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