ARIZONA STATE UNIVERSITY
KIN 335 BIOMECHANICS
LAB #7: THE REACTION BOARD METHOD FOR LOCATING THE CENTER OF MASS (CENTER OF
GRAVITY) OF THE HUMAN BODY
Reading Assignment: McGinnis (2005), pp. 129-143; Hay & Reid (1988). Anatomy, Mechanics, and
Human Motion, Englewood Cliffs, NJ: Prentice Hall, pp. 186-200. Note, the Hay and Reid supplemental
reading (posted separately on the class web page) is crucial to fully understanding this lab. Hay and Reid
present the reaction board method in detail and provide the terminology and equations used in this lab.
Introduction and Theory: The center of mass (CM) is the point on a body that moves in the same way that
a particle subject to the same external forces would move. For example, when a point mass (approximated
by a steel ball or shot) is thrown or put, it moves in a parabolic path under the influence of gravity. The CM
of a long jumper follows a similar parabolic path while airborne, and it is the only point on the body to do this
(see Figure 1). The CM can be considered to be the average (mean) location of all the particles of body
mass.
Because the CM of a body is dependent on the distribution of its mass, the CM location for a rigid body (i.e.,
one that does not experience any change in shape) will be fixed. In contrast, the CM of a body whose mass
distribution can change (e.g., the human body) will not have a fixed location. In addition, it is important to
keep in mind that the CM location may sometimes fall outside of the body. A doughnut, for example, has its
CM in the “hole” in its middle.
Figure 1. The CM of a long jumper follows a parabolic path while airborne.
If the body is placed in a gravitational field, this point is also called the center of gravity (CG). Thus, while
the body always has a CM regardless of the presence of gravity, it does not always have a CG (e.g., while
floating in outer space in the absence of gravity).
For human motion analysis, two primary methods have been used to assess CM location: a) a reaction
board technique which is easily applied to static positions, and b) a segmentation method, the more versatile
of the two since it can be applied to dynamic situations, which involves an estimation of individual segment
masses and positions. In this lab, you will be introduced to the reaction board method. The segmental
method will be presented in a separate handout and/or assignment.
Purpose: To compute the CM location along the longitudinal axis of the body in a supine position using the
reaction board technique.
CM 1
Reaction Board Method: The direct method of calculating the CM involves a device known as a reaction
board. It consists of a long rigid board supported at each end on “knife edges” (see Figure 2) Under one
end is a scale, the other end is simply elevated such that the board is level. The initial scale reading (R1) as
well as the length of the board between the knife-edges (d) are noted before a person lies on it (see Figure
3). The scale reading increases to a new value (R2). The placement of the added weight (x) relative to the
foot end (A) determines how much of the person’s weight (W) is reflected as an increase in the scale
reading. If the CM of the person falls exactly half way between the knife edges, then the increase in the
scale reading (R2 – R1) will be exactly half of the person’s weight. (Note that the person’s height is not
necessarily the same as the distance d as shown in Figure 2.) Thus, by measuring the increase in scale
reading and knowing the person’s weight, one can calculate the distance (x) from the feet to the person’s
CM. The equation that is used is
( - )
x = R2 R1 d
W
(1)
To compare between people, this distance x should be expressed as a percentage of a person’s standing
height (h). For the average male, this percentage is about 57%. For the average female, this percentage is
about 55% (see Figure 3). Note: The complete derivation of Equation 1 can be found in Hay & Reid (1988,
pp. 193-196). The student should be prepared to derive this equation using the Free Body Diagrams shown
in Figure 2 and the principles of static equilibrium.
Procedures: Each student should obtain an accurate measure of height and weight. Omphalion (navel or
belly button) height will also be measured. The weight should be measured with the same scale as used for
the reaction board (why?). The initial scale reading (R1) and distance between the knife-edges of the board
(d) will be recorded. The student will then carefully lie down on the board with arms at one’s sides. Be sure
to line up the soles of the feet with the inferior knife-edge of the board. A new scale reading (R2) will be
recorded.
The student then raises his or her right arm above the head (without shoulder tilt) and a new scale reading
will be recorded. Next, a shoulder tilt will be added and a new scale reading recorded. Finally both arms are
raised above the head and a new scale reading will be recorded. These extra scale readings will be used to
calculate where the CM is located when one raises each arm, in turn, above the head. In general, the CM
moves up within the body 3-5 centimeters per arm. Be careful to keep the soles of the feet lined up with the
end of the board for each position.
