Edward Muybridge 1830-1904

Locomotor kinematics= quantification of limb and body motion

Locomotor dynamics= analysis of forces and moments

Lecture # 16: Running and Walking

Walking

=

Inverted pendulum

frictionless pendulum swings forever exchange kinetic & potential energy

kinetic

gravitationalpotential

one stride

one stride

Walking

v

y

y

h, height of center of mass

h

mgh (GPE)

v ½ mv2 (KE)

stride 1 stride 2

G.P.E.& K.E.are out of phase(exchangepossible)

Walking1) No aerial phase2) exchange of

G.P.E. and K.E.

Simulated Biped Robotic Biped

Walking

What keeps mass following this arc?

Walking

v0

Lrequiredcentripetal acceleration =

v02/L

Only source of downward acceleration is g.

Therefore, mass follows arc if g > v02/L

Only source of downward acceleration is g.

Therefore, mass follows arc if g > v02/L….

…or v02/gL < 1

v02/gL is called Froude number (a dimensionless #),

also defined as ratio of inertial to gravitational forces.

DETERMINES WALK-TO-RUN TRANSITION!

WalkingWalkingv0

L

Example 1: Does this work for humans?What is predicted walk-to-run transition speed?

V = (gL)-½

L = 0.9 mg = 9.8 m/s2

V = 3 m/s – ‘jogging’ speed for most people

Example 2: What is walk-to-run transition on moon?

V = (gL)-½

L = 0.9 mg = 0.17 x 9.8 = 1.6 m/s2

V = 1.2 m/s – ‘jogging’ speed on moon

Example 3: What is walk-to-run transition for ant?

V = (gL)-½

L = 0.001 mg = 9.8 m/s2

V = 0.1 m/s ~ 100 body lengthsfor humans ~ 3 body lengths

Running

=

spring mass model

swing stance swingstance

Runningswingstance

height, hL

-yx

dx/dt = constant

Uvert dy/dt

h

GPE

-k LEPE

KE

E.P.E.& K.E.are partially out of phase(exchangepossible)

ballistic ballisticKE-EPE

exchangeKE-EPE

exchange

structuralelement(bone)

tensileelement(ligament/tendon)

elasticelement(tendon)

actuator(muscle)

Running

GaitsWalkd.f. >0.5

Left

Right

stance swing

stancestance+swing

dutyfactor =

Rund.f. < 0.5

Left

Right

aerial phase

Hop0< d.f.<1

Left

Right

Quadrapedal Gaits

stancestance+swing

dutyfactor =Walk

Left Front

Left Hind

Right Front

Right Hind

always 3 feet on ground

Run

Left Front

Left Hind

Right Front

Right Hind

aerial phase(trot)

Run

Left Front

Left Hind

Right Front

Right Hind

aerial phase(pace)

Run

Left Front

Left Hind

Right Front

Right Hind

aerial phase(bound)

Run

Left Front

Left Hind

Right Front

Right Hind

aerial phase(gallop)

COM

Left Front

Left Hind

Left Middle

Right Front

Right Hind

Right Middle

Hexapedal Gait = Tripod