Transcript Dynamometry - University of Ottawa

Forces and Moments of Force
D. Gordon E. Robertson, PhD, FCSB
Biomechanics Laboratory,
School of Human Kinetics,
University of Ottawa, Ottawa, Canada
Force
• a push or pull
• physical property that causes a mass
to accelerate (i.e., change of speed, v,
or direction, w)
• vector possessing both a magnitude
and a direction and adds according to
the Parallelogram Law
• a resultant force is the sum of two or
more forces
Fa+b = Fa + Fb
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The Resultant Force
•
•
sum of all external forces acting on a body
according to Newton’s Second Law the
resultant force is proportional to the body’s
acceleration. I.e., using a consistent system
of units:
F = m a
•
Where,
m = mass in kilograms
a = acceleration in m/s2
F = force in newtons
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Types of Forces
External forces are environmental forces which act on
the body or the forces exerted by other objects that
come into contact with the body.
Examples:
• gravitational forces especially the earth’s
• frictional forces of surfaces and fluids
• ground reaction forces (includes friction)
• drag (viscous) forces of air (wind) or water
• impact forces of objects
• springs (poles, cables, springboards)
• buoyant force of water
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Types of Forces
Internal forces are forces that originate and terminate
within the body. Sum of all internal forces within any
body is always equal to zero (zero vector).
Examples:
• muscle forces (through tendons)
• bone-on-bone forces (including cartilage)
• ligamentous forces
• joint capsular forces and skin
• fluid (viscous) forces
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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, motor) 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, BioDex and electrical meters
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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: tensiometer, KinCom, Cybex, Biodex,
spring scale, force platform
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Tensiometer
• essentially a spring-type sensor
• measures tension (magnitude of a force)
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Strain Link
• uses strain gauges to measure tiny length
changes in a material that are proporional to
the applied force
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Strain Gauge Transducers
strain link
transducer
S-link load
cell (used in
underwater
weighing lab)
• strain link measured forces from a rowing ergometer
• S-link used during underwater weighing to compute
body density and lean body mass
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Power Dynamometers
potentiometer
lever arm
strain link
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Strain Gauge Lever
• uses strain gauges to measure bending
moment, which can then be used to compute
applied force (Cybex, Kincom, Biodex)
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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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AMTI Force Platforms
small model
standard model
glass-top model
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Pressure Mapping Systems
• Pedar measures
pressures from a matrix
of capacitive sensors to
display a pressure map
• Tekscan F-Scan
measures normal forces
using resistive ink
sensors to display a
force tensor of the
pressure distribution
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Moment of Force
• turning effect of a force
• physical property which causes a rigid
body to change its angular acceleration
• vector quantity with units of newton
metres (N.m)
• also known as a torque or force couple
depending upon its application
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The Resultant Moment of
Force
• sum of all external moments of force acting on
a rigid body
• according to Newton-Euler equations the
resultant moment of force is proportional to
the body’s angular acceleration. I.e., using a
consistent system of units and a particular axis
(A, usually at the centre of gravity)
 MA = IA a
where
IA = moment of inertia about A in kg.m2
a = acceleration in rad/s2
MA = moment of force in N.m
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Types of Moments of Force
External moments are environmental forces
which act on the body or the forces exerted by
other objects which come into contact with
the body.
Examples:
• vertical moment of ground reaction force
• force couple of ground reaction forces
• drill
• eccentric forces
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Types of Moments of Force
Internal moments are moments of force that
originate and terminate within the body. Sum
of all internal moments of force within any
body is always equal to zero (zero vector).
Examples:
• muscle forces (through tendons)
• bone-on-bone forces (including cartilage)
• ligamentous forces
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Moment Transducers
• devices for changing force into analog or
digital signals suitable for recording or
monitoring
• typically require power supply and output
device
• types:
– springs
– strain gauge (most common)
– piezoelectric (usually in force platforms)
• Examples: KinCom, Cybex, Biodex, force
platforms
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Strain Gauge Transducers
torque
transducer
(for forearm
axial torque)
bending
moment
(rowing oar
lock pin)
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Strain Gauge Lever
• uses strain gauges to measure bending
moment and torque (Cybex, Kincom,
Biodex)
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Force Platforms
• devices usually embedded in a
laboratory walkway for measuring
ground reaction forces and moments
of force
• Typically measures vertical (free)
moment of force (Mz) but can also be
designed to measure gripping
moments
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Force Platforms
Kistler
AMTI In
laboratory
stairway
Bertec
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Moments of Inertia
(a)
(b)
(c)
I
2.5 I
5I
(e)
(d)
10 I
10 I
(f)
3.5 I
(g)
2.5 I
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Quick Release Experiment
• used to measure
moments of inertia
non-invasively
• assumes no friction in
the joints
• performed in the
horizontal plane to
eliminate gravity
effects
• angular acceleration
is measured by video
analysis or
electrogoniometry
(a) before release
force transducer
150.0 N
(b) after release
30.0 cm
a = 50.0 rad/s²
axis of rotation
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Law of Reaction
Third Law of Motion
• For every force there must be a reaction force,
equal in magnitude but opposite in direction,
that acts on a different body (e.g., ground)
F=–R
• to increase the size of an action force you must
be able to have an object or surface that can
create a large reaction
• action and reaction are arbitrary designations
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Reaction Forces
reaction
axis of
rotation
centripetal
180 cm
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Reaction Forces
direction of
motion
action
force
centripetal
force
centre of curvature
track
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Banking of Tracks
• Ground reaction force (Fg) should pass
through centre of gravity, otherwise the
person rotates (about A/P axis).
• To run the bend, Fg must provide a radial
acceleration. I.e.,
Fr = mar = –mvt2/r (recall ar = rw2 = vt2/r)
where
r is radius of curvature of the bend
vt is transverse velocity (race speed)
m is mass
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Banking of Tracks
centre of
gravity
normal
force = Fg
weight

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Banking of Tracks
centre of
gravity
weight and
normal cause
rotation
normal
force = Fg
weight

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Banking of Tracks
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Banking of Tracks
y
+
r
centripetal force
= – mvt2/r
add banking

Ideal angle of banking =  = tan-1(vt2/rg)
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Banking of Tracks
y
+
r
banking permits
a normal force
that acts through
centre of gravity
causing no
rotation
centripetal force
= – mvt2/r

Ideal angle of banking =  = tan-1(vt2/rg)
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Banking of Tracks
• since  = s / r thus r = s / 
• for sprinting at 10.0 m/s
• 100 bend: r = 100 / p = 31.8 metres
 = tan-1 [102 / (31.8 x 9.81) ]
= 17.8 degrees
• 50 m bend: r = 50 / p = 15.9 metres
 = tan-1 [102 / (15.9 x 9.81) ]
= 32.6 degrees
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