Homework 1 - F23 Solution

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University of Michigan *

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250

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Mechanical Engineering

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Feb 20, 2024

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ME250 | F23 | University of Michigan HW1: Lectures 2, 3, and 4 (40 pts) - SOLUTIONS Design Process, Concept Generation, Static Analysis Due Tuesday, September 19th by 11:59 pm on Canvas This is an individual assignment, and your solution must be entirely prepared by you. Homework assignments must be completed on your own (unless they are team assignments), however you are encouraged to discuss the problems with your classmates. Upload a PDF of your solution to the Assignments tab on Canvas. Problem 1: Functional Requirements (10 pts) Sensible approaches could include: interviews with soldiers; interviews with army doctors and medical staff about the injuries they see; focus groups with soldiers, doctors, and equipment providers; medical data records; consult biomedical science experts A. Functional Requirements: a. Exoskeleton must weigh less than 10 lbs. CORRECT +2 point for identifying as correct b. Exoskeleton should be able to be put on and removed by a soldier quickly. INCORRECT because it is not measurable +1 points for identifying as incorrect +1 point for reasoning c. Exoskeleton lithium-ion batteries should maintain a constant average power level of 75 Watts for a period of 48 hours INCORRECT includes design because of batteries +1 point for identifying as incorrect +1 point for reasoning d. Exoskeleton should not be visible when worn in combat
INCORRECT due to visibility not being measurable +1 point for identifying as incorrect +1 point for reasoning B. Write one new functional requirement for an assistive robotic exoskeleton Should state what it must do, not limit design, and be measurable/include target value. +2 points for a correct FR Problem 2: Concept Generation and Concept Sketching (12 pts) 1. During the video segments for Lecture 03, you were asked at two points to complete an activity. a. Generate at least three new concepts for a trash can using a Brainstorming Exercise. Describe each of the concepts by using a phrase, or using a quick sketch that is labeled. i. 1 pts per concept provided for a total of 3 pts b. Create new concepts for a plane by creating a 3 x 3 Morphological Chart using Functional Decomposition. Simply creating the chart, with 3 subfunctions and 3 solutions for each subfunction, is enough for this assignment. You do not need to write out the potential concepts after you have written the potential solutions in the chart. i. 1 pt per concept provided within the morphological chart for a total of 9 pts Problem 3: Static Analysis (18 pts) A. Label the following box with forces to create a free body diagram for the slip/tip of the tractor. You may treat the entire tractor as one body (i.e., a box on an inclined plane). The normal force N and the point of rotation ‘o’ have been provided for you. (4 pts)
+0.5 pt for each correct force +0.5 pt for each correct force approximate orientation (mg should be vertical, F should be horizontal, and Ff should be aligned with axes) +1 pt for no extraneous forces OK if mg and/or F are split into axes B. Write the SYMBOLIC equilibrium equations for the free body diagram, but do NOT solve. Use the provided point ‘o’ as your moment center. Report your answers in the boxes provided. (6 pts) Σ F x : 0 = F oxen *cos(θ) - M tractor *g*sin(θ) - F f Where F f = μ*N (optional) Σ F y : 0 = N - F oxen *sin(θ) - M tractor *g*cos(θ) Σ M o : 0 = 0.5*L wheelbase *M tractor *g*cos(θ) + 0.5*D wheel *M tractor *g*sin(θ) - F oxen *0.5*D wheel *cos(θ)
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+1 pt for including all correct variables (each graded separately) +1 pt for correct equations (each graded separately) (6 pts total) Consider correct free body diagram C. Using the values provided in the table, and g = 10 m/s 2 , determine whether the tractor will tip or slip. Defend your answer with justification. (8 pts) Tip condition: ΣM o < 0: ΣM o = 0.5*L wheelbase *M tractor *g*cos(θ) + 0.5*D wheel *M tractor *g*sin(θ) - F*0.5*D wheel *cos(θ) ΣM o = 0.5*4*4,000*10*cos(20) + 0.5*2.5*4,000*10*sin(20) - 22,000*0.5*2.5*cos(20) ΣM o = 75175.41 + 17101.01 - 25841.55 ΣM o = 66434.87 66435 > 0, so it will NOT tip Slip condition: ΣF x > 0: ΣF x = F*cos(θ) - M tractor *g*sin(θ) - F f ΣF x = F*cos(θ) - M tractor *g*sin(θ) - μ*N N = F*sin(θ) + M tractor *g*cos(θ) ΣF x = F*cos(θ) - M tractor *g*sin(θ) - μ*(F*sin(θ) + M tractor *g*cos(θ)) ΣF x = 22,000*cos(20) - 4,000*10*sin(20) - 0.16*(22,000*sin(20) + 4,000*10*cos(20)) ΣF x = 20673.24 - 13680.81 - 7217.94 ΣF x = -225.51
-226 < 0, so it will NOT SLIP +2 pt for attempting tip condition/calculation +1.5 pts if tip calculation is correct +1 pt for correctly stating the tractor will not slip +2 pt for attempting slip condition/calculation +1.5 pts if slip calculation is correct