ADVANCED BIOMECHANICS OF PHYSICAL ACTIVITY
Laboratory Experiments: Measurement and Interpretation of Ground Reaction
Forces, Center of Pressure, and Impulse-Momentum Relationships
Dr. Eugene W. Brown
Purposes:
This laboratory experiment has several purposes. They include:
1.
developing an understanding of the terminology associated with the use of
force platforms;
2.
showing how to set up and use a force platform system to collect kinematic
data;
3.
explaining the concept of center of pressure and its relationship to forces
applied to a force platform;
4.
teaching the use of the Trapezoid and Simpson’s Rule for calculating areas
under curves associated with parameters equally spaced in time;
5.
developing an understanding of the concept of “productive” impulse;
6.
reviewing the relationships between the Law of Conservation of Energy,
impact velocity, and area under a force-time curve;
7.
reviewing relationships between the Law of Conservation of Energy and the
Law of Uniformly Accelerated Motion;
8.
reviewing vector addition and resolution and the calculation of projectile
range;
9.
developing an understanding between impulse-momentum relationships; and
10. understanding how the acceleration of individual segments of the body
influence the shape of a force-time curve
List of Equipment and Supplies:
1.
APAS system and software for recording and displaying ground reaction
forces, center of pressure, and impulse
2.
AMTI force platform for recording Fx, Fy, Fz, x, y, and z
3.
AMTI supplied calibration parameters
4.
a subject who is free of orthopedic problems that can engage in vertical,
horizontal, and drop jumps without concern for injury
5.
9V batteries
6.
tape measure
7.
jump and reach measurement device
8.
transparent graph paper large enough to cover the top surface of force
platform
9.
marking pen
10. ladder(s)
11. suspension bar for the drop jumps
12.
13.
14.
Definition of Terms:
1.
Anterior-posterior force – force relative to the front and back of the body;
shear force parallel to the surface of the force platform (Figure 1)
normal force (-Fz)
medial force (-Fx)
posterior force (-Fy)
anterior force (+Fy)
lateral force (+Fx)
Figure 1 – Orthogonal forces.
2.
3.
4.
Axis system – three dimensional Cartesian coordinate system relative to the
force platform; X is medial-lateral, Y is anterior-posterior, and Z is
vertical
Center of gravity – the center of mass distribution of an object (e.g., the
human body or body parts)
Center of pressure – X,Y Cartesian coordinates of the resultant ground
reaction force vector on the force platform; note that the Z coordinate0,
(see AMTI supplied value)
Xp = -(moment about the Y axis)/Fz = -(y)/ Fz
Yp = (moment about the X axis)/Fz= (x)/ Fz
*T. Shimba (1984). An estimation of center of gravity from force platform data. Journal of Biomechanics, 17(1), 53-60.
5.
6.
7.
Force platform – instrumented rigid metal plate used to electronically measure
orthogonal ground reaction forces; moments about the X, Y, and Z axes;
and the center of pressure
Ground reaction force – force vector equal and opposite to the sum of the
forces experienced by the surface of the force platform
Impulse – equal to the product of force and time(Ft); measured in units of
Newton seconds (Ns)
-----------------------------------------------------------------------------------------------------------F = ma  force causes an acceleration of a mass
F = m(v/t)  substituting (v/t) for acceleration
Ft = mv  impulse = change in momentum
8.
9.
10.
11.
12.
13.
14.
Integral – the area under a curve (e.g., area under the force x time curve is the
product of these two parameters and is equal to impulse
Medial-lateral force – force in the direction of the left or right sides of the
body; shear force parallel to the surface of the force platform (Figure 1)
Moment – a turning force; the product of force and perpendicular distance of
the line of force to the point of rotation; measured in Newton meters
(Nm)
Momentum - a product of mass and velocity (mv); measured in units of
kgm/second
Normal force – force perpendicular to the surface of the force platform
(Figure 1)
Orthogonal – X, Y, and Z axes of Cartesian coordinate system used to
represent the directions of independent forces and moments about these
axes
Simpson’s Rule – an equation that uses a parabolic function to represent the
area under a curve (integral)
tn
 tn  t0 

  
  
     
Fdt


 3n  F t 0  4 F t1  2 F t 2  ...  2F t n2  4F t n1  F t n


t0
where t is the discrete even increments of time beginning with t0 and ending
with tn; note that an odd number of sampled time values is required to result in
an even number of intervals
force (N)
t0
t1
t2
tn
time (sec)
Figure 2 – Force-time curve (impulse) over the time interval t0 – tn.
15.
