bme lab report 1

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University Of Connecticut *

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3600

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Mechanical Engineering

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Dec 6, 2023

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Lab 1: Trunk Bending Analysis Written by: Isabella Rojas Group Members: Rachel Turanchik, Manav Surti, Chase Williams BME 3600 Lab Section 001L Group 1

Table of Contents Title Page: ........................................................................................................................................ 1 Table of Contents: ............................................................................................................................ 2 Introduction: ..................................................................................................................................... 3 Methods: ....................................................................................................................................... 4-7 Results: ....................................................................................................................................... 8-10 Discussion: ................................................................................................................................ 11-12 Conclusion: .................................................................................................................................... 13 References: ..................................................................................................................................... 14 Appendix: ................................................................................................................................. 15-18

Introduction This first lab was on trunk bending analysis, focusing on the forces acting upon the body when placed in different positions, including bearing different loads also. The lab is composed of two parts, where in part A, the system we are studying is the trunk bending. The trunk bending analysis utilizes the torso, arms, and legs of the body. This consists of multiple different positions of bending over tables or leaning face-first against a wall, each position being slightly different than the last to determine the change in the forces acting on the body. Part B consists of the knee bending analysis, using the upper and lower half of the leg. When the subject is in a squatting position, the knees will be bent while the torso is kept at an upright angle. The subject is put into 3 different positions while holding weights and squatting. By performing these experiments and calculating the forces acting on the body, these forces can be converted to stresses and strains. The purpose of this lab is to analyze the forces acting on the body in an average everyday scenario. The body is constantly moving and being put into different positions as well as bearing different loads. In this lab static analysis of a human physiological system will be performed to determine forces associated with body positioning. This is important as trunk bending is an activity people perform everyday without realizing just how large of a load is being put onto their lower backs in different positions. By performing an analysis of the static loads in each position it can be determined, the forces and bending moments the body must endure on a daily basis which could even help doctors diagnose people who are having lower back pain.

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Methods Part A of this lab consisted of the trunk bending analysis. There were a total of 4 different positions to be analyzed in this section of the lab. There were 5 main steps which were completed during the trunk bending analysis for each position. The first step was to record the weight and height of the subject onto the data sheet. The next step would be to record the length of the total arm, trunk, and total leg segments of the subject. The third step is to place the sandbag on a chair or table that approximates the height required for position 1. The fourth step is to have the subject take position 1 and record the appropriate angle and distances on the data sheet. The fifth and final step is simply repeat steps 3 and 4 for positions 2,3,and 4. These five steps were the baseline for the experiment and repeated for every position. Now, the first position known as position 1 has the subject standing upright while slightly bending forwards to lean on a table at waist height. The first measurement made was D1, the horizontal distance from the legs of the subject to their hands on the table. Next, H1 was measured, which was the distance from the ground to the height of the subject's hands on the table. Then, there were two angles measured. First was angle ɑ which is the angle from the subjects legs to their torso. The second angle β is the angle between the subject's torso and their arms. The second position was similar to position 1 except the subject was bending much lower to the ground onto a stool. In this position the distance between the subject;s legs and hands must remain constant from position 1. The new measurements include H2 which is the height from the ground to the subjects hands located on the stool. Once again the two angles ɑ and β must be measured where angle ɑ is the angle between the subjects legs and torso and angle β is the angle between the subjects torso and arms. The next position, position 3 is similar to position 1 where the subject is standing upright and bending over onto a table at waist height. The main difference is that the subject is a new,

further distance from the table denoted as D2. The height of the table must remain constant from position 1 once again being H1. Finally the two angles measured are angles ɑ and β where angle ɑ is the angle between the subjects legs and torso and angle β is the angle between the subjects torso and arms. The fourth and final position for the trunk bending analysis is a new position where the subject is standing upright with their arms and hands reaching above their heads and leaning forward onto a wall. The distance between the wall and the subject's legs must be kept constant from position 1 being denoted as D1. Then, the height from the ground to the subject's hands on the wall must be measured and denoted as H3. Finally, once again the angles ɑ and β must be measured where angle ɑ is the angle between the subjects legs and torso and angle β is the angle between the subjects torso and arms. The second part of this experiment was part B the knee bending analysis. The subject is put into an upright position and must squat down to different heights while holding 10 lb weights in each of their hands. In this position the subject must bend down to three different heights where the distance is measured from the floor to their hands. These measurements are denoted as T1, T2, and T3 and are approximately 18”, 21”, and 24” respectively. The angle that the subject's knee bends must also be measured being denoted as θ. In this position the subject must keep their torso and head upright in a straight rigid form while only bending their knees. For all of these positions and measurements there are a few assumptions that were made. The first being that each part of the body is rigid. This means that for the torso bending analysis the entire arm is one rigid part of the body, the torso, and legs meaning the upper and lower legs are all rigid and one part of the body. As for part B of the experiment, the knee bending analysis shows the upper and lower leg are two separate rigid parts. Another assumption was to ignore the food segment, meaning the leg simply ended at the ankle joint. The next assumption made is that

