I Simple Analyses...
Transcript of Lecture 2: Terrestrial Locomotion I Simple Analyses...
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Lecture 2: Terrestrial Locomotion I Simple Analyses of Ballistic Movement. 1. Recap: Jumping...2. Current approaches for analyzing terrestrial
locomotion.3. Gaits and patterns of limb motion4. Ballistic walking and the inverted pendulum
Comfort level with physics: 3.32 + 0.84
Comfort level with calculus: 2.80 + 1.12
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α = 55y
x
|uo| = 3.4 m/s
m= 3 10-3 kg
uo= [uo cos α, uo sin α]
After take-off forces sum to zero
No air resistance
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Survey question: the moon has 1/6 earth g. Because of that lower gravitational acceleration
(a)You would walk faster on the moon(b)You would walk slower on the moon(c)There would be no difference in your walking
speed
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1. Recap: Jumping...2. Current approaches for analyzing
terrestrial locomotion.3. Gaits and patterns of limb motion4. Ballistic walking and the inverted
pendulum
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Log
Cost
of T
rans
port
Log Body Mass (kg)-5 -4 -3 -2 -1 0 1 2 3 4 5 6
2.0
1.0
0
-1.0
-2.0
antmouse
lizardrabbit
dogchetah
humanelephant
fly beebat
pigeonfish
shark dolphin
human
Cost (P/WV; E/Wd) of transport declines with body sizeBIG DOG
ASIMO
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Muscle forces are manifest as ground reaction forces and energy (PE,KE) exchanges of the body
Is KE red or blue?KE = mv2/2PE = mgh
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Movement Biomechanics
stride length
time (s) -> 0 0.5 1.0
1. Recap: Jumping...2. Current approaches for analyzing terrestrial locomotion.3. Gaits and patterns of limb motion4. Ballistic walking and the inverted pendulum
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GAITS•stride length: distance between footfalls of the same foot
•stride frequency: number of footfalls per time•duty factor: fraction of stride time that a foot is on the ground (human walking = 0.5 - 0.6, running = 0.35). Gaits with duty factors less than 0.5 imply airborne phases.
• relative phase: time a foot is set down as a fraction of the stride time.
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V
Ballistic Walking: The Inverted Pendulum
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V
Ballistic Walking: The Inverted Pendulum
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stride length
V
Ballistic Walking: The Inverted Pendulum
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Ballistic Walking: The Inverted Pendulum
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Ballistic Walking: The Inverted PendulumSurvey question: the moon has 1/6 earth g. Would you be
able to walk faster on the moon?
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Modifiers of the radius of curvature Lumbar flexionPelvic rotationPelvic tilt
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Lumbar flexionPelvic rotationPelvic tiltPlantar flexion
http://www.biomotionlab.ca/Demos/BMLwalker.html
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How fast did T. rex run?
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10
5
2
1 0.1 0.5 1 2 5 10 20Rela
tive
Strid
e Le
ngth
S/L
S
LFr = V2/ g L