BIOMECHANICAL ANALYSIS OF PHYSICAL ACTIVITY
Laboratory Experiments: Measurement and Interpretation of the Kinematics of the
Center of Gravity of the Human Body
Dr. Eugene W. Brown
Purposes:
These laboratory experiments have several purposes. They include:
1.
developing or reviewing the concepts of levers,
2.
understanding how to use a reaction board to calculate the center of gravity
of the human body,
3.
understanding how to use the segmental method to calculate the center of
gravity of the human body,
4.
understanding the use of Walton templates in determining the center of mass
of various segments of the human body,
5.
reviewing concepts of mass segment parameters,
6.
understanding the concept of the center of gravity,
7.
reviewing concepts of projectiles and vectors,
8.
developing an understanding of experimental methods in biomechanics,
9.
learning how to use a camera for two dimensional videography,
10. understanding the relationship of experimental error to measurements
recorded,
11. preparing subjects for participation in research experiments,
12. setting up experimental procedures in biomechanics,
13. understanding how to calculate field and frame rates, and
14. learning how to report the results of laboratory experiments.
List of Equipment and Supplies
1.
acetate grids
2.
adult male and female subjects
3.
background curtain
4.
block to support reaction board
5.
calculator
6.
camera tripod
7.
carpenter’s square
8.
computer and software for down loading video images
9.
fiducial markers
10. laser pointer
11. level
12. mass-segment data sheet
13. plumb bob
14. reaction board
15. reference measure (meter stick)
16. subject and trial board and numbers
17. tape
18. tape measure
19. timing light box
20.
21.
22.
23.
24.
25.
26.
27.
video camera
video tape
Walton Template
weight scale
Definition of Terms:
1.
center of gravity – center of mass distribution of an object
2.
equilibrium – a condition in which the sum of all forces and torques acting on
an object equals zero resulting in a constant linear and angular velocity
3.
fiducial – two or more marks placed in the field of view of a video or motion
picture camera (usually at the outer edges of the field of view) to be used
to align sequential images to a laboratory coordinate system
4.
field rate – the number of pictures of video captured in a known period of time
(e.g., 30 fields/second)
5.
frame rate - the number of pictures of motion picture film captured in a known
period of time (e.g., 100 frames/second)
6.
optic axis of lens – line perpendicular to the long axis of a lens
7.
perspective error – error which occurs when parts of a body or implement lie
outside the principle photographic plane; image of segment closer to the
camera appears larger and segment farther away appears smaller
8.
plumb bob – weighted string that hangs vertical which is used for spatial
orientation
9.
reaction board – board that is used as a lever to transmit force to weighted
scale for purposes of determining the center of mass of objects (e.g.,
human body) placed on it
10. reference measure – an object of known length (e.g., meter stick) that is
placed in a plane that is perpendicular to the optic axis of the lens of a
camera that is used to assist in determining distance measurements in the
same plane
11. segmental method – procedure used to calculate the center of mass of a multisegmented system (e.g., human body, horse) that is based on known
segment masses and mass centers of gravity of a similar model (e.g.,
cadaver of a human, cadaver of a horse)
12. timing lights – electronic device that uses lights to accurately display time
13. vector – a measure that is represented by magnitude and direction (e.g.,
displacement, velocity, acceleration, force, momentum)
14. Walton template – a standard measurement device, unique to each segment of
the body, that is used to determine the location of the center of gravity of
each body segment based on known proportions of the center of gravity
from the proximal and distal ends of each segment
14. whole body method – a procedure for determining the location of the center of
gravity of a multi-segmented system (e.g., human body, horse) in one
configuration without regard for the position of individual segments
(e.g., reaction board, pendulum)
15.
16.
Review:
1.
2.
Projectile
Vectors
Reaction Board for the Calculation of Whole Body Center of Gravity
Basically, the reaction board method for the calculation of the center of gravity of the
whole body is based on the principle of levers. In a static lever system, the sum of the
forces and the sum of the torques are equal to zero. The reaction board system is such a
system. If an imaginary fulcrum is placed at the knife edge aligned with the dorsum of
the feet, the sum of the positive (counterclockwise) torques and negative (clockwise)
torques must equal to zero. In other words:
(Fs)( Lb) = (Wtboard)( 1/2Lb) + (Wtbody)( Lcg)
In this equation, the only variable that is not known is the location of Lcg. Therefore, we
can solve for this parameter.
