Edward Muybridge 1830-1904 Locomotor kinematics = quantification of limb and body motion Locomotor...
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Transcript of Edward Muybridge 1830-1904 Locomotor kinematics = quantification of limb and body motion Locomotor...
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