Problem Set #6

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University of Guelph *

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2270

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Mechanical Engineering

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Jan 9, 2024

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Principles of Biomechanics 1 HK*2270 Problem Set #6 PART A. STATIC QUILIBRUM & BONE/BONE FORCES Similar to Problem Set #4, read the questions carefully. When setting up your equations of static equilibrium consider what you know/don’t know. Do you first need to calculate Net joint Moment to help you solve for the muscle forces (F m )? Can you use information about Muscle forces to determine the moment about a particular joint? 2. (a) Given the information below, calculate the muscle force (Fsme) at the shoulder joint that maintains this static position. 2 (b). Given the calculated muscle force (above) and joint reaction forces provided (in illustration box above), calculate the bone-on-bone forces (x, y) produced at the shoulder joint with respect to the upper arm. Hint! You will need to calculate the X and Y muscle force components. For Question 1 Note that: M shoulder = 231.1 Nm Jrx = 201.2 N Jry = 989.4 N 1 (a). A man holds a 10 kg box in his hand as illustrated (right). The forearm+hand mass is 1.9 kg. The relative elbow angle is 90 degrees with the forearm as the horizontal. A single muscle equivalent for the elbow flexors inserts at 80 degrees to the forearm at a length of 4.4 cm from the elbow’s center of rotation. Calculate the required elbow flexor muscle force to hold the posture in static equilibrium. (b) Calculate the Bone on Bone Forces at the elbow required to sustain this posture.

Principles of Biomechanics 2 2 (c) Calculate the total compression and shear forces at the shoulder joint. Be sure to use an appropriate, anatomically relevant axis system for these calculations. Please use the Bone on Bone forces provided below : 3 (a). Using the information provided in the diagram below, draw a free body diagram for each situation (A) and (B) then calculate the net joint moment (assume static equilibrium) required to sustain each of the arm postures illustrated. Based on the results of these calculations, which arm position would you recommend for an individual to use in order to carry their groceries home on the bus, and why? (b) On a dare that you accept from your roommate, you decide to use Position B to walk home from Zhers with your groceries. What is the muscle force you will require to sustain this posture of the shoulder? The close up figure for Fig B should help with this question, note that r = 7.2 cm . (c) What are the bone on bone forces you will experience at the shoulder joint if you sustain Posture B? c a = 41 cm b = 10 cm c = 27 cm d = 14 cm e = 21 cm f = 41 cm g = 32 cm mass of arm = 2.1 kg mass of zehrs bag = 4.2 kg zehrs zehrs f g a A B e d b For Question 5: Close Up of Fig B zehrs B F sme r 43° Diagram:

Principles of Biomechanics 3 4 (a). One of your peers in the class has been working on a challenging biomechanics question. He has already calculated the net joint reaction forces for the foot segment acting at the ankle joint (Fig 4A, note the arrows indicate the direction of the forces and moment she calculated at the ankle joint for the foot). The mass of the shank segment is 6.9 kg. Using a link segment analysis technique (don’t forget Newton’s Third law!) and the information he has already verified as being correct, i) draw a free body diagram of the shank segment, ii) assume static equilibrium and calculate the net joint forces and moment for the knee joint (Fig 4B), iii) indicate if the moment that is being sustained at the knee joint is abduction or adduction . (b) Muscles and ligaments that surround the knee joint (F SEM ) pull at 48° at a point 5.3 cm from the knee joint axis. In the space provided, calculate the magnitude of the force (F sme ) that will be required to maintain the net joint moment for the static posture of the shank that you calculated in Part A. Assume there are no other tissues that can create a moment of force about the knee joint. For Question 6 For Question 6

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Principles of Biomechanics 4 PART A. STATIC QUILIBRUM - ANSWERS * Note: More significant digits have been included in some of these solutions to make it easier for you to check your answers. 1. (a) M elbow = +38.49 Nm ; F muscle = 888.9 N (b) Bone on Bone forces: BnBx = +153.43 N and BnBy = -758.7 N 2. (a) Fsme = 3590 N (b) Fsme-x = 3592 cos 22 = 3329.5 N Fsme-y = 3592 sin 22 = 1345.6 N BnBx = -3128.6 N = - 3129 N BnBy = - 355.9 N = 2340 N 2(c) + Compression due to BnBx =678 cos 43 = - 495.86 N + Shear due to BnBx =678 sin 43 = + 462.4 N - Compression due to BnBy = 423 cos 47= - 288.49 N - Shear due to BnBy = 423 sin 43= -309.36 N Total Compression = -784 N Total Shear = + 153.04 N 3. (a) Net Joint Moment for Posture A = 2.061 Nm . Net Joint Moment for Posture B = 21.105 Nm . I would recommend posture A as the net joint moment generated at the shoulder joint is considerably less (b) Muscle force required to sustain the static posture is 429.8 N (c) Bone on bone forces: BnBx = 314.36 N and BnBy = -231.9 N 4. (a) Net Joint moment for the knee is - 53.62 Nm (b) F sme = 1361.6 N

Principles of Biomechanics 5 PART B. LINK SEGMENT MODELING 1. A person is standing still on one foot as indicated (see figure below). A force plate reading tells us that the vertical ground reaction force acts underneath the foot, 6.3 cm anterior (forward) from the ankle joint. No horizontal ground reaction force was found. The following masses are given: i) total body mass = 80.0 kg ii) thigh mass = 8.0 kg iii) lower leg (shank) mass = 3.68 kg iv) foot mass = 1.2 kg Calculate the net joint forces and moments at the ankle AND knee joints. Hint: You will need to use a Link Segment approach to solve this question. From the calculated net joint moments and with the with the orientation/position of the leg as illustrated below, indicate if the moment being generated about the ankle and knee joints to maintain this static position is dorsi-or plantar flexion (ankle) and flexion or extension (knee). Which corresponding muscle groups should then be active about each joint to maintain this static leg posture? 4 cm 24 cm 26 cm 20 cm 110 ° 70 ° Y+ X+ M + 4 cm 24 cm 26 cm 20 cm 110 ° 70 ° Y+ X+ M + Y+ X+ M +

Principles of Biomechanics 6 2. A friend has just completed a biomechanical analysis and has given you the following information about knee joint based on his calculations for the lower leg segment. Using a LINK SEGMENT approach, continue the calculations for the thigh segment; calculate the net joint moment at the HIP. Note that the mass of the thigh is 10.30 kg. PART B. LINK SEGMENT MODELING - ANSWERS 1. FOOT: F ankle-x = 0 N; F ankle-y = -773 N; Moment at Ankle = -48.97 Nm (Plantar Flexors: Gastrocs, Soleus ) LOWER LEG: F knee-x = 0 N; F knee-y = -736.9 N; Moment at Knee = 64.9 Nm (knee extensors: Quadriceps ) 2. (Note that this question does not ask you to solve for the Joint reaction forces at the hip) Net joint Moment at Hip = -328.3 Nm

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