Fs
Key:
Fs – force read at the scale; upward force applied to the board by
the scale
Wtbody – weight of the body acting downward at the center of
mass of the body
Wtboard – weight of the board acting downward at the center of
the board
Lb – length of the board
Lcg – distance of the center of gravity of the body to the dorsum
of the feet
Wtboard
1/2Lb
Wtbody
Lcg
Lb
Segmental Method for the Calculation of Center of Gravity of the Body
This method is based on segmental mass proportions derived from cadaver studies. If we
can approximate (1) the proportion of weight (mass) that each segment is of the whole
body and (2) the location of the center of gravity of individual segments in a Cartesian
axis system, we can approximate the location of the center of gravity in an image of the
human body. This image can be a picture, a series of pictures in a film, or a series of
pictures in a video sequence. Note that this method results in only an approximation for
the location of the center of gravity of the human body because we can not guarantee that
the proportions of the live individual are exactly the same as the proportions of the
cadavers upon which this method is based. The steps in this process are as follows:
1. Locate the ends of the defined segments according to the link segment boundaries
and place a mark at these points. This will result in marks at the end of the second
toe, ankle, knee, hip knuckle III of the hand, wrist, shoulder, seventh cervical
vertebra, and top of the head. Be careful to perceive the segments as three
dimensional images, even though the picture is seen in two dimensions.
2. Join the segments to form a stick figure consisting of 14 segments. Note that the
trunk segment goes from the seventh cervical vertebra to the midpoint of the line
connecting the two hips
3. Determine the coordinates of the extremes of each of the 14 segments.
4. Use cadaver data on the location of the center of gravity as a proportion of segment
length from the proximal and distal ends of the segments (see Segmental Method –
Center of Gravity Table) to determine the location of the center of gravity of each
of the segments in the picture. Note that a special template called the Walton
template can be used for this step.
5. Enter the coordinates of the center of gravity of each segment into the table
provided (see Segmental Method – Center of Gravity Table) and multiply these
values by the respective body segment proportion of weight (mass).
6. The sum of these products is the calculated location of the center of gravity of the
body relative to the coordinate system being used.
Body
Segment
1. Trunk
Segmental Method – Center of Gravity Table
Center of Mass Proportion
X–
XY–
Location from: of Body
Value of Product Value of
Weight
the
the
Center
Center
Prox.
Distal
of
of
End
End
Gravity
Gravity
.562
.438
.486
2. Head
and
Neck
3. R.
Thigh
4. R.
Shank
5. R. Foot
.567
.433
.079
.433
.567
.097
.433
.567
.045
.5
.5
.014
6. L.
Thigh
7. L.
Shank
8. L. Foot
.433
.567
.097
.433
.567
.045
.5
.5
.014
9. R. Arm
.436
.564
.027
10. R.
Forearm
11. R.
Hand
12. L.
Arm
13. L.
Forearm
14. L.
Hand
.43
.57
.014
.506
.494
.006
.436
.564
.027
.43
.57
.014
.506
.494
.006
=.971
X
product
Y
product
YProduct
General Methods and Procedures:
There will be 3 experiments to highlight the position and movement of the center of
gravity of the human body. In addition, principles of projectile movement will be
reviewed. Students must share the responsibility of carrying out these
experiments!!! The general methods and procedures for each of these experiments is as
follows:
1.
Subject Preparation
a.
The subjects should be dressed with minimal clothing (tank top or no
shirt and shorts) to (1)minimize the influence of clothing on the position
of the center of gravity of the body and (2)not obstruct the view of the
body and body landmarks.
b.
Before collecting data, each subject should be familiar with the setting
and task requirements.
c.
Each subject should not be exposed to any physical harm as a result of
performance and/or physical limitations.
d.
For any strenuous activity, subjects should be provided with a warm up
and a few practice trials. They must also be apprised of the tasks they
are being asked to perform. This may reduce the chance of injury.
2.
Set Up of Reaction Board
a.
See figure in section entitled Reaction Board for the Calculation of
Whole Body Center of Gravity.
b.
The board must be supported at both ends (at one end by the platform of
a weight scale and at the other end by a board).
c.
One knife edge of the reaction board should be centered on the platform
of the weight scale and the other should be centered on the wooden
support.
d.
The surface of the reaction board must be level.
e.
The reaction board must support the subjects’ weight without
appreciably bowing or breaking.
3.
Set Up of Video Camera
a.
The video camera must be positioned relatively far from the reaction
board to minimize perspective error.
b.
Level the camera and orient the optic axis of its lens so that it is
perpendicular to the long axis of the reaction board and plane of
movement.
c.
Use the lens to zoom in and focus on the activity plane. Then zoom out
to make the field of view as small as possible to maximize the subject
size. Make sure the entire subject or performance sequence can just be
seen in the field of view.
d.
Place a plumb bob, reference measure, fiducials, and timing lights in the
field of view.
e.
Use a contrasting curtain in the background to highlight the subjects and
reaction board.
4.
Calibration of Field Rate of Video Camera
a.
Video tape the timing lights.
b.
Determine the time from the timing lights for field one.
c.
d.
Count fields from field one to some other field approximately three
seconds later in time.
