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

What do all these animals have in

common?

Locomotion• Complex interaction of the neuromuscular and

musculoskeletal systems• Comes in many forms:

oBipedal: oWalkoRunoSprinto Hop

oQuadipedaloWalkoTrotoGallop

• How do we study something so complex?

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

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 MassMotion

Center of mass- balance point of body

Center of MassMotion

Walking Running

WalkVelocity decreasesHeight increases

Velocity increasesHeight decreases

RunVelocity decreases Height decreases

Velocity increasesHeight 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 = massv = velocityk = kinetic, t = translational

m

Ek,t = 0.5 mv2

v

Gravitational potential energy (Ep,g)

mg = weight of object

ry = vertical position of object

Ep,g = mgry

ry

mg

Elastic energy: energy stored when a spring is stretched or

compressed

Stretched(Energy stored)

Rest length(no energy stored)

Compressed(Energy stored)

Spring

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)

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

Mechanical Energy in Walking

Mid-stance

KE minimized at mid-stanceand GPE maximized at mid-

stance

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

Alexander (1992)

Vertical motion allows mechanical energy

exchange

Walking as Inverted Pendulum

Kineticenergy

Gravitational Potential

Energy

Totalenergy

Time (s)

Single support phase

Perfect Inverted Pendulum

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

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

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

Mechanical Energy in Running

KE and GPE minimized at mid-stance

Mid-stance

KE (J)

GPE (J)

TotalEnergy (J)

Time (s)

Stance phase of running

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

Leg Angle Stiffness

Speed (m/s) Speed (m/s)Farley et al., 1993

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