Biomechanics: components of the human body · 9/9/2014 · • Series elasticity allows muscle to...
Transcript of Biomechanics: components of the human body · 9/9/2014 · • Series elasticity allows muscle to...
Biomechanics
MCE 493/593 & ECE 492/592 Prosthesis Design and Control
September 9. 2014
Antonie J. (Ton) van den Bogert Mechanical Engineering
Cleveland State University
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Viewpoint
• Scientific background – physics, (comparative) anatomy
– & a little bit of neurophysiology
• Engineering background – mechanical engineering
– & a little bit of control engineering
• What does a prosthetic designer need to know? – design and control of human limbs
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Components
• Skeleton and joints (mechanical linkage) – kinematics, statics
• Muscles – mechanical properties
– “motor” specifications
– how they are attached to the skeleton
• Neural control – sensors
– circuits
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Joints
• Ball joints, 3 DOF
– hip, shoulder
• Hinge joints (revolute joints), 1 DOF
– elbow
• Universal joints, 2 DOF
– wrist, ankle
• Knee
– can be approximated as a hinge (but more later)
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Kinematics
• Human arm has 7 degrees of freedom (excluding fingers) – one more than required for hand positioning
– is the extra DOF useful?
– are prosthetic arms designed the same way?
https://www.youtube.com/watch?v=R0_mLumx-6Y
DEKA Arm
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Kinematics
• Human leg has approximately 6 degrees of freedom
– foot can have any position and orientation relative to pelvis
– why is this important?
• Are prosthetic legs designed the same way?
http://www.austpar.com/portals/prosthetics/c-leg.php
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Knee joint
rotation in transverse plane internal rotation – external rotation range of motion about ± 10 degrees mostly controlled by ligaments (passive) neglected in prosthetic limb design
rotation in sagittal plane flexion – extension range of motion: 160 degrees mostly controlled by muscles (active)
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Knee joint as a 4-bar linkage
human knee 4-bar (polycentric) prosthetic knee
instant center of rotation
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Polycentric knee vs. stance control
C-Leg ($50,000) microprocessor controlled hydraulic damper
polycentric knee www.d-rev.org $80
Mauch SNS ($5,000) hydraulic damper with mechanical switching of damping coefficient
pro and con of each concept?
http://d-rev.org/media/?video=kamal-jaipurknee
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Human leg operates close to kinematic singularity of the 2-link leg
• Robots and animals seem to avoid such postures
• Why do people do this? • Implications for prosthesis design
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Relationship between knee torque and external force
• 1-DOF model
– q: knee flexion angle
– y: downward direction
• Velocity Jacobian
• Dynamics equation
• Static case, neglect leg weight:
q
y Fy
yT FJqgqqqCqqM )(),()(
2sin qLFy
does minus sign make sense?
L
L
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Standing up from deep squat
• Is not done well by current prostheses (why?)
• Homework assignment (on the course website)
• What motor torque and motor speed are required?
• Find a commercially available motor with this capability
• Are size and weight appropriate for a prosthetic limb?
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fascicle: bundle of cells cell (muscle fiber): 50-100 mm, 1-10 cm long myofibril: 1-2 mm diameter
structure of skeletal muscle
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sarcomere is the basic contractile unit
2 mm
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mechanism of contraction http://www.mrc-lmb.cam.ac.uk/myosin/motility/XBcycle.html
actin filament
myosin filament & myosin head (crossbridge)
ATP ADP
ATP is energy source of muscle contraction - needed for crossbridge to detach - rigor mortis: crossbridges remain attached
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muscle activation: electricity
Luigi Galvani (1737-1798) action potential travels along fiber
release of Ca ions from sarcoplasmic reticulum
Ca ions bind to Troponin C in actin filament
myosin heads can now attach to actin filament
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Effect of stimulation frequency on force rat gastrocnemius, supramaximal pulses (100 ms) on nerve cuff
electrode
Roszek & Huijing, 1997
Hz
Hz
Hz
Hz
twitches
fused tetanus
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Motor units
• a set of muscle fibers that are all innervated by the same motor neuron
• 10 fibers (eye muscle) to 1000+ fibers (gastrocnemius)
• number of motor units decreases with age
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Fiber types
• Type I or type S (slow) - Slow twitch, fatigue-resistant (smallest)
• Type IIa or type FR (fast, resistant) - Fast twitch, fatigue-resistant (larger)
• Type IIb or type FF (fast, fatigable) - Fast twitch, easily fatigable units (largest force)
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Motor unit recruitment
Walmsley et al. (1978)
• CNS: smallest MU first
• Electrical (FES): largest first,
therefore it is hard to control
muscle force
http://nmrc.bu.edu/tutorials/motor_units/
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• Frog semitendinosus,
single fiber, fixed ends
(isometric)
• activate muscle
• measure force
• turn off activation
• change length
• repeat
Mechanical properties dependence of force on length in activated muscle tissue
Gordon, Huxley & Julian, J Physiol, 1966 21
Mechanical properties contribution of passive and active properties to isometric force-length
relationship (whole muscle)
“optimal” fiber length
passive force
total force
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Force-length relationship becomes a torque-angle relationship that can be measured
Pincivero et al., J Biomech 2004. Maximum extensor torque as a function of knee flexion angle At which knee angle are the fibers shortened?