Calculate the field rate.
Field rate =
5.
number of fields – one
time transpired from field one to last field
Data Collection
a.
All data should be collected as accurately as possible.
b.
As data is being collected, note where inaccuracies occur and potentially
use this information to justify results.
Specific Methods and Procedures:
In addition to the general methods and procedures, the 3 experiments have their own
specific methods and procedures that must be followed.
Experiment 1 – Whole Body Calculation of the Center of Gravity via Reaction
Board – Lying Position
a.
Accurately determine the X-value location of the center of mass of the
reaction board; assume the location is ½ total length of homogeneous
board (i.e., measure board in metric units and divide by 2).
b.
Determine the weight of the reaction board in metric units by weighing
it on a calibrated scale.
c.
Check the alignment of the “knife edges” (angle iron) on both ends of
the reaction board. Their vertical surface should be aligned with the
ends of the reaction board.
d.
Check the height of the wooden block that is used to support the reaction
board. It should be equal in height to the height of the surface of the
scale. Thus, the reaction board, supported by the scale and wooden
block will be level.
e.
Weigh each subject in metric units as accurately as possible on a
calibrated scale. Each subject should be wearing only shorts and tank
top.
f.
Accurately measure the height of each subject using the metric system.
g.
Position one knife edge of the reaction board on center of the scale and
the other on the center of the supporting wooden block.
h.
Prior to getting a subject’s weight on the reaction board, have him/her
straddle the reaction board and lower his/ her body gently onto the
board.
i.
Once a subject is on the reaction board, have him/her assume a
stationary anatomical position with the hands at the sides of his/her body
and the dorsum of the feet perpendicular to the floor and coplanar with
the vertical surface of the knife edge. The head must be oriented in the
Frankfort plane.
j.
Accurately weigh each subject on the reaction board in metric units.
k.
Each student is responsible for calculating his/her own center of mass
location in metric unit as a distance form the dorsum of the feet. Show
your work.
l.
Each student is responsible for calculating his/her own percentage of
total body height that the location of the center of gravity of the body is
from the dorsum of the feet and recording this value on the class record
sheet (see Class Record Sheet). Percents should be recorded in the
appropriate gender category. Show your work.
m. Each student is responsible for calculating the mean and standard
deviation of the percents for the male and female groups. Show your
work.
Experiment 2 – Whole Body Calculation of the Center of Gravity via Reaction
Board Versus Segmental Method – Three Support Positions
a.
Place a video camera with the optic axis of its lens horizontal and also
perpendicular to the long axis of the reaction board.
b.
Each subject must carefully assume three different support positions on
the reaction board: one with the body weight toward the front edge of
the base of support (anterior), one with the body weight centered over
the base of support (balanced), and one with the body weight toward the
back edge of the base of support (posterior).
c.
In the field of view of the video camera, place a (1) contrasting curtain,
(2) plumb bob, (3) calibration measure, and (4) fiducials.
d.
Simultaneously capturing the video images and force values from the
scale of the three support positions of each subject. Note that the body
of the subject should just fit into the field of view of the camera.
e.
Each student is responsible for their measure, in metric units, of the
distance of the near and far edge of their base to the knife edge (0,0
position) for each of the three support positions.
f.
Each student is responsible for following the same methods and
procedures used in Experiment 1 for determining the horizontal position
of their center of gravity relative to the knife edge on the wooden block
(i.e., use the reaction board technique). Show your work.
g.
Each student is responsible for applying the segmental method (whole
body method) and cadaver data to their captured video images, to
calculate their horizontal location (X value only) of the center of gravity
of the body for each of their three support positions. Students are
responsible for transforming the units to laboratory (real world) units
relative to the knife edge (zero X value). Show your work.
Experiment 3 – Projectile Behavior of the Center of Gravity of the Human Body
a.
Select one subject, free of any physically limiting factors, to perform a
standing long jump.
b.
Use a starting line for the standing long jumps and position a tape
measure to facilitate the measurement of the distance of the jumps.
Jump distances should be measured in metric units from the tips of the
toes on take off (edge of the starting line) to the tips of the toes on
landing.
c.
Provide warm up for the subject and several lead up jumps (less than allout practice jumps).
d.
e.
f.
g.
h.
i.
j.
k.
l.
During the practice jumps, position the video camera with the optic axis
of its lens horizontal and also perpendicular to the long axis of the
primary plane of movement for the standing long jump. Also, minimize
the field of view so that the entire performance of the standing long
jump (take off to landing) just fits into the field of view. In other words,
maximize the size of the subject in the field of view.
In the field of view of the video camera, place a (1) contrasting curtain,
(2) plumb bob, (3) calibration measure, (4) fiducials, and (5) timing light
box.
Video tape the timing light box for three or more seconds and calculate
the time interval between frames. Show your work.
