kin_test_2_05

kin_test_2_05 - Machine Design I (ME-4133) - Test II...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Machine Design I (ME-4133) - 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 ⋅⋅⋅⋅⋅⋅⋅⋅ Scale 1 in./s ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 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 ) . ⋅⋅⋅⋅⋅⋅⋅⋅ ⋅⋅⋅⋅⋅⋅⋅⋅ ω = 2 rad/s ⋅⋅⋅⋅⋅⋅⋅⋅ A B Scale 1 in./s 2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 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 & is also shown. What is the angular acceleration ω of the link? 1 in./s 2 & ω= ⋅⋅ ⋅⋅ ⋅⋅ 4 in./s 2 ⋅⋅ ⋅⋅ ⋅⋅⋅ ⋅⋅⋅ &⋅ A ⋅ ω × rB / ⋅ ⋅⋅⋅ ⋅⋅⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ Scale ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 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 & angular acceleration ω of the link? 1 in./s 2 & ω= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ aB ⋅⋅ ⋅⋅ ⋅ Scale ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ rad/s 2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ ⋅ 0⋅ ⋅⋅ ⋅ ⋅ ⋅ ⋅⋅ aA ⋅⋅ ⋅ ⋅ ⋅ 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. ⋅⋅⋅⋅⋅⋅⋅⋅ ⋅⋅⋅⋅⋅⋅⋅⋅ ω2 = 2 rad/s B ⋅⋅⋅⋅⋅⋅⋅⋅ Scale 2 A ⋅⋅⋅⋅⋅⋅⋅⋅ 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 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 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 ⋅ ⋅ Scale 1 in./s ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ ⋅0 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅v B ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ B 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 & 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 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ Scale 1 in./s 2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ 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. ⋅ ⋅ Scale 1 in./s 2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ A v A = 2 in./s 2 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. ⋅ ⋅ ⋅ Scale 1 in./s 2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 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 & 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 ...
View Full Document

This note was uploaded on 12/02/2011 for the course ME 4133 taught by Professor Ram during the Fall '06 term at LSU.

Ask a homework question - tutors are online