Homework 1 - F23 Solution
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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
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