for part A of the experiment the hands each have a load of 10 lbs, and the support (chair, etc.) holding the weight does not exist. The materials used in this experiment include a scale, yard stick, 10 lb sandbags, tape measure, goniometer, and the Anthropometric data table. Figure 1 Figure 2 First Position First Position Labeled Figure 3 Figure 4 Second Position Third Position

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Figure 5 Figure 6 Fourth Position Fifth Position Figure 7

Results Table 1: Subject Body Measurements Subject Name Chase Williams Height [in.] 76.5 Wight [lbs.] 184 Total Arm Length [in.] 33 Trunk Length [in.] 20 Total Leg Length [in.] 42 Thigh Length [in.] 18 Lower Leg Length [in.] 20 Table 2: Trunk Bending Data Position #1 Position #2 Position #3 Position #4 Height [in.] H 1 = 35 H 2 = 24 H 1 = 35 H 3 = 78.5 Distance [in.] D 1 = 27 D 1 = 27 D 2 = 35 D 1 = 27 Leg - Trunk angle (ɑ) 160° 128° 142° 172° Trunk - Arm angle (β) 66° 121° 118° 130° Table 3: Knee Bending Data Distance T [in.] Angle θ [°] Position # 1 18 62 Position # 2 21 71 Position # 3 24 87

Table 4: Trunk Bending Results X Directional Force [lbs] Y Directional Force [lbs] Axial Force (R a ) [lbs] Shear Force (R S ) [lbs] Bending Moment at Hip (M Hip ) [lbs.in] Position #1 0 122.24 108.4 67.3 590.4 Position #2 0 122.24 57.4 114.7 1098.6 Position #3 0 122.24 106.6 76.3 677.2 Position #4 10 132.24 114.3 83.4 748.9 It is seen from the table that in the trunk bending results, position 4 has the highest axial force at 114.3 lbs and position 2 has the highest shear force at 114.7 lbs. It can also be observed that position 2 had the lowest axial force at 57.4 and position 1 had the lowest shear force at 67.3. As for the bending moment at the hip it can be seen that position 1 had the lowest bending moment at 590.4 lbs.in. Meanwhile, position 2 has the highest bending moment of the four positions at 1098.6 lbs.in. Positions 1,2, and 3 all share x directional forces and y directional forces at 0 lbs and 122.24 lbs respectively. Meanwhile position 4 has an x directional force of 10 lbs and a y directional force of 132.24 lbs.

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Table 5: Knee Bending Results X Directional Force [lbs] Y Directional Force [lbs] Bending Moment at Knee (M Knee ) [lbs.in] T 1 0 132.38 -1872.98 T 2 0 132.38 -1775.13 T 3 0 132.38 -1569.45 It can be seen in the knee bending results table that T 1 , T 2 , and T 3 all share an X directional force of 0 lbs. They all also share a Y directional force of 132.38 lbs. However, each position does have a differing bending moment in the knee. T 1 has the highest bending moment at -1872.98 lbs.in. Meanwhile T 3 has the lowest bending moment of the three at -1569.45 lbs.in.

Discussion After conducting the experiment there were some very interesting results. First up is the trunk bending analysis. To start, one of the most interesting things to notice is that for positions one through three there was 0 lbs of force in the X direction. And then, even for the fourth position there is only a measly 10 lbs of force in the X direction. This seems strange, especially when looking at the force in the Y direction and seeing that there is upwards of 122.248 lbs for positions one through three and 132.24 lbs in position four. When looking at the free body diagrams for the arms, it’s seen that the only force acting in the X direction is F BX . And since it is known the sum of forces must equal to 0 since this is a static analysis, this means F BX itself is equal to 0. Then, by looking at the free body diagram for the torso, there are only two forces in the X direction. These being F BX and F CX . Once again it is known that the sum of forces must be equivalent to 0. And since F BX is equal to 0, F CX must also be equal to 0. This changes in position 4 however, since the hands are pushing in the X direction rather than the Y direction. This is also why there is so much force in the Y direction, as this comes from the weight of the arms, trunk, hands, etc. Next up is the axial and shear forces acting on the trunk. The biggest axial force comes from being in position 4 at 114.3. This makes sense as axial force means the force is along the same direction as the object itself, in this case the spine. Since the subject is in more of an upright position, it would make sense there is more force in the axial direction from the weight of the trunk, arms, etc. As for shear force, position 2 has the largest at 114.7 lbs. This also makes sense because the subject is the most bent over in this position. The more the subject bends over an object, the more force is being applied perpendicular to the subject spine. This also causes position 2 to have the largest bending moment at 1098.6 lb.in. At first this seems like a ridiculously big number. 1098.6 lbs seems like a large amount of force to be applied to the