Apply the segmental method and cadaver data to the captured sequential
video images, to calculate the horizontal and vertical location (X and Y
values) of the center of gravity of the body for each of the selected
fields. Note that these fields must include the images for take off and
landing, first and last two airborne positions, as well as some regular
temporal sequence beginning at take off. Also, select one field that
visually appears to represent the highest vertical position of the body
during the airborne phase of the standing long jump. Show your work.
Use the horizontal and vertical position of the center of gravity of the
body for the first and second airborne positions and the calculated time
interval between fields of video to determine the resultant velocity
vector (magnitude and direction) of the center of gravity in laboratory
units. Show your
work.
Calculate the magnitudes of the horizontal and vertical velocity vectors
of the center of gravity of the body in laboratory units from the first and
second airborne positions and the known time interval between fields of
video. Show your work.
Use the horizontal and vertical position of the center of gravity of the
body for the last two airborne positions and the calculated time interval
between fields of video to determine the resultant velocity vector
(magnitude and direction) of the center of gravity in laboratory units.
Show your work.
Calculate the magnitudes of the horizontal and vertical velocity vectors
of the center of gravity of the body in laboratory units from the last two
airborne positions and the known time interval between fields of video.
Show your work.
Calculate the horizontal velocity vector in laboratory units for some
interval in the middle of the airborne phase. Show your work.
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. Your format should differ from the normal scientific format in that
you must show your work (i.e., how you calculated your results). If there are several
iterations of the same calculation process, you only need to show the first to demonstrate
your understanding.
Experiment 1 – Whole Body Calculation of the Center of Gravity via Reaction
Board – Lying Position
1.
Compare the percent of total body height that the center of gravity is for the
male and female groups.
2.
Are the mean percents in accord with expectations? Explain why or why not.
Experiment 2 – Whole Body Calculation of the Center of Gravity via Reaction
Board Versus Segmental Method – Three Support Positions
1.
Were the horizontal positions, relative to the knife edge on the wooden block,
of the center of gravity of your body the same for the reaction board and
segmental methods for each of the three positions? Explain why or why not.
2.
Which of the two methods do you think is more accurate for determining the
horizontal position of the center of gravity of your body? Explain.
Experiment 3 – Projectile Behavior of the Center of Gravity of the Human Body
1.
Was the “take off” velocity vector calculated from the first two airborne fields
of video as expected for someone attempting to achieve a maximum standing
long jump? Explain.
2.
Was the “landing” velocity vector calculated from the last two airborne fields
of video as expected for someone attempting to achieve a maximum standing
long jump? Explain.
3.
What relationship did you find between the velocity vector for “take off” and
landing? Was or was not this result expected? Explain.
4.
What relationship did you find between the horizontal velocity vectors for
“take off”, “landing” and the horizontal velocity vector calculated for the
middle of the airborne phase? Was or was not this result expected? Explain.
5.
Was the maximum height of the center of gravity as expected on the basis of
the vertical velocity vector at “take off”? Explain.
Class Record Sheet
Name
Standing Height
(cm)
Height of Center of
Gravity (cm)
Females
1.
2.
3.
4.
5.
6.
Mean (sd):
Males
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Mean (sd):
Height of CG as a
% of total Body
Height
BIOMECHANICAL ANALYSIS OF PHYSICAL ACTIVITY
Laboratory Experiments: Measurement and Interpretation of the Kinematics of the
Center of Gravity of the Human Body
Dr. Eugene W. Brown
Purposes:
These laboratory experiments have several purposes. They include:
1.
developing or reviewing the concepts of levers,
2.
understanding how to use a reaction board to calculate the center of gravity
of the human body,
3.
understanding how to use the segmental method to calculate the center of
gravity of the human body,
4.
understanding the use of Walton templates in determining the center of mass
of various segments of the human body,
5.
reviewing concepts of mass segment parameters,
6.
understanding the concept of the center of gravity,
7.
reviewing concepts of projectiles and vectors,
8.
developing an understanding of experimental methods in biomechanics,
9.
learning how to use a camera for two dimensional videography,
10. understanding the relationship of experimental error to measurements
recorded,
11. preparing subjects for participation in research experiments,
12. setting up experimental procedures in biomechanics,
13. understanding how to calculate field and frame rates, and
14. learning how to report the results of laboratory experiments.
List of Equipment and Supplies
1.
acetate grids
2.
adult male and female subjects
3.
background curtain
4.
block to support reaction board
5.
calculator
6.
camera tripod
7.
carpenter’s square
8.
computer and software for down loading video images
9.
fiducial markers
10. laser pointer
11. level
12. mass-segment data sheet
13. plumb bob
14. reaction board
15. reference measure (meter stick)
16. subject and trial board and numbers
17. tape
18. tape measure
19. timing light box
20.
