Unformatted text preview: Machine Design I (ME4133)  Test II
Attempt all 22 questions, 5% each, and accumulate up to 110%
Time 140 minutes. (Friendly advice: Attempt the bonus questions last)
Justify your answers with the applicable equation, or with a short sentence or two All figures are drawn to their actual dimensions
Student Name: ___________________________ Last 4 digits of ID number: 1. Points A and B are attached to the ends of the link shown in the figure. The link rotates with
angular velocity ω as shown. Draw the vector ω × rB / A
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⋅ A ω = 2 rad/s B AB = 2 in. 2. Points A and B are attached to the ends of the link shown in the figure. The link rotates with
angular velocity ω as shown. Draw the vector ω × (ω × rB / A ) .
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ω = 2 rad/s
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B
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⋅ AB = 2 in. &
3. Points A and B are attached to the ends of the link shown in the figure. The vector ω × rB / A
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is also shown. What is the angular acceleration ω of the link? 1 in./s 2 &
ω= ⋅⋅
⋅⋅
⋅⋅
4 in./s 2
⋅⋅
⋅⋅ ⋅⋅⋅
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&⋅ A
⋅ ω × rB / ⋅
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⋅ ⋅ ⋅ ⋅ ⋅ ⋅ rad/s 2 ⋅ ⋅ A B
AB = 2 in. CCW or CW ? 1 4. Points A and B are attached to the ends of the link shown in the figure. Their accelerations
a A and a B also shown in the figure. Complete the acceleration diagram and determine the
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angular acceleration ω of the link? 1 in./s 2 &
ω= ⋅
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aB
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⋅ ⋅ rad/s 2 ⋅
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⋅ 0⋅
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aA
⋅⋅ ⋅
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⋅ 5 in./s 2 ⋅ ⋅ 2 2 in./s 2 aB aA A B
AB = 2 in. CCW or CW ? 5. Slider B moves toward A with a speed of 1 in./s . At the same time Link 2 rotates with angular
velocity of ω 2 = 2 rad/s CCW. Draw the Coriolis acceleration of B with respect to an
observer at A.
⋅⋅⋅⋅⋅⋅⋅⋅
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ω2 = 2 rad/s
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Scale
2
A
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1 in./s 2
AB = 2 in.
⋅⋅⋅⋅⋅⋅⋅⋅
vB / A = 1 in./s
1
⋅⋅⋅⋅⋅⋅⋅⋅ 6. Slider B moves toward A with constant speed of 1 in./s . At the same time Link 2 rotates with
constant angular velocity of ω 2 = 2 rad/s CCW. Draw the acceleration of B. Scale 1 in./s 2 ⋅
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⋅ ω2 = 2 rad/s
2 A 1 2 AB = 2 in. B
vB / A = 1 in./s 7. An observer is attached to Link 2 at A, as shown in the figure. The velocity v B of B is given.
Complete the velocity diagram associated with the equation v B = v A + v B / A + ω 2 × rB / A ⋅
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3 2 A 1
1 8. An observer is attached to Link 2 at A, as shown in the figure. Complete the acceleration
diagram associated with the equation
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a B = a A + a B / A + ω 2 × (ω 2 × rB / A ) + 2ω 2 × v B / A + ω 2 × rB / A ⋅
⋅
⋅ ⋅ a⋅ 0
⋅
B
⋅⋅⋅
⋅⋅⋅
⋅⋅⋅ ⋅r
⋅ ω 2 ⋅× (ω 2 × ⋅ B / A )
⋅⋅⋅⋅
⋅⋅⋅⋅
&
⋅ ⋅ ω 2 ⋅× rB⋅/ A ⋅
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⋅ ⋅ Scale 1 in./s 2 ⋅
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⋅ ⋅⋅ B 3 2 A 1
1 9. Disk 2, of radius R = 1 in. , rolls on the ground without slip. Point A moves with constant
velocity v A = 2 , as shown in the figure. Point B, on disk 2, is the instantaneous point of
contact between disk 2 and the ground. Draw the acceleration of point B. ⋅
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B 1 3 10. Disk 2, of radius R = 1 in. , rolls on the ground without slip. Point A moves with constant
velocity v A = 2 , as shown in the figure. Draw the acceleration of point B. ⋅
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⋅ A B v A = 2 in./s 2 1
11. Disk 3, with center B, rolls on Link 2 without slip. What is the direction of the acceleration of
point B with respect to an observer at A, which is attached to Link 2?
