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Lab #2: Center of Mass
INTRODUCTION
Determination of the body's center of mass is an important part of most biomechanical analyses.
Typically a balance board method is used to determine the center of mass location for a static situation.
While this is an accurate and straight forward method, it is not practical for analyzing an activity with a
range of body positions. For such an analysis, an alternative approach is to determine the center of mass
location from an image of the motion at some point or points in time. This might be done from a printed
photo or from a series of frames of cine film which record a complete movement pattern. The details of
this approach are outlined below.
METHODS
The center of mass is an ideal point about which the torques due to body segment weights is zero. It can
be determined in the following manner:
1.
Choose some arbitrary reference point as origin of the coordinate system to be used.
2.
Determine the center of mass location of each segment of the body (x, y-pair of coordinates).
3.
Calculate the torque about the reference point due to each segment (based on the segment's mass
and position).
4.
Sum the torques about the reference point for all the segments (one sum for x-direction and one
for y-direction).
5.
Divide the sum of the torques by the total body mass to determine the center of mass location with
respect to the reference point.
In applying this method to real situations, anthropometric information about human body segments is
used to determine the location of each segment's center of mass and each segment's mass. Each of these
body segment parameters (BSP) is usually expressed as a percentage value. In the case of location of the
segment's center of mass, it is described as a percent of segment length from the proximal end. In the
case of segment mass, it is described as a percent of total body mass. Such BSP data come from cadaver
studies performed in various labs during the past century. The most frequently cited of these studies are
those of Dempster (1955) and Clauser, McConville and Young (1969), which are based on cadaver
dissection studies. One frequently cited source of BSP's was published by Plagenhoef et al (1983).
Summaries of these studies are included in many textbooks (e.g., Hamill & Knutzen, 2015, p. 449-455).
COMPUTING BODY CENTER OF MASS
The body center of mass can be computed from the center of masses and the masses of the segments:
(x, y) = coordinates of the body center of mass
i = segment number
(xi, yi) = the x & y coordinates of the body center of mass of segment i
mi = mass of segment i
In other words, the body center of mass coordinates are equal to the sum of the products of segmental
mass and segmental CM coordinates divided by the body mass (∑mi).
In applying this method to real situations, anthropometric information about human body segments is
used to determine the location of each segment's center of mass and each segment's mass. Each of these
body segment parameters (BSP) is usually expressed as a percentage value. In the case of location of the
segment's center of mass, it is described as a percent of segment length from the proximal end. In the
case of segment mass, it is described as a percent of total body mass. Such BSP data come from cadaver
studies performed in various labs during the past century. The most frequently cited of these studies are
those of Dempster (1955) and Clauser, McConville and Young (1969). Summaries of these studies are
included in many textbooks.
As an example of how these body segment parameters are used, consider a male's thigh segment located
as illustrated in the figure. If this person's whole body mass was 80 kg, the thigh mass can be determined
as a percent of 80 kg, ie. 10.5% of 80 = 8.4 kg (where 10.5% is the thigh segment mass percent from
Plagenhoef).
The thigh center of mass location can be determined from the proximal and distal point coordinates and
the segment length percent. If for the thigh the center of mass is located at about 43.3% of the length
from the proximal end, the specific coordinates can be determined as follows:
Segment CM X Position = Xproximal + (Length %) (Xdistal - Xproximal)
Xthigh = 10 + (.433) (70 - 10) = 35.98
Ythigh = 30 + (.433) (40 - 30) = 34.33
DATA
Whole body center of mass determination is based upon knowing segmental center of mass locations
which in turn are based upon segmental end point positions.
1.
First, determine each segment's end points. In the figure below, proximal and distal ends of left
side segments have been marked.
Segment
X (cm) Y (cm)
L Toe
178
288
L Heel
158
277
L Ankle
167
286
L Knee
131
335
L Hip
87
257
L Shoulder
72
149
L Elbow
87
101
L Wrist
97
40
L Finger Tip 88
12
R Toe
67
467
R Heel
102
449
R Ankle
88
441
R Knee
76
354
R Hip
58
267
R Shoulder
60
155
R Elbow
102
198
R Wrist
131
224
R Finger Tip 156
243
Base of Neck 60
140
Head Top
89
44
2.
Use the endpoint coordinates to determine segment center of mass coordinates. Enter segment
endpoint coordinates into a spreadsheet arranged something like the illustration below. Add a column
which has segmental length percent (as shown in red). Then using the formula described in the lab,
determine each segment's center of mass location.
3.
Combine these segment coordinates with segment masses to determine each segment's torque
about some reference point (the origin). Once segmental center of mass positions are known, these can
be used with the segment mass percent to determine a "torque" about an axis. This is really a mass *
length calculation. If the torques created by each segment are summed the result is equal to the torque
of the whole body mass acting at the center of mass location. This idea allows determining the unknown
whole body CM location. In your spreadsheet, add a column with the segment mass percent. Then write
formulas for each segment's torque in each direction. Finally, sum the torques and divide by total body
mass (100%).
4.
Use total torque to determine whole body center of mass location.
PROCEDURE
1.
On a relatively large picture of a human in action, determine locations of the following anatomical
landmarks: toe, heel, ankle, knee, hip, shoulder, elbow, and wrist, third knuckle (MCP), C7-T1 and top of
head. For data collection, a printout of a data table will simplify recording of coordinate information. Use
the attached picture of a runner for your analysis.
2.