21.
22.
23.
24.
25.
26.
27.
video camera
video tape
Walton Template
weight scale
Definition of Terms:
1.
center of gravity – center of mass distribution of an object
2.
equilibrium – a condition in which the sum of all forces and torques acting on
an object equals zero resulting in a constant linear and angular velocity
3.
fiducial – two or more marks placed in the field of view of a video or motion
picture camera (usually at the outer edges of the field of view) to be used
to align sequential images to a laboratory coordinate system
4.
field rate – the number of pictures of video captured in a known period of time
(e.g., 30 fields/second)
5.
frame rate - the number of pictures of motion picture film captured in a known
period of time (e.g., 100 frames/second)
6.
optic axis of lens – line perpendicular to the long axis of a lens
7.
perspective error – error which occurs when parts of a body or implement lie
outside the principle photographic plane; image of segment closer to the
camera appears larger and segment farther away appears smaller
8.
plumb bob – weighted string that hangs vertical which is used for spatial
orientation
9.
reaction board – board that is used as a lever to transmit force to weighted
scale for purposes of determining the center of mass of objects (e.g.,
human body) placed on it
10. reference measure – an object of known length (e.g., meter stick) that is
placed in a plane that is perpendicular to the optic axis of the lens of a
camera that is used to assist in determining distance measurements in the
same plane
11. segmental method – procedure used to calculate the center of mass of a multisegmented system (e.g., human body, horse) that is based on known
segment masses and mass centers of gravity of a similar model (e.g.,
cadaver of a human, cadaver of a horse)
12. timing lights – electronic device that uses lights to accurately display time
13. vector – a measure that is represented by magnitude and direction (e.g.,
displacement, velocity, acceleration, force, momentum)
14. Walton template – a standard measurement device, unique to each segment of
the body, that is used to determine the location of the center of gravity of
each body segment based on known proportions of the center of gravity
from the proximal and distal ends of each segment
14. whole body method – a procedure for determining the location of the center of
gravity of a multi-segmented system (e.g., human body, horse) in one
configuration without regard for the position of individual segments
(e.g., reaction board, pendulum)
15.
16.
Review:
1.
2.
Projectile
Vectors
Reaction Board for the Calculation of Whole Body Center of Gravity
Basically, the reaction board method for the calculation of the center of gravity of the
whole body is based on the principle of levers. In a static lever system, the sum of the
forces and the sum of the torques are equal to zero. The reaction board system is such a
system. If an imaginary fulcrum is placed at the knife edge aligned with the dorsum of
the feet, the sum of the positive (counterclockwise) torques and negative (clockwise)
torques must equal to zero. In other words:
(Fs)( Lb) = (Wtboard)( 1/2Lb) + (Wtbody)( Lcg)
In this equation, the only variable that is not known is the location of Lcg. Therefore, we
can solve for this parameter.
Fs
Key:
Fs – force read at the scale; upward force applied to the board by
the scale
Wtbody – weight of the body acting downward at the center of
mass of the body
Wtboard – weight of the board acting downward at the center of
the board
Lb – length of the board
Lcg – distance of the center of gravity of the body to the dorsum
of the feet
Wtboard
1/2Lb
Wtbody
Lcg
Lb
Segmental Method for the Calculation of Center of Gravity of the Body
This method is based on segmental mass proportions derived from cadaver studies. If we
can approximate (1) the proportion of weight (mass) that each segment is of the whole
body and (2) the location of the center of gravity of individual segments in a Cartesian
axis system, we can approximate the location of the center of gravity in an image of the
human body. This image can be a picture, a series of pictures in a film, or a series of
pictures in a video sequence. Note that this method results in only an approximation for
the location of the center of gravity of the human body because we can not guarantee that
the proportions of the live individual are exactly the same as the proportions of the
cadavers upon which this method is based. The steps in this process are as follows:
1. Locate the ends of the defined segments according to the link segment boundaries
and place a mark at these points. This will result in marks at the end of the second
toe, ankle, knee, hip knuckle III of the hand, wrist, shoulder, seventh cervical
vertebra, and top of the head. Be careful to perceive the segments as three
dimensional images, even though the picture is seen in two dimensions.
2. Join the segments to form a stick figure consisting of 14 segments. Note that the
trunk segment goes from the seventh cervical vertebra to the midpoint of the line
connecting the two hips
3. Determine the coordinates of the extremes of each of the 14 segments.
4. Use cadaver data on the location of the center of gravity as a proportion of segment
length from the proximal and distal ends of the segments (see Segmental Method –
Center of Gravity Table) to determine the location of the center of gravity of each
of the segments in the picture. Note that a special template called the Walton
template can be used for this step.
5. Enter the coordinates of the center of gravity of each segment into the table
provided (see Segmental Method – Center of Gravity Table) and multiply these
values by the respective body segment proportion of weight (mass).
