EXERCISE%20PROBLEMS-3

EXERCISE%20PROBLEMS-3 - Supplemental Exercise Problems for...

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- 39 - Supplemental Exercise Problems for Chapter 3 Problem 3.1 For the mechanism shown, write the loop equations for position, velocity, and acceleration. Show all angles and vectors used on the drawing and identify all variables. For the position defined by the data below, find 1 4 v C and 1 4 a C if link 2 rotates with constant angular velocity. AB BC = = = ° = 1 4 90 1 cm, cm, , ˙ rad/ s θ θ A B 2 C 3 4 θ Problem 3.2 In the mechanism shown, ˙ φ is 10 rad/s CCW. Use the loop equation approach to determine the velocity of point B 4 for the position defined by φ = 60˚. 3 4 φ 2 10 inches B Problem 3.3 In the mechanism given, 1 v B 2 is 10 in/s to the right (constant). Use the loop equation approach to determine 1 v A 4 and 1 a A 4 . Use point O as the origin of your coordinate system. 30˚ A B 2 3 4 1 v B 2 AB = 10 inches O
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- 40 - Problem 3.4 In the mechanism shown, Link 3 slides on link 2, and link 4 is pinned to link 3. Link 4 also slides on the frame (link 1). If 1 ϖ 2 = 10 rad/s CCW, use the loop-equation approach to determine the velocity of link 4 for the position defined by φ = 45˚. 3 φ 2 10 inches 4 A B Problem 3.5 Use loop equations to determine the velocity and acceleration of point B on link 4. 2 3 1 ϖ 2 = 1 rad sec 1 α 2 = 0 B 4 x y 3 in A 30˚ Problem 3.6 Use loop equations to determine the angular velocity and acceleration of link 3 if v B 4 is a constant 10 in/s to the left and 1 θ 3 is 30˚. 2 3 x y 3 in A B 4 θ 1 3 B 4 v
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- 41 - Problem 3.7 The shock absorber mechanism on a mountain bicycle is a four-bar linkage as shown. The frame of the bike is link 1, the fork and tire assembly is link 3, and the connecting linkage are links 2 and 4. As the bicycle goes over a bump in the position shown, the angular velocity of link 2 relative to the frame is 1 2 ϖ is 205 (rad/s), and the angular acceleration is 1 2 α is 60 (rad/s 2 ), both in the clockwise direction. Compute the angular velocity and angular acceleration of link 