Can we explain reduced gravity trends without springs?
S. Javad Hasaneini, Chris J.B. Macnab, John E.A. Bertram, and Henry Leung{s.j.hasaneini, cmacnab, jbertram, leungh}@ucalgary.ca, University of Calgary, Canada
OBSERVATIONS
• Metabolic power in running decreases withgravity faster than in walking.
• Previous explanation (Farley and McMahon[1]) based on elasticity in running vs. poten-tial/kinetic energy exchanges in walking
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Cos
t of
Tra
nspo
rt
(meta
bol
ic)
(J/K
g/m
)
Gravity (% g)
Walk
V=1 m/s
Run
V=3 m/s
BIPED MODEL WITHOUT SPRINGS• Realistic mass distribution• Periodic gaits: walking, and running• Extended double support is allowed in walking• Dynamic optimization finds the gaits
• Cost function: mechanical COT = positive workstep length×body mass
• Step length and step frequency are free• Optimizations simulate reduced gravity in two
ways:
• ’hip-lift’ (constant upward force, like experi-ment)
• ’reduced-g’ (reduced g on all body parts)
Actuated
Hips
Feet stay flat
Actuated
Compound
Ankle
Linear Actuators
MODEL PREDICTIONS (ENERGETIC COST)• Model predictions consistent with observations
• Cost cross-overs even without springs
• The energetics is determined by the balance be-tween the stance and swing leg works for mini-mum net cost.
• ’Hip-lift’ and reduced-g optimizations give almostidentical results.
• Springs decrease the cost of running, improvingthe estimates of cross-over gravity levels.
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0 25 50 75 100
Gravity (% g)
Cos
t of
Tra
nspo
rt
(mech
anic
al)
(J/K
g/m
)
Walk
V=1.1 m/s
Walk
V=1.6 m/s
Run
V=3.3 m/s
REFERENCES
[1] C.T. Farley, and T.A. McMahon, “Energetics of walking and running: insights from simulated reduced-gravity experiments,” J.Appl. Physiol., 73(6): 2709-2712, 1992.
[2] A.D. Kuo, “A simple model of bipedal walking predicts the preferred speed-step length relationship,” J. Biomech. Eng., 123(3):264-269, 2001.
KINEMATICSExperiment
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Run
V=2.2 m/s
Walk
V=1.1 m/s
Gravity (% g)
Ste
p Leng
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1/ L
eg
Leng
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Model Prediction
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1.0
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2.0
2.5
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Run
V=3.3 m/s
Walk
V=1.1 m/s
Gravity (% g)
Ste
p Leng
th (
1/ L
eg
Leng
th)
• For walking and running: decreased g results inincreased step length.
• Step length predictions for ’hip-lift’ are slightlyshorter than for reduced-g.
• Optimizations under-estimate step length.
• An extra cost term for fast leg swing (e.g.force/time) improves step length estimates [2].
REDUCED GRAVITY SIMULATOR (CONSTANT UPWARD FORCE)The reduced gravity apparatus based on zero-rest-length springs:
Harness’ Height
Adjusting Winch
Treadmill
Rolling
Trolley
Lever
Spring
Loading/Unloading and
Zero-Rest-Length Spring
Adjusting Winch
Force (Gravity)
Adjusting Grids
Cable
Force Transducer Level Line
Cable
Cable
Designed by Andy Ruina
FINAL COMMENTS• Experimental results support model predictions
• The optimization here predicts energetic and kine-maytic trends without using springs: runningmore affected by gravity than walking
• Main determinant in optimization: trade offs be-tween leg swing and stance costs.
• Some optimization details:
• Some trends are explicable with collision an-gles.
• Optimization in running shows constant costper step as gravity is reduced =⇒ COT ∝ g.
OPEN QUESTIONS• How would springs change these results?
• Besides energy efficiency, what is the role ofpassive compliance in biological locomotion?
ACKNOWLEDGMENTThanks to Prof. Andy Ruina for his technical sup-port and suggestions.