6. The sum of these products is the calculated location of the center of gravity of the
body relative to the coordinate system being used.
Body
Segment
1. Trunk
Segmental Method – Center of Gravity Table
Center of Mass Proportion
X–
XY–
Location from: of Body
Value of Product Value of
Weight
the
the
Center
Center
Prox.
Distal
of
of
End
End
Gravity
Gravity
.562
.438
.486
2. Head
and
Neck
3. R.
Thigh
4. R.
Shank
5. R. Foot
.567
.433
.079
.433
.567
.097
.433
.567
.045
.5
.5
.014
6. L.
Thigh
7. L.
Shank
8. L. Foot
.433
.567
.097
.433
.567
.045
.5
.5
.014
9. R. Arm
.436
.564
.027
10. R.
Forearm
11. R.
Hand
12. L.
Arm
13. L.
Forearm
14. L.
Hand
.43
.57
.014
.506
.494
.006
.436
.564
.027
.43
.57
.014
.506
.494
.006
=.971
X
product
Y
product
YProduct
General Methods and Procedures:
There will be 3 experiments to highlight the position and movement of the center of
gravity of the human body. In addition, principles of projectile movement will be
reviewed. Students must share the responsibility of carrying out these
experiments!!! The general methods and procedures for each of these experiments is as
follows:
1.
Subject Preparation
a.
The subjects should be dressed with minimal clothing (tank top or no
shirt and shorts) to (1)minimize the influence of clothing on the position
of the center of gravity of the body and (2)not obstruct the view of the
body and body landmarks.
b.
Before collecting data, each subject should be familiar with the setting
and task requirements.
c.
Each subject should not be exposed to any physical harm as a result of
performance and/or physical limitations.
d.
For any strenuous activity, subjects should be provided with a warm up
and a few practice trials. They must also be apprised of the tasks they
are being asked to perform. This may reduce the chance of injury.
2.
Set Up of Reaction Board
a.
See figure in section entitled Reaction Board for the Calculation of
Whole Body Center of Gravity.
b.
The board must be supported at both ends (at one end by the platform of
a weight scale and at the other end by a board).
c.
One knife edge of the reaction board should be centered on the platform
of the weight scale and the other should be centered on the wooden
support.
d.
The surface of the reaction board must be level.
e.
The reaction board must support the subjects’ weight without
appreciably bowing or breaking.
3.
Set Up of Video Camera
a.
The video camera must be positioned relatively far from the reaction
board to minimize perspective error.
b.
Level the camera and orient the optic axis of its lens so that it is
perpendicular to the long axis of the reaction board and plane of
movement.
c.
Use the lens to zoom in and focus on the activity plane. Then zoom out
to make the field of view as small as possible to maximize the subject
size. Make sure the entire subject or performance sequence can just be
seen in the field of view.
d.
Place a plumb bob, reference measure, fiducials, and timing lights in the
field of view.
e.
Use a contrasting curtain in the background to highlight the subjects and
reaction board.
4.
Calibration of Field Rate of Video Camera
a.
Video tape the timing lights.
b.
Determine the time from the timing lights for field one.
c.
d.
Count fields from field one to some other field approximately three
seconds later in time.
Calculate the field rate.
Field rate =
5.
number of fields – one
time transpired from field one to last field
Data Collection
a.
All data should be collected as accurately as possible.
b.
As data is being collected, note where inaccuracies occur and potentially
use this information to justify results.
Specific Methods and Procedures:
In addition to the general methods and procedures, the 3 experiments have their own
specific methods and procedures that must be followed.
Experiment 1 – Whole Body Calculation of the Center of Gravity via Reaction
Board – Lying Position
a.
Accurately determine the X-value location of the center of mass of the
reaction board; assume the location is ½ total length of homogeneous
board (i.e., measure board in metric units and divide by 2).
b.
Determine the weight of the reaction board in metric units by weighing
it on a calibrated scale.
c.
Check the alignment of the “knife edges” (angle iron) on both ends of
the reaction board. Their vertical surface should be aligned with the
ends of the reaction board.
d.
Check the height of the wooden block that is used to support the reaction
board. It should be equal in height to the height of the surface of the
scale. Thus, the reaction board, supported by the scale and wooden
block will be level.
e.
Weigh each subject in metric units as accurately as possible on a
calibrated scale. Each subject should be wearing only shorts and tank
top.
f.
Accurately measure the height of each subject using the metric system.
g.
Position one knife edge of the reaction board on center of the scale and
the other on the center of the supporting wooden block.
h.
Prior to getting a subject’s weight on the reaction board, have him/her
straddle the reaction board and lower his/ her body gently onto the
board.
i.
