Download 1 - Faculty of Health Sciences

Dynamometry
D. Gordon E. Robertson, PhD, FCSB
Biomechanics Laboratory,
School of Human Kinetics,
University of Ottawa, Ottawa, Canada
Biomechanics Laboratory, uOttawa
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Dynamometry
• measurement of force, moment of force
(torque) or power
• torque is a moment of force that acts through
the longitudinal axis of an object (e.g., torque
wrench, screw driver, engine) but is also
used as another name for moment of force
• power is force times velocity (F.v) or moment
of force times angular velocity (Mw)
• Examples of power dynamometers are the
KinCom, Cybex, home electrical meter
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Force Transducers
• devices for changing force into analog or digital
signals suitable for recording or monitoring
• typically require power supply and output device
• types:
–
–
–
–
–
spring driven (tensiometry, bathroom scale)
strain gauge (most common)
linear variable differential transformer (LVDT)
Hall-effect (in some AMTI force platforms)
piezoelectric (usually in force platforms)
• Examples: cable tensiometer, KinCom, Cybex,
Biodex, fish scale, force platform
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Tensiometer
• measures tension (non-directional force)
in a cable, wire, tendon, etc.
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Strain Gauge Force Transducers
• uses the linear relationship between strain
(deformation, compression, tension) in
materials to the applied force (stress)
• materials are selected that have relatively large
elastic regions
• if material reaches
plastic region it is
permanently
deformed and needs
replacement
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Stress-Strain Measurements
• Instron 5567
(Neurotrauma Impact
Science Laboratory,
uOttawa) accurately
measures stress and
strain for a wide
variety of materials
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Strain Gauges
•
•
•
•
can be uniaxial, biaxial, multiaxial
require DC power supply (battery)
can be wired singly, in pairs, or quartets
can measure force, torque, or bending moment
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Strain Link
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Strain Gauge Transducers
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Power Dynamometers
potentiometer
lever arm
strain link
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Strain Gauge Lever
Cybex
KinCom
• use strain gauges to measure normal force
• moment is computed by multiplying by lever length
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Bending Moment for
Moment of Force
• this knee brace was wired to measure
bending moment
• it could therefore directly measure
varus/valgus forces at the knee
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Strain Gauge Force Transducers
Advantages:
– can measure static loads
– inexpensive
– can be built into wide variety of devices (pedals, oars,
paddles, skates, seats, prostheses …)
– portable
Disadvantages:
–
–
–
–
–
need calibration
range is limited
easily damaged
temperature and pressure sensitive
crosstalk can affect signal (bending vs. tension, etc.)
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Force Platforms
• devices usually embedded in a laboratory
walkway for measuring ground reaction
forces
• Examples: Kistler, AMTI, Bertek
• Types:
– strain gauge (AMTI, Bertek)
– piezoelectric (Kistler)
– Hall-effect (AMTI)
• Typically measure at least three components
of ground reaction force (Fx, Fy, Fz) and can
include centre of pressure (ax, ay) and
vertical (free) moment of force (Mz)
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Kistler Force Platforms
portable
standard
clear top
in treadmill
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Piezoelectric Force Platforms
Advantages:
– higher frequency response
– more accurate
– wide sensitivity range (1 N/V to 10 kN/V)
Disadvantages:
– electronics must be used to measure static
forces, drift occurs during static
measurements
– expensive, cannot be custom-built
– require 8 A/D channels
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AMTI Force Platforms
small model
standard model
glass-top model
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Strain Gauge Force Platforms
Advantages:
– ability to measure static loads suitable for
postural studies
– inexpensive, can be custom-built
– fewer A/D channels required (typically 6 vs. 8)
Disadvantages:
– typically fewer sensitivity settings
– poorer frequency response
– less accurate
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Equations for Computing
Centres of Pressure
• centre of pressure locations are not measured
directly
• Kistler:
x = – (a[Fx23 –Fx14 ] – Fx z) /Fz
y = (b[Fy12 –Fy34] – Fy z) /Fz
• AMTI:
x = – (My + Fx z) /Fz
y = (Mx – Fx z) /Fz
• Notice division by vertical force (Fz). This
means centre of pressures can only be
calculated when there is non-zero vertical force.
Typically Fz must be > 25 N.
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Impulse
• Force platforms can measure impulse
during takeoffs and landings
• When the subject performs a jump from a
static position, the takeoff velocity and
displacement of the centre of gravity can
be quantified
Impulse =

t1
t0
Fdt ≈ (S F ) Dt
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Takeoff Velocity
• To compute takeoff velocity
divide the impulse by body mass
• For the vertical velocity, body
weight must be subtracted
vhorizontal = Impulsehorizontal / m
vvertical = (Impulsevertical – W t ) / m
• where m is mass, W is body
weight, and t is the duration of
the impulse
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Centre of Gravity
Displacement
• Displacement of the centre of gravity
can also be quantified by double
integrating the ground reaction forces.
• First divide the forces by mass then
double integrate assuming the initial
velocity is zero and the initial position
is zero. Be sure to subtract body
weight from vertical forces.
• Care must be taken to remove any
“drift” from the force signals.
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Centre of Gravity
Displacement
• shorizontal =
t1
t1
t0
t0
 
( Fhorizontal / m)dt
t1
t1
t0
t0
 
• svertical =
t1
t1
t0
t0
 
2
( F / m)dt 2
([ Fvertical  W ] / m)dt 2
• To compensate for drift (especially with
Kistler force platforms) high-pass
filtering is necessary.
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Squat Jump (BioProc2)
• Example
of a
vertical
squat
jump
(starts in
full
squat)
• red is
vertical
force,
cyan is
AP force
airborne phase
body weight line
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Centre of Gravity (BioProc3)
• Squat
depth was
1.39 cm
• Takeoff
height was
79.6 cm
• Jump
height was
28.3 cm
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