(a) In the direction parallel to AB 3 • (b) In the direction perpendicular to AB B ω2 (c) In the direction parallel to Link 2 A (d) In the direction perpendicular to Link 2 2 1
Circle your answer (e) At infinity, perpendicular to the ground 12. Points A and B are attached to a rigid body. Which one of the following cases is impossible? Answer: Case ___________
aA aA A aB A aB
B B Case (b) Case (a) aA
aB A A aA aB
B B Case (c) 4 Case (d) 13. Link 2 rotates with angular velocity ω 2 = 1 rad/s as shown in the figure. Slider 3 slides on
link 4. Draw a velocity diagram for pin A and determine form it the angular velocity of link 4. 4
A 3 2 ω2 = 1 rad/s 4
O2 O4 1 1 14. Link 2 rotates with constant angular velocity ω 2 = 1 rad/s as shown in the figure. Slider 3
slides on link 4. Draw an acceleration diagram for pin A and determine form it the angular
acceleration of link 4. (You may use some of the quantities obtained in Question 13) 4
A 3 2 ω2 = 1 rad/s 4
O2 O4 5 1 1 15. Disk 4 rolls on the ground without slip. Complete the velocity diagram associated with the
equation v B = v A + v B / A + ω 3 × rB / A , and determine ω 3 from it. 4
B
vA 0 1 3 ω2 = 1 rad/s
O2
A 16. Disk 4 rolls on the ground without slip. Draw the velocity diagram associated with the
equation v B = v A + v B / A + ω 3 × rB / A , and determine ω 4 from it. 4 O2 ω2 = 1 rad/s B 3 A 6 1 17. Disk 3 rolls on the ground with no slip. Point B on disk 3 moves to the right with
velocity v B = 2 in./s . Complete the velocity diagram expressing the velocity of B with
respect to an observer at A, which is attached to link 2, and determine the angular velocity ω2
of link 2. Sliding contact 2 • B A
0 vB 1 2 in./s 3 1 No slip 18. Disk 3 rolls on the ground with no slip. Point B on disk 3 moves to the right with constant
velocity v B = 2 in./s . Draw the acceleration diagram expressing the acceleration of B with
respect to an observer at A, which is attached to link 2, and determine the angular
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acceleration ω2 of link 2. (You may use some of the quantities obtained in Question 17) Sliding contact 2 • B A 1 3 1 7 vB No slip 19. Slider 2 slides on the ground with velocity v A = 2 in./s. Slider 4 slides on link 3. Complete
the velocity diagram expressing the velocity of B with respect to an observer at A, which is
attached to link 3, and determine the angular velocity ω 4 of link 4.
3
B
4 vA 0
2 in./s
3 1 v A = 2 in./s A 2 1 20. Slider 4 slides on link 2. Slider 5 slides on link 3. Pin C connects slider 4 to slider 5. The
angular velocities of links 2 and 3 are shown in the figure. By using velocity diagram,
determine the velocity v C of pin C.
2 ω3 = 1 in./s 5 C
3 B 3 4 2 ω2 = 1 in./s
A 1 8 1 Bonus Question 21
21. The velocity v P of point P in the pantograph is shown in the figure below. By using velocity
diagram determine the velocity v B of point B .
Dimensions: Links 2, 3 ,and 4 are 1.5 in. long.
Link 5 is 4 in. long 3 A
5 O2 1 C 2 4 5 B P 90
v P = 10 in./s 9 o Bonus Question 22
22. A rigid body ℜ with two points, A and B, attached to it, are shown in the figure. The
accelerations of A and B are also shown. Draw the point C on ℜ which has zero
acceleration. aA 1 in./s 2
aB 2 in./s 2 A B ℜ 10 ...
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 Fall '06
 Ram
 Acceleration, Machine Design, Angular velocity, Velocity, Physical quantities, in./s

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