Once a subject is on the reaction board, have him/her assume a
stationary anatomical position with the hands at the sides of his/her body
and the dorsum of the feet perpendicular to the floor and coplanar with
the vertical surface of the knife edge. The head must be oriented in the
Frankfort plane.
j.
Accurately weigh each subject on the reaction board in metric units.
k.
Each student is responsible for calculating his/her own center of mass
location in metric unit as a distance form the dorsum of the feet. Show
your work.
l.
Each student is responsible for calculating his/her own percentage of
total body height that the location of the center of gravity of the body is
from the dorsum of the feet and recording this value on the class record
sheet (see Class Record Sheet). Percents should be recorded in the
appropriate gender category. Show your work.
m. Each student is responsible for calculating the mean and standard
deviation of the percents for the male and female groups. Show your
work.
Experiment 2 – Whole Body Calculation of the Center of Gravity via Reaction
Board Versus Segmental Method – Three Support Positions
a.
Place a video camera with the optic axis of its lens horizontal and also
perpendicular to the long axis of the reaction board.
b.
Each subject must carefully assume three different support positions on
the reaction board: one with the body weight toward the front edge of
the base of support (anterior), one with the body weight centered over
the base of support (balanced), and one with the body weight toward the
back edge of the base of support (posterior).
c.
In the field of view of the video camera, place a (1) contrasting curtain,
(2) plumb bob, (3) calibration measure, and (4) fiducials.
d.
Simultaneously capturing the video images and force values from the
scale of the three support positions of each subject. Note that the body
of the subject should just fit into the field of view of the camera.
e.
Each student is responsible for their measure, in metric units, of the
distance of the near and far edge of their base to the knife edge (0,0
position) for each of the three support positions.
f.
Each student is responsible for following the same methods and
procedures used in Experiment 1 for determining the horizontal position
of their center of gravity relative to the knife edge on the wooden block
(i.e., use the reaction board technique). Show your work.
g.
Each student is responsible for applying the segmental method (whole
body method) and cadaver data to their captured video images, to
calculate their horizontal location (X value only) of the center of gravity
of the body for each of their three support positions. Students are
responsible for transforming the units to laboratory (real world) units
relative to the knife edge (zero X value). Show your work.
Experiment 3 – Projectile Behavior of the Center of Gravity of the Human Body
a.
Select one subject, free of any physically limiting factors, to perform a
standing long jump.
b.
Use a starting line for the standing long jumps and position a tape
measure to facilitate the measurement of the distance of the jumps.
Jump distances should be measured in metric units from the tips of the
toes on take off (edge of the starting line) to the tips of the toes on
landing.
c.
Provide warm up for the subject and several lead up jumps (less than allout practice jumps).
d.
e.
f.
g.
h.
i.
j.
k.
m.
During the practice jumps, position the video camera with the optic axis
of its lens horizontal and also perpendicular to the long axis of the
primary plane of movement for the standing long jump. Also, minimize
the field of view so that the entire performance of the standing long
jump (take off to landing) just fits into the field of view. In other words,
maximize the size of the subject in the field of view.
In the field of view of the video camera, place a (1) contrasting curtain,
(2) plumb bob, (3) calibration measure, (4) fiducials, and (5) timing light
box.
Video tape the timing light box for three or more seconds and calculate
the time interval between frames. Show your work.
Apply the segmental method and cadaver data to the captured sequential
video images, to calculate the horizontal and vertical location (X and Y
values) of the center of gravity of the body for each of the selected
fields. Note that these fields must include the images for take off and
landing, first and last two airborne positions, as well as some regular
temporal sequence beginning at take off. Also, select one field that
visually appears to represent the highest vertical position of the body
during the airborne phase of the standing long jump. Show your work.
Use the horizontal and vertical position of the center of gravity of the
body for the first and second airborne positions and the calculated time
interval between fields of video to determine the resultant velocity
vector (magnitude and direction) of the center of gravity in laboratory
units. Show your
work.
Calculate the magnitudes of the horizontal and vertical velocity vectors
of the center of gravity of the body in laboratory units from the first and
second airborne positions and the known time interval between fields of
video. Show your work.
Use the horizontal and vertical position of the center of gravity of the
body for the last two airborne positions and the calculated time interval
between fields of video to determine the resultant velocity vector
(magnitude and direction) of the center of gravity in laboratory units.
Show your work.
Calculate the magnitudes of the horizontal and vertical velocity vectors
of the center of gravity of the body in laboratory units from the last two
airborne positions and the known time interval between fields of video.
Show your work.
Calculate the horizontal velocity vector in laboratory units for some
interval in the middle of the airborne phase. Show your work.
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. Your format should differ from the normal scientific format in that
you must show your work (i.e., how you calculated your results). If there are several
iterations of the same calculation process, you only need to show the first to demonstrate
your understanding.