Enter the segment end point coordinates into a spreadsheet. Combined with segment length
percent, determine segment center of mass locations.
3.
Using segmental mass percent, determine torque for each segment.
4.
Sum the torques for all the segments and determine the whole body center of mass location.
5.
Printout your spreadsheet results. Return to the picture you have analyzed and locate where on
the image the whole body center of mass is located using the computer image coordinates. Mark this
point on a printout of the picture.
DATA TABLE FOR SEGMENTAL POSITIONS
PROXIMAL
DISTAL
x (cm) y (cm) x (cm) y (cm)
LENGTH
PERCENT
SEGMENT CM
x (cm) y (cm)
MASS
TORQUE
PERCENT x (N/m) y (N/m)
RIGHT FOOT
50.00%
1.33%
LEFT FOOT
50.00%
1.33%
RIGHT LEG
41.90%
5.35%
LEFT LEG
41.90%
5.35%
RIGHT THIGH
42.80%
11.75%
LEFT THIGH
42.80%
11.75%
RIGHT UPPER ARM
45.80%
2.90%
LEFT UPPER ARM
45.80%
2.90%
RIGHT FOREARM
43.40%
1.57%
LEFT FOREARM
43.40%
1.57%
RIGHT HAND
46.80%
0.50%
LEFT HAND
46.80%
0.50%
HEAD
55.00%
8.20%
50.00%
45.00%
LEFT TRUNK
RIGHT TRUNK
TRUNK
100%
SUMMARY
Based on your data collection, analysis and results briefly summarize the procedures used to determine
whole body center of mass. In addition, discuss the specific image used in the lab and how center of mass
relates to such performance. In your summary and discussion, include responses to the following
questions.
1.
For the body configuration analyzed, was the calculated center of mass position within the volume
of the body? Under what configurations would you expect the center of mass not to be within the volume
of the body?
2.
Was the calculated center of mass position over the base of support in the photo analyzed? Under
what conditions does the center of mass have to be over the base of support and when does it not have to
be?
3.
The process of estimating the center of mass location based on body segment parameters (the
segmental masses and locations) introduces some estimation errors into the calculations. What errors
were involved in this whole process? Which are the most significant errors?
Saint Xavier University
Department of Exercise Science
Lab Report Template
Cover Page
• Lab #
• Experiment title
• Group members
• Due date
Specific Aims (1 paragraph)
This paragraph should state the specific objectives for that experiment. Do not copy
directly from the lab manual.
Background (1-3 paragraphs)
This should describe topics covered in throughout the experiment, specifically covering the
basic anatomy and physiology of the system(s) involved for the lab. Also important terms
and concepts should be clearly defined. I recommend using your textbook for background
material.
Copying of the manual will not be accepted.
Methods (1-3 paragraphs)
Describe the procedure you used to collect your data. Include the equipment and materials
used, indication of electrode placement, and specify modifications (esp. type or length of
exercise performed by subject). The subject profile should be in this section. This section
should give enough information that your experiment could be duplicated. However, it is
not necessary to write every part of your procedure down, like turning on the computer. It
is alright to assume that you are writing this for a fellow exercise physiology lab student.
This should be written in the past tense.
Results (1-2 paragraphs)
State the results you obtained. You must reproduce ALL data tables from lab sheets in the
report. You may cut and paste once the results have been entered into the tables. The
results should be stated but not discussed extensively, e.g. heart rate was found to increase
after exercise. Be sure to include units in the graphs and tables and also label everything
(axes, figures, tables) appropriately. Any required equations/calculated values should be
included in this section.
Discussion (1-3 pages)
Discuss the results of your experiment. What do your results mean? Be sure to reference
the relevant exercise physiology in your discussion. What are some of the limitations of the
study? What were some possible sources of error specific to your experiment? You must
answer ALL of the discussion questions at the end of each lab in this section. The questions
should be answered in order and written in paragraph form. Do not format as Q&A.
Conclusions (1 paragraph)
State the conclusions for this experiment. What was the main result of the experiment? Do
not repeat your discussion section here.
References
All references used should be included in their own section and must be referenced in
proper format (APA or AMA).
Examples:
Schembre, S. M., & Riebe, D. A. (2011). Non-exercise estimation of VO(2)max using
the International Physical Activity Questionnaire. Meas Phys Educ Exerc Sci, 15(3),
168-181.
Sun, X. G., Hansen, J. E., Ting, H., Chuang, M. L., Stringer, W. W., Adame, D., &
Wasserman, K. (2000). Comparison of exercise cardiac output by the Fick principle
using oxygen and carbon dioxide. Chest, 118(3), 631-640.
General Lab Report Instructions
• Reports should be single-spaced and printed on one side of the page. 12 point font,
Cambria font with 1 inch margins.
• A good report reads like it was the work of one author – proof read it as a group.
• Tables should not be split on two pages. The entire table should fit on 1 sheet.
• Write in a professional style.
• Most of the lab report should be in past tense as it describes work you did.
• Figures and drawings (and graphs) – should be given a caption below the image.
o If you include images from the web or from a book or a magazine, be sure to
cite the source, otherwise it is plagiarism. Best way is to put in the figure
caption something like, "Image (or figure) reproduced from .......". If you
modify a figure, put, "Figure adapted from ......". If the image is from the web,
use the URL as the citation.
• Graphs – 2D graphics represent data more realistically than 3D graphics.
• Tables – should be number and a title placed above the table.
o Any abbreviations or definitions should be below the table.
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