Lab+7+-+Center+of+Mass+-+Handout copy

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Dec 6, 2023

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KHP 415 - Biomechanics and Human Movement 1 Section: Name: KHP 415 - Biomechanics of Human Movement Laboratory Lab 7 – Center of Mass (a.k.a. Center of Gravity) of the Body Reading Hay (1978), pp. 120-139 Introduction The purpose of this lab is to estimate COM location based on reaction board and segmentation methods. COM is the theoretical location that represents the balance point of the body in a gravitational field. The COM of a body depends on the distribution of the mass and could be either located inside the body or outside the body. Two major methods used to estimate the COM location: 1) reaction board method (easy to apply in static position) 2) segmentation method (can be applied in both dynamic and static conditions) Equipment Reaction board, ruler, calculator. Report Consult with your TA regarding report format. Tasks Part I: Reaction Board Method Figure 1. Reaction Board Method The reaction board, a long and rigid wooden board is supported by a scale as the board is level. The measurement of the COM location is based on the principle of static equilibrium in which the sum of all moments or torques acting about an axis of rotation equals zero: ΣM A = 0 With reaction board unloaded (left panel) the equation of static equilibrium is written as: ΣM A = (R 1 ×d) – (m b ×x b ) Where R 1 is the scale reading, d is the moment arm of R 1 , m b is the board weight and x b is the moment arm of the board weight (distance from axis A to the COM of the board). With a subject lying on the reaction board the equation changes to:

KHP 415 - Biomechanics and Human Movement 2 Section: Name: ΣM A = (R 2 ×d) – (m b ×x b ) – (M×x) Where R 2 is the scale reading as board loaded, W is the subject’s body weight and x is the moment arm of COM of the subject (COM location needs to be found out). The location of COM can be solved combining the above two equations: x = (R 2 – R 1 )×d/M Reaction Board Data Collection and Analysis Procedures (20 points) 1. Identify one person in your group who will be tested. Obtain an accurate measure of height (h) and body mass (M) using the same scale which will be used for the reaction board: BM (M) = __87.6__ kg Height (h) = _187.5__ cm 2. Record the initial scale reading when the reaction board is unloaded (R 1 ) and the distance between the edges of the board (d) : R 1 = _7.5___ kg Length (d) = _196__cm 3. Instruct the subject to lie supine on the reaction board, taking care to align the soles of the subject's feet with axis A (see Figure). a. Record the scale reading, R 2A , while the subject lies on the board with both arms at sides: R 2A = __54.5____ kg b. Record the scale reading, R 2B , while the subject lies on the board with one arm raised overhead: R 2B = 56.2____ kg c. Record the scale reading, R 2C , while the subject lies on the board with both arms raised overhead: R 2C = _57.6___ kg 4. Compute the distance from axis A to the subject's COM (x) in absolute terms (cm) and then as a percentage of the subject's body height. Perform these calculations for each of the three arm positions R 2(A,B,C) (A) Arms at sides ............................ x = ____105.16__ cm x = __56____ % body height (B) One arm raised overhead ........... x = ______108.96 cm x = __58.1____ % body height (C) Both arms raised overhead ........ x = ______ 112.1 cm x = __59.8____ % body height Discussion Questions : (8 points each) 1.What might account for gender differences in the location of the COM (Figure 1 right panel)? Because of body shape and anatomy. The female will have larger lower bodies so a lower center of mass makes a difference 2. In which direction does the COM shift when the arms are raised overhead? What was the relative shift in the COM position when comparing conditions B and C (i.e., one arm vs. two arms shifted overhead)? Would the shift in COM position have been larger or smaller if the subject had held a 5 kg weight in each hand? Why? The center of mass shifts more towards the feet when the arms are raised above the head.When arms of the head the COM went higher up on the body. The should’ve would have been larger because it would have been an added mass to the shift. 3. How does your subject's computed COM location expressed as a percentage of body height compare with values reported for the general adult population (Figure 1 right panel)?