Experiment 1 – Whole Body Calculation of the Center of Gravity via Reaction
Board – Lying Position
1.
Compare the percent of total body height that the center of gravity is for the
male and female groups. (2 points)
2.
Are the mean percents in accord with expectations? Explain why or why not.
(2 points)
Experiment 2 – Whole Body Calculation of the Center of Gravity via Reaction
Board Versus Segmental Method – Three Support Positions
1.
Were the horizontal positions, relative to the knife edge on the wooden block,
of the center of gravity of your body the same for the reaction board and
segmental methods for each of the three positions? Explain why or why not.
(6 points)
2.
Which of the two methods do you think is more accurate for determining the
horizontal position of the center of gravity of your body? Explain. (4 points)
Experiment 3 – Projectile Behavior of the Center of Gravity of the Human Body
1.
Was the “take off” velocity vector calculated from the first two airborne fields
of video as expected for someone attempting to achieve a maximum standing
long jump? Explain. (6 points)
2.
Was the “landing” velocity vector calculated from the last two airborne fields
of video as expected for someone attempting to achieve a maximum standing
long jump? Explain. (6 points)
3.
What relationship did you find between the velocity vector for “take off” and
landing? Was or was not this result expected? Explain. (2 points)
4.
What relationship did you find between the horizontal velocity vectors for
“take off”, “landing” and the horizontal velocity vector calculated for the
middle of the airborne phase? Was or was not this result expected? Explain.
(4 points)
5.
Was the maximum height of the center of gravity as expected on the basis of
the vertical velocity vector at “take off”? Explain. (6 points)
Class Record Sheet
Name
Weight
(kg)
1.
S.M.
62.3
Standing
Fs
Height
(kg)
(cm)
Females
163.195
42.27
Height of
Center of
Gravity (cm)
Height of CG
as a % of total
Body Height
102.18
62.6
2.
M.D.
64.41
168.275
42.41
98.9
58.7
3.
E.C.
64.86
161.29
39.68
90.33
56.0
4.
J.A.
56.69
158.75
37.19
94.65
59.62
5.
6.
Mean (sd):
Males
63.50
1.
C.Z.
100.24
179.07
105.498
58.9
2.
A.C.
97.52
187.325
62.14
105.68
56.4
3.
G.H.
87.54
178.435
56.69
105.401
59.06
4.
J.T.
77.79
180.34
51.25
104.79
58.0
5.
M.G.
65.43
179.705
43.99
102.58
57.0
6.
T.K.
79.61
180.34
51.25
102.357
56.76
7.
B.J.L.
84.36
172.72
51.71
97.68
56.56
8.
T.E.
97.06
177.8
60.10
91.62
51.5
9.
J.S.
115.21
187.96
74.84
111.27
59.1
10. U.V.
80.51
184.15
52.84
105.136
57.09
11. J.A.
73.02
179.07
47.17
100.55
56.15
12. J.H.
73.48
180.34
48.98
104.79
58.11
Mean (sd):
BIOMECHANICAL ANALYSIS OF PHYSICAL ACTIVITY
Laboratory Experiments: Measurement and Interpretation of the Kinematics of the
Center of Gravity of the Human Body
Grade Report
Student: ________________________________
Write-up Area/Comments
Experiment 1 – Whole Body Calculation of the Center of Gravity
via Reaction Board – Lying Position
1. Compare the percent of total body height that the center of
gravity is for the male and female groups.
2.
Are the mean percents in accord with expectations? Explain
why or why not.
Points
Received
Points
Possible
2
2
Experiment 2 – Whole Body Calculation of the Center of Gravity
via Reaction Board Versus Segmental Method – Three Support
Positions
1. Were the horizontal positions, relative to the knife edge on
the wooden block, of the center of gravity of your body the
same for the reaction board and segmental methods for each
of the three positions? Explain why or why not.
6
2.
4
Which of the two methods do you think is more accurate for
determining the horizontal position of the center of gravity
of your body? Explain.
Experiment 3 – Projectile Behavior of the Center of Gravity of the
Human Body
1. Was the “take off” velocity vector calculated from the first
two airborne fields of video as expected for someone
attempting to achieve a maximum standing long jump?
Explain.
6
2.
Was the “landing” velocity vector calculated from the last
two airborne fields of video as expected for someone
attempting to achieve a maximum standing long jump?
Explain.
6
3.
What relationship did you find between the velocity vector
for “take off” and landing? Was or was not this result
expected? Explain.
2
4.
What relationship did you find between the horizontal
velocity vectors for “take off”, “landing” and the horizontal
velocity vector calculated for the middle of the airborne
phase? Was or was not this result expected? Explain.
4
5.
Was the maximum height of the center of gravity as
expected on the basis of the vertical velocity vector at “take
off”? Explain.
6
Total Points:
Grade:
38