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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1

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0 25 50 75 100

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

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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)

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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

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0 25 50 75 100

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.