KHP 415 - Biomechanics and Human Movement 3 Section: Name: 4. Assuming that the gymnast in Figure 2 is maintaining a static position, where would you expect his line of gravity (i.e., a vertical line passing through the COM) to intersect the ground relative to his hands? Explain. We would expect it to be perpendicular from both hands so that it’s at equilibrium 5. In order to reach as high as possible in a vertical jump, what position should an athlete adopt at the peak of the jump? Refer to Hay (1993), p. 126. The text says that at the peak of the jump, one should have one arm down which should increases distance by 1 inch. Figure 2. Gymnast Part II: Segmentation Method The segmentation method is based on calculating the weighted average of the center of mass locations of the individual body segments: Σ (m i ×x i ) = M B ×X B and Σ (m i ×y i ) = M B ×Y B Where m i represents the weight of individual segment i , x i and y i represent the x and y coordinates of the COM of segment i . BM is the total body mass and X B and Y B represent the x and y coordinates of the total body COM. Segmentation Procedures Compute the whole body COM location for an eight-segment representation of the person in Figure 3. Use only the right side of the figure for your measurements. A sample calculation for the determination of the whole body COM is provided in Hay (1978), pp. 136-138. (Tables 1 and 2 are worth 8 points each, as is your marked version of Figure 3) 1. Print one extra copy of Figure 3 (page 6 on the handout) and save the original in case you make a mistake. 2. Make an educated guess of the location of the whole body COM. You will compare this estimated COM with your calculated location. 3. Carefully mark the position of the segment endpoints (see Figure 3 and Hay, p. 137). Refer to Figures 4 and 5 for extra information on segment endpoints. 4. Construct a stick figure representation of the individual by drawing straight lines between appropriate segment endpoints (see Hay, p. 137). 5. Measure the length of each segment in millimeters ( note that these are millimeters measured on the page, not the actual length) and record the values in Table 1. Using these lengths and the data expressing the locations of body segment COM's as a percentage of segment length from the noted

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KHP 415 - Biomechanics and Human Movement 4 Section: Name: reference point (provided in Table 1), compute the distance of the COM of each body segment from the same landmark. Using these computed distances, mark the segment COM locations on your working copy. 6. For each segment, measure the horizontal and vertical perpendicular distances from the segment COM to the x and y axes in millimeters (i.e., the x and y cartesian coordinates of each segment COM), and record these values in Table 2. Note: the x coordinate is the perpendicular distance from the y-axis (i.e., vertical axis), the y coordinate is the perpendicular distance from the x-axis (i.e., horizontal axis). 7. To find the mass-weighted center of mass coordinates, multiply the relative weight of each segment by its distance from the axis. Do this for both the horizontal and vertical axes and record the results in Table 2. 8. For each axis, sum the mass-weighted center of mass coordinates and record the result in Table 2. 9. Compute the location of the total body COM relative to the horizontal and vertical axes by dividing the sum of mass-weighted center of mass coordinates by the total relative body weight (i.e., 100, which represents 100% of body weight). Record these values in Table 2 and then measure and mark this location (i.e., X B , Y B ) on your working photocopy. 10. Double check your segment markings and computations. Common errors include measuring segment COM locations from the wrong end of the segment (for nearly all segments, the segment COM lies closer to the proximal end than the distal end). Discussion Questions (8 points each) 1. Considering the position of the body segments, is your estimated total body COM reasonable? How does it compare to your guess (from step 2)? Explain. I think the center of mass is going to be in the upper thighs because that seems to be where most of the body weight is. My guess was correct, the COM is in the upper thighs. 2. The segment mass and COM values provided in Table 1 are based on elderly male cadavers . How do you think a (living) male athlete's values would compare? How do you think a (living) female athlete's values would compare? I think a male athlete will be more flexible than an elderly male so their center of mass may be every more towards their trunk. I think a female would be even more flexible than both the elderly male and the male athlete so her center of mass may be even lower.

KHP 415 - Biomechanics and Human Movement 5 Section: Name: Table 1. (8 points). Segment lengths and segment COM locations as a percentage of segment length measured from the proximal end. Segment Length (mm) COM location (%) COM location (mm) Head 30 .464 from vertex 13.92 Trunk 43 .438 from supersternale 18.834 Upper arm 37 .491 from shoulder 18.167 Forearm 25 .418 from elbow 10.45 Hand 12 .820 from wrist 9.84 Thigh 47 .400 from hip 18.8 Shank 46 .418 from knee 19.228 Foot 32 .449 from heel 14.368 Table 2. (8 points) Data summary for segmental computation of body COM. Segment weights are expressed as a percentage of total body weight; distances should be in millimeters. Segment Relative mass ( m i ) Horizontal COM distance ( x i in mm) Weighted x- coordinates ( m i x i ) Vertical COM distance ( y i in mm) Weighted y- coordinates ( m i y i ) Head 7.3%=0.073 95 6.935 85 6.2 Trunk 50.7=0.507 52 26.36 91 46.137 Upper arm 5.2 74 3.848 68 3.36 Forearm 3.2 75 2.4 37 1.184 Hand 1.4 78 1.092 15 0.21 Thigh 20.6 37 7.622 90 18.54 Shank 8.6 45 3.87 44 3.784 Foot 3.0 50 1.5 11 0.33 m i = 100% m i y i =53.6 m i x i = 79.6 Total body center of mass location: X B = mm Y B = 53.6 mm