Results. Complete steps 1-5 below including answering the questions in steps 3-5. Write your answers on
the answer sheet attached to this handout. Show example calculations in the space provided. Also answer
the discussion questions on page CM4.
1. Using Equation 1, calculate the distance (x) from the feet to the CM for each body position (arms down,
one arm up without shoulder tilt, one arm up with shoulder tilt, and two arms up). Express these
distances both in absolute units (centimeters) and as percentages of the student’s height. Write your
answers on the answer sheet on page 5 of this handout.
2. Calculate your CM location relative to your omphalion (navel) for each condition, e.g., the CM falls 2
centimeters below or 1 centimeter above the navel, etc. Add these values to your answer sheet.
3. Compared to the arms down condition, how many centimeters (not %) did your CM move up when one
arm was raised above the head (with and without shoulder tilt)?
4. Compared to the arms down condition, how many centimeters (not %) did your CM move up when both
arms were raised above the head?
5. For the arms down condition, compare your results to the average (55% for women, 57% for men) for
the general population. Why might you be different than the average person (if you are indeed different,
realizing that a simple error might have been made either in the data collected or in your calculations)?
CM 2
2.0m
Figure 2. Approximate dimensions (a) and Free
Body Diagrams of the Reaction Board without a
person lying on it (b) and with a person lying on it
(c). Note, it is not necessary that the length of the
reaction board be the same as the person’s
height. This is a coincidence in this figure.
Figure 3. Relative heights of the CM of
the typical female (left) and male (right)
as percentages of standing height.
CM 3
Discussion Questions. (Type up your answers to these discussion questions.)
1. What might account for sex differences in the CM location?
2. Why does the CM shift upward when the arms are raised above the head? (Explain in mechanical
terms. Hint: it has something to do with moments.)
3. Do you expect any shift in CM location when a shoulder tilt is added to the one-arm-up condition? Why
or why not?
4. Do you think the position of the CM to be higher, lower, or at the same level within the body when the
body is standing up as when the body is lying down? Why or why not? (Hint: What does gravity do to
the position of the internal organs and fluids within your body?)
5. Assuming that the gymnast in Figure 4 is maintaining a static position (and not falling), where would you
expect the position of her CM to lie relative to her base of support? What would happen if her “line of
gravity” moved outside of her base of support (as shown in dotted lines)? Explain.
6. In order to reach the highest in a vertical jump, what position of the arms should an athlete adopt at
takeoff and the peak of the jump? Why? (Hint, see Figure 5 below.)
Height of
Reach above
Center of Mass
Maximum Height
Center of Mass is
Raised (same for
all three)
Figure 4. Unstable equilibrium.
Figure 5. Possible body positions used in a vertical jump and reach.
Similar concepts in Figure 5.15 on page 136 of McGinnis (2005).
Note: Figures 1, 4, and 5 come from Hay, J.G. (1993). The Biomechanics of Sports Techniques, Englewood
Cliffs, NJ: Prentice Hall. Figures 2 and 3 come from Hay, J.G. & Reid, J.G. (1988). Anatomy, Mechanics,
and Human Motion, Englewood Cliffs, NJ: Prentice Hall.
Lab Report due Wednesday November 22 at 9:40 AM. With the exception of the table on page CM5 that
can be hand-written, please type up your report (double spaced, please).
CM 4
Name_____________________________________
Answer Sheet
Raw Data:
Example calculations:
Reaction Board Length (d)
_____________
Your standing height (h)
_____________
Your omphalion (navel) height (xo)
_____________
Your body weight (W)
_____________
Initial Scale Reading (R1)
_____________
Final Scale Readings (R2)
a. Both arms down
_____________
b. One arm up w/o shoulder tilt
_____________
c. One arm up with shoulder tilt
_____________
d. Both arms up
_____________
Calculated Data:
Calculate your body CM location relative to the bottoms of your feet (x), your navel (x–xo), or
your both-arms-down CM location (x-xa):
x (cm)
x (% of h)
x–xo (cm)
x-xa (cm)
_________
_________
_________ .
b. One arm up w/o shoulder tilt
_________
_________
_________
_________
c. One arm up with shoulder tilt
_________
_________
_________
_________
d. Both arms up
_________
_________
_________
_________
a. Both arms down
xa
0.0
.
CM 5