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Non-isometric conditions
• Force-velocity property
*quick release experiments
1. Stimulate the muscle fiber to isometric force F0 at L0.
2. Release the catch after the muscle force reaches steady state.
3. Isotonic contraction (constant force)
4. Steady-state
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shortening velocity (fiber lengths per second)
force
isometric force
-10 -5 0 5 10 0
0.5
1
1.5
isometric eccentric concentric
• Vmax is about 10 fiber lengths per second (mixed fiber type muscle)
• a (the Hill constant) is about 0.25
• maximal eccentric force is 20-100% larger than maximal isometric force
AV Hill, Proc Royal Soc 1938; B Katz, J Physiol (Lond) 1939
FORCE-VELOCITY RELATIONSHIP OF ACTIVE MUSCLE FIBER
aVV
VV
F
F
iso
max
max
Hill’s equation for concentric contraction:
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Power-velocity curve
-10 -5 0 5 10 -2
-1.5
-1
-0.5
0
0.5
1
1.5
2
shortening velocity (fiber lengths per second)
• power (Watts) =
force (Newton) * velocity (m/s)
• peak power output occurs at
about 33% of maximal
shortening velocity • in bicycling, choose a gear
that causes the main
muscles to operate at a
shortening speed of 3-4 fiber
lengths per second
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The force-length-velocity relationship
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Muscle architecture
parallel-fibered pennate
with same muscle volume, more force (more fibers in parallel) but shorter fibers and therefore a smaller shortening range
Physiological Cross-Sectional Area (PCSA): muscle volume divided by average fiber length. Muscle strength is determined by PCSA:
kPa 250cm N 25 -2max
PCSAF maxmax
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Peak power per kg muscle mass
mass = 1; % assume a 1 kg muscle density = 1000; % density, in kg per cubic meter volume = mass/density; fiberlength = 0.08; % typical for human leg muscle PCSA = volume/fiberlength; Fmax = 250e3*PCSA % maximal isometric force Vmax = 10*fiberlength; V = 0:0.01:1; % look at speeds up to 1 m/s a = 0.25; % Hill constant F = Fmax.*(Vmax-V)./(Vmax+V/a); % Hill equation F = max(F,0); % only positive forces are possible P = F.*V; % compute power plot(V,P); xlabel('contraction velocity (m/s) ') ylabel('power output at full activation (W) ');
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Muscle vs. motor
• Muscle – average power 100 W/kg
• muscle is not always at optimal length
• muscle is not always at optimal velocity
– efficiency 25% (75% heat)
– max contraction speed 0.5 – 1.0 m/s
• Electric motor (example) – 200 W, 300 g (667 W/kg)
– efficiency 89%
– max speed depends on design and gearbox
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Series Elasticity
• Contractile force is transmitted through an elastic aponeurosis and (often a long) tendon
• How does such a combined muscle-tendon unit function?
• Advantages – allows efficient “pogo-
stick” effects in locomotion, with almost no muscle length change
– other advantages?
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Three-element Hill muscle model
• Contractile Element (active tissue), Parallel Elastic Element, and Series Elastic Element (passive properties)
• Force response to dynamic length changes
– computer model
– experiment
bone bone
neural stimulation
PEE
CE
SEE
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mathematical model
1 cm 2.5 cm
motor controls muscle length Lm(t)
max.stim
CE SEE
Force in contractile element:
dt
dLgLfaVgLfFaF CE
CECECECE )()()(max
activation (between zero and one)
isometric force-length relationship (between 0 and 1)
velocity-dependence (between 0 and 1.5)
-10 -5 0 5 10 0
0.5
1
1.5
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mathematical model
motor controls muscle length Lm(t)
max.stim
CE SEE
Force in series elastic element:
slack2
slack
slack
if)(
if0
LLLLk
LLF
SEESEE
Lslack
LSEE
FSEE
Because CE and SEE are in series • FCE = FSEE • LCE + LSEE = Lm(t)
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Muscle contraction dynamics
motor controls muscle length Lm(t)
max.stim
CE SEE
)(
))((
: for solve
))(()(
)()(
max
2slack
2slackmax
2slackmax
CE
CEminvCE
CE
CEmCE
CE
SEECE
CE
SEECE
LfFa
LLtLkg
dt
dL
dt
dL
LLtLkdt
dLgLfFa
LLkdt
dLgLfFa
FF
differential equation, solve for state variable LCE(t) and then compute muscle force 2
slack ))()(( LtLtLkF CEmSEE
Matlab program available on course website 35
simulation of ramp stretch experiment
motor controls muscle length Lm(t)
max.stim
CE
SEE
• Muscle has high “short-range stiffness”
• May play a role in control and stability
of movement
• Theoretical models can predict this
behavior
• Hill model
• crossbridge models (chemical kinetics)
Dynamic shortening against inertial load Galantis et al., J Physiol 2000
computational model
muscle velocity
endpoint velocity
http://www.rvc.ac.uk/Research/Video/ccspringmasslinear.dcr
“power amplification”
• Series elasticity allows muscle to work at a shortening velocity
that is different than the endpoint velocity
• Peak power output of muscle-tendon complex can be about 40% higher
than if the muscle acted alone (jumping, throwing)
• Also measured in human experiments
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Elastic tissue can generate catapult-like effects
• When muscle fibers alone are too slow
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Kurokawa et al., 2001 human jumping (homework assignment) Wilson et al., Nature 2003
horse galloping BE: elastic energy stored in biceps KE,PE: kinetic/potential energy of limb
Natural oscillations in a horse forelimb simulated with 3-element Hill muscle models
Wilson et al., Nature 2001
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