Trapezoid Rule – an equation that uses the sum of trapezoids to represent the
area under a curve (integral)
force (N)
t0
t1
t2
t3
t4
time (sec)
t5
t6
Figure 3 – Approximation of the area under the force-time curve by a series of 6
rectangles.
The area under the force-time curve can be divided into several rectangles, with known
width and representative height, and then summed to approximate the area under the
curve. To determine the representative height (hi) of each rectangle, the following
equation applies:
F(ti) + F(ti+1)
hi = _______________ , where i = 0 – 6 and F(ti) is the force at ti.
2
Therefore, the area of the rectangle is determined by hi(t) which is equal to the area of a
trapezoid. Therefore,
5
t
to Fdt  0 hi t  
6
of the areas of the 6 trapezoids.
As t  0 with an increasing number of trapezoids, the calculated area becomes closer to
the actual area under the curve.
General Methods and Procedures:
There will be 5 experiments to highlight the different purposes of this laboratory.
Students must share the responsibilities of carrying out these experiments. The
general methods and procedures for each of these experiments is as follows:
1.
Subject Preparation
a.
The subject should be dressed for activity (various jumps) in athletic
shoes, socks, t-shirt, and shorts.
b.
Use the force platform system to obtain and record the weight of the
subject (wearing activity cloths and shoes).
c.
Before collecting data in each of the experiments, the subject should be
familiarized with the setting and tasks to be performed.
d.
It is appropriate to provide a warm up and a few practice trials. This
may reduce the chance of injury.
2.
Positioning the Force Platform –
a.
Review the function and structure of the activity deck of the
Biomechanics Research Station.
b.
Take all suggested precautions and position the force platform, access
panels, and configuration spacers for this series of experiments.
3.
Calibration of the Force Platform System – The only calibration that can be
performed locally is a static evaluation of the vertical force records.
Generally, calibration of force platforms requires special equipment and must
be done by the manufacturer. Our system was recently sent back to the
manufacturer for calibration and can be assumed to be accurate, especially for
the experiments that will be conducted. A demonstration will
be given on the how the calibration coefficients supplied by the manufacturer
are used in conjunction with the APAS system.
4.
Data Collection – Records saved and subsequently printed from each
experiment must be properly identified with the following information:
subject ID#, type of physical activity performed, experiment number, trial,
type of data, and sampling frequency.
Specific Methods and Procedures:
In addition to the general methods and procedures, the 5 individual experiments have
their own specific methods and procedures that must be followed. Prior to collecting data
for these experiments, have the subject stand on the force platform and record body
weight at 100Hz. Use 1000Hz for all subsequent records.
Experiment 1 – Center of Pressure
a.
Lightly adhere transparent graph paper to force platform with its axis
system aligned with the axis system of the force platform.
b.
Label the axis system of the adhered graph paper indicating the unit
increments and directions.
c.
Have the subject assume a standing position, on the adhered graph
paper, with the palms of the hands facing the thighs and the feet spread
apart, but within the borders of the graph paper and force platform.
d.
Carefully draw an outline of the shoes on the adhered graph paper.
***Once the outline of the shoes is completed, the subject should not
e.
reposition the feet until this experiment is completed.***
For each of four leaning positions (forward, backward, side-right, and
side-left), have the subject assume a stationary posture and record the
ground reaction forces and moments for a short interval of time. A low
sampling frequency should be used.
Experiment 2- Drop Jumps with Soft and Hard Landing
a.
The subject assumes a suspended position, hanging from the hands, with the
soles of the shoes approximately one meter directly above the force platform
and oriented as if standing on the floor.
b.
Measure the vertical distance from the soles of the shoes to the surface
of the force platform.
c.
The subject performs two drop jumps. In the first, the goal is to
“absorb” the force of the landing. The second should be performed like
a gymnast “sticking” the landing.
d.
After each style of landing, the subject must quickly attempt to
assume the same stationary body configuration, with the upper
extremities over head, as when suspended before the drop jump.
Experiment 3 – Maximum Vertical Jump and Reach with One- and Two-Foot
Take-Off
a.
Use standard protocol to record a jump and reach test with exceptions
specific to this experiment:
1) The subject should assume a standing position with the body and
extremities configured similar to the configuration that will be
taken at the peak of the jump and reach (i.e., upper extremities
over head). The subject must hold this position with minimum
movement until signaled to jump.
2) The person giving the signal to jump should say “Ready”, then
immediately trigger the force platform system to record, and them
immediately say “Jump.”
3) The subject should stand motionless until commanded to jump. At
that point, a quick jump and reach movement for maximum height
should be executed.
