KIN 335 - Biomechanics LAB: Center of Mass (Center of Gravity) of the Human Body Reading Assignment: Bishop, R.D. & Hay, J.G. (1979). Basketball: the mechanics of hanging in the air. Medicine and Science in Sports, 11 (3), 274-277. Introduction: When a body is acted upon by gravity, all of the mass particles of which the body is composed experience a force of attraction directed toward the Earth’s center. The resultant force of all of these small attractive forces is the body’s weight and the location at which the resultant force is assumed to act is the center of gravity (CG) of the body. Looking at the CG differently, it is the theoretical location that represents the balance point of the body in a gravitational field (i.e., the point about which all mass particles that make up the body will be balanced in Earth’s gravity). In some simplified analyses of movement, the CG is the location at which all of the body’s weight is sometimes assumed to be concentrated and is the point that reflects the general motion of the body as a whole (Figure 1). Because the CG of a body is dependent on the distribution of its mass, the CG location for a rigid body (i.e., one that does not experience any change in shape) will be fixed. In contrast, the CG of a body whose mass distribution can change (i.e., the human body) will not have a fixed location. In addition, it is important to keep in mind that the CG location may sometimes fall outside of the body. A doughnut, for example, has its CG in the “hole” in its middle. For human motion analysis, two methods have been traditionally used to assess CG 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 both methods. Purpose: 1) To compute the CG location along the longitudinal axis of the body in a supine position using the reaction board technique, and 2) to compute the CG location of an individual captured in a still photograph using the segmentation method. Part 1. Reaction Board Method The direct method of calculating the CG involves a device known as a reaction board. The reaction board consists of a long rigid board which is supported as each end on “knife edges” (see Figure 1). Under one end of the board is a scale. The other end is simply elevated such that the board is level. Measurement of the CG location is based on the principle of static equilibrium (i.e., analysis of a static or stationary position of objects) in which the sum of all moments or torques acting on a system about a reference axis of rotation (A) equals zero. When the reaction board is unloaded (refer to Figure 1), the equation of static equilibrium is: MA=∑0 (1) The equation used to calculate the location of the CG relative to the reference axis is derived as follows: MRdwxAbb=− =∑()( )10 (2) where R1 equals the scale reading when the board is not loaded; d is the distance between the supporting knife edges (i.e., the moment arm of R1 with respect to axis A); wb is the weight of the board; and xb is the distance from axis A to the center of gravity of the board (i.e., the moment arm of wb with respect to axis A).When a person assumes a prescribed position on the reaction board (see Figure 2), the equation of static equilibrium becomes: MRdWxwxAbb=−− =∑()()( )20 (3) where W equals the person’s body weight and x is the distance from axis A to the CG of the person’s body (i.e., the moment arm of W with respect to axis A). Rearranging equation 2, we can show that: ()( )Rd w xbb1= (4) Substituting (R1d) for (wbxb) in equation 3, the equation of static equilibrium when a person is in a prescribed position can be rewritten as: ()()()Rd Wx Rd210−−= (5) Finally, solving for x (i.e., the location of the CG with respect to axis A), xRRWd=−⋅()21 (6) Therefore, in the case of the reaction board technique shown in Figure 2 (see the following page), it is not necessary to measure the weight and location of the center of gravity of the board. The contribution of the weight of the board to the moments produced about axis A is accounted for by the scale reading taken from the system when the board is unloaded (R1). Consequently, determination of the CG location of a body with respect to a reference axis of rotation involves four steps: 1. A scale reading is taken when the reaction board is unloaded (R1). 2. Subject assumes the desired position on the reaction board. 3. A second scale reading is taken (R2) with the subject maintaining the desired position. 4. The CG location (x) with respect to the reference axis is calculated using equation 6.Procedures: 1. Identify one person in your group who will be tested. Obtain an accurate measure of height (h) and weight (W) using the same scale which will be used for the reaction board: Weight (W) = ______ lb Height (h) = ______ in 2. Record the initial scale reading (R1) and the distance between the knife edges of the board (d). R1 = ______ lb Length (d) = ______ in 3. Instruct the participant to lie supine on the reaction board taking care to align the soles of the participant’s feet with axis A (see Figure 2). a. Record scale reading, R2A, while the participant lies on the board with arms at sides. R2A = ______ lb b. Record scale reading, R2B, while the participant lies on the board with one arm raised overhead. R2B = ______ lb c. Record scale reading, R2C, while the participant lies on the board with both arms raised overhead. R2C = ______ lb 4. Using equation 6, compute the distance from axis A to the participant’s CG in absolute terms (inches) and then as a percentage of the participant’s standing height. Perform these calculations for each measure of R2(A,B,C). Arms at sides (A): x = ______ in x = ______ % height One arm elevated (B): x = ______ in x = ______ % height Both arms elevated (C): x = ______ in x = ______ % height Discussion Questions: (Note: These are not to be handed in. Use these to help you study for upcoming quizzes and examinations.) 1. What might account for gender differences in the location of the CG? 2. Why does the CG shift upward when the arms are raised above the head? (You