human body. This could certainly be a main factor as to why so many people are affected by lower back pain when bending over. Especially if this were to be repeated over and over across a lifetime. Next, part B of the experiment consisted of the knee bending analysis. Once again, similar to the trunk analysis the X force is 0 lbs for all three positions. This is strange as it seems like from bending the knees in an outward position there would be some sort of X component to the force, however, there is not. What’s also interesting is that for all three positions they also share the same Y component of force being 132.38 lbs. This is also similar to the trunk bending analysis which shares similar Y force components for each position. Once again, the major component changing in each position is the bending moment. The position with the largest bending moment is T 1 with -1872.98 lb.in. The reason there is a negative sign is because of the direction of the moment. A positive moment means it occurs in the counterclockwise direction while a negative moment means it occurs in the clockwise direction. As seen in the free body diagram for the knee bending analysis, the moment M Knee is in the counterclockwise direction, meaning that the moment calculated is actually a negative number. Anyways, it makes sense that T 1 has the largest bending moment, because it requires the subject to squat down to the lowest position, which certainly would put a lot more strain on the subject's knees. Overall, these results were as expected for the most part, however some of the values are much higher than expected

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Conclusion Overall, while being a simple, straightforward lab, this analysis of trunk bending and knee bending has a lot of real-world applications. For instance, if a patient presented complaining of lower back pain whenever they bent over, the precise forces and moments acting on the patient might be estimated and observed by completing the trunk bending study. This also holds true for patient squatting analysis of knee bending. Not only that, but it might even assist engineers in creating brand-new braces or medical equipment for use in patients. These supports or tools might lessen the force being applied to a patient, so lessening pain and enhancing quality of life. Finally, there is a crucial conclusion to draw from this analysis.

References BME 3600 Biomechanics. (2023). Anthropomorphic Table. Lab Handout BME 3600 Biomechanics. (2023). Lab #1 Trunk Bending Analysis . Lab Handout Davis, L. (n.d.). Deformation of tissues. Body Physics Motion to Metabolism. https://openoregon.pressbooks.pub/bodyphysics/chapter/elasticity-and-hookes-law/ Felton, P. J., Yeadon, M. R., & King., M. A. (2017). How Does the Assumption of Coincident Hip and Shoulder Joint Centres Affect Planar Simulation Models. Force . Exercise Sciences Department. (n.d.). https://exsc.byu.edu/biomechanics/seeley/force Hussien, K. (n.d.). Force On and in the Body . Lee, S. S. M., & Piazza, S. J. (2009). Built for Speed: Musculoskeletal Structure and Sprinting Ability.

Appendix Formulas used for calculations: A1: ΣF x = ΣF y = ΣM = 0 A2: ΣF xArm = F BX = 0 A3: ΣF yArm = F BY - W Arm + W Hand = 0 A4: ΣM BArm = M Shoulder - W Arm * L 5 + W Hand *L 6 = 0 A5: ΣF xArm = F Bx - W Hand = 0 A6: ΣF yArm = F BY - W Arm = 0 A7: ΣM BArm = M Shoulder - W Arm * L 11 + W Hand * L 12 = 0 A8: ΣF xTorso = -F BX + F CX = 0 A9: ΣF yTorso = -F BY + F CY - W Torso = 0 A10: ΣM CTorso = M Hip -W Torso * L 8 - F BY * L 9 + F BX * L 10 - M Shoulder = 0 A11: F Axial = F CX * Cos(Ɛ) + F CY * Cos(ω) A12: F Shear = F CY * Cos(Ɛ) - F CX * Cos(ω) A13: ΣF xLeg = F Dx = 0 A14: ΣF YLeg = F DY - W Thigh - W Arm - W Trunk - W Sandbag = 0 A15: ΣM D = M Knee + W Thigh * L 13 + W Arm * L 14 + W Trunk * L 14 + W Sandbag * L 14

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