4) When landing, after the jump for maximum height, the subject
must straddle the feet so that landing does not occur on the force
platform.
b.
Repeat 1)-4), except the subject performs the jump and reach test
from a one-foot take-off.
Experiment 4 – Standing Long Jump for Maximum Distance
a.
The subject must place the toes of his/her shoes slightly behind a starting
line on the force platform and make a maximum standing long jump.
b.
If the subject lands without falling, measure the distance of the jump
from the starting line to a line just forward of the toes of the shoes.
c.
If the subject does not land without falling or shuffling his/her feet, the
jump must be repeated.
Experiment 5 – Standing Long-and-High Jump
a.
The subject must place the toes of his/her shoes slightly behind a starting
line on the force platform and make a jump that emphasizes a
combination of height and distance.
b.
If the subject lands without falling, measure the distance of the jump
from the starting line to a line just forward of the toes of the shoes.
c.
If the subject does not land without falling or shuffling his/her feet, the
jump must be repeated.
Results:
The results are the responses to the statements that follow. They are to be written in a
scientific format. You should develop figures, graphs, and spreadsheet tables and refer to
these in your write-up to make the results easy to read. Also, include and label graphs
generated as output from the APAS system to highlight how you obtained your results.
Your format should differ from the normal scientific format in that you must show your
work (i.e., how you calculated the results). If there are several iterations of the same
calculation process, you only need to show the first to demonstrate your understanding.
Experiment 1 – Center of Pressure
1.
Use values for Fz, and moments about the X and Y axes obtained from the
APAS to determine the center of pressure for the four leaning positions.
Show your work.
2.
Record the X, Y Cartesian coordinates of several points on the outline
drawing of the soles of the shoes. Use these points to redraw the outline of
the soles of the shoes on a smaller sheet of graph paper.
3.
On the graph paper with the redrawn outline of the soles of the shoes, label
points representing the coordinates of the center of pressure for the four body
positions.
4.
Explain the results of this experiment.
Experiment 2- Drop Jumps with Soft and Hard Landing
1.
Identify the magnitude and direction of the maximum vertical, anteriorposterior, and medial-lateral forces for the two styles of drop jump.
2.
Identify the time for the starting and ending point of the vertical force-time
curves for the two drop jumps (“absorb” and “stick”). Note that the start
should be the time at which the force becomes greater than zero and the end
should be the point at which the force values become equal to the subject’s
body weight.
3.
Use the APAS software to determine the vertical impulse (area under the
force-time curve) associated with each of the drop jumps from the time
designated as the start to the time designated as the end. Report these values
and the sampling rate.
4.
Divide the total time (start to end) into 10 equal time intervals and calculate
the area under the vertical force-time curve for the “absorb” drop jump using
the Trapezoid Rule. Show your work. Compare the results to the value
obtained from the APAS system. What do you think is (are) the reason(s) for
5.
6.
the differences? Repeat this process for 20 equal time intervals. Show your
work. Is this calculated impulse closer to the value obtained from the APAS
system than the one calculated from the 10 time intervals? Explain.
Divide the total time (start to end) into 10 equal time intervals and calculate
the area under the vertical force-time curve for the “stick” drop jump using the
Simpson’s Rule. Show your work. Compare the results to the value obtained
from the APAS system and the results obtained from the Trapezoid Rule when
10 intervals were used. What do you think is (are) the reason(s) for the
differences between the areas calculated by the Trapezoid and Simpson’s
Rules and the value from the APAS system?
Use the vertical impulse from the “absorb” drop jump to verify the measured
height from which the subject dropped to the surface of the force platform.
Show your work.
-----------------------------------------------------------------------------------------------------------Note: Because of the Law of Conservation of Energy, the potential energy (mgh) in the
suspended position is equal to the kinetic energy (½mv2) at the point of landing.
mgh = ½mv2 ,
where m = mass of subject, g = acceleration of gravity (9.81meters/second2),
h = height on drop, and v = velocity immediately prior to landing.
h = (½v2)/g ,
where v = v = change in velocity of the mass of the subject from the initial contact with
the force platform to the point at which the subject is standing in a stationary position in
the same configuration as when suspended.
“productive” impulse* = change in momentum
or
ft =mv , where f = force and t = time
Therefore, v = (ft)/m and
h = {½[(ft)/m]2}/g
---------------------------------------------------------------------------------------------------* In the vertical direction, the value that is used in calculating v is the area under the
force time curve minus the impulse associated with the person’s body weight over the
same time interval. This difference might be termed “productive” impulse.
body weight = mg
vertical force
(N)
time (sec.)
starting
time
ending
time
A
B
Figure 4 – Productive impulse. (Area under curve A minus area under curve B (body
weight x time) equals productive impulse. There is no impulse associated with body
weight for force-time curves in the anterior-posterior and medial-lateral directions
because the body’s weight only acts in the vertical direction.)
7.
8.
Calculate the difference between the distance dropped as determined with the
tape measure and as determined using the Law of Conservation of Energy and
impulse-momentum relationships. Provide plausible reasons for this
difference.
Compare the productive impulse for the two styles of landing. Were these
values expected? Explain.
Experiment 3 – Maximum Vertical Jump and Reach with One- and Two-Foot
Take-Off
1.
Identify the time for the starting and ending points of the vertical force-time
curves for the two jumping techniques (one-foot and two-foot take-off). Note
that the start should be the time at which the force begins to differ from the
subject’s body weight and the end should be the point at which the force
values become equal to zero.
2.
Use the APAS software to determine the vertical impulse (area under the
force-time curve) associated with each of the two jumping techniques from
the time designated as the start to the time designated as the end. Report these
values. Subtract the impulse associated with body weight over the same
interval of time (start to end) and report the “productive” impulses. Show
your work.
3.
Use the vertical “productive” impulse from the two-foot take-off to verify the
measured height of the jump and reach test. Show your work.
-----------------------------------------------------------------------------------------------------------Note: The following equations are obtained from the Laws of Uniformly Accelerated
Motion:
vf = vi + gt ,
where vf = final velocity, vi = initial velocity,
g = acceleration of gravity (9.81meters/second2), and t = time in seconds.
In the vertical jump, the final velocity at the peak of the jump is zero. The initial velocity
is the velocity at which the subject leaves the force platform. This is associated with the
“productive” impulse and is equal to v.
“productive” impulse = change in momentum
or
ft =mv
v = (ft)/m = vi
The initial velocity value is entered into the equation vf = vi + gt (or 0 = vi + gt) to
determine the time to the peak of the jump.
h = vit + ½gt2
The height of the jump can be determined from this equation.
4.
Calculate the difference between the vertical distances in the two-foot take-off
as determined by the jump and reach test and as determined using the Laws of
Uniformly Accelerated Motion and impulse-momentum relationships. Show
your work. Provide plausible reasons for this difference.
5.
Explain how the equation
f = m1a1 + m2a2 + m3a3 + m1a1 + … mnan ,
where each ma represents the acceleration of a different part of the body,
composed of n parts,
relates to variations in the force-time curves of the two techniques of jumping.
Experiment 4 – Standing Long Jump for Maximum Distance
1.
Identify the time for the starting and ending points of the vertical and anteriorposterior force-time curves for the standing long jump for maximum distance.
Note that the starting time for both curves should be the time at which the
vertical force begins to differ from the subject’s body weight and the end
should be the point at which the force values become equal to zero.
2.
Use the APAS software to determine the vertical impulse (area under the
force-time curve) from the time designated as the start to the time designated
as the end. Subtract the impulse associated with body weight over the same
interval of time (start to end) and obtain the vertical “productive” impulse.
Show your work.
3.
Use the APAS software to determine the anterior-posterior impulse (area
under the force-time curve) from the same time designated as the start to the
time same time designated as the end.
4.
Use the vertical “productive” impulse and the anterior-posterior impulse to
calculate the vertical and horizontal take-off velocities, respectively. Show
your work.
5.
Use the vertical and horizontal take-off velocities to determine the magnitude
and direction (angle relative to the horizontal) of the resultant take-off
velocity. Show your work.
6.
Assume that the height of the center of gravity of the body, above the ground,
is the same for take-off and landing in the standing long jump for maximum
distance. Use the vertical and horizontal take-off velocities to calculate the
distance jumped. Show your work.
Note: From the Laws of Uniformly Accelerated Motion,
vf = vi + gt .
From this equation the time to the vertical peak of the jump can be calculated. Since the
time to the peak is the same as the time back to the ground, the total time is 2t. The
anterior-posterior component of velocity can be assumed to be constant. Therefore, the
horizontal distance jumped can be calculated by
distance jumped = (anterior-posterior velocity)(2t).
7.
Determine the difference between the measured distance jumped and the
distance calculated from the vertical and anterior-posterior velocity vectors at
take-off for the standing long jump for maximum distance. Provide plausible
reasons for this difference.
Experiment 5 – Standing Long-and-High Jump
1.
Repeat 1-5 from Experiment 4.
2.
Compare and contrast the vertical, anterior-posterior, and resultant velocity
vectors and the angle of take-off from Experiment 4 and Experiment 5. What
relationships were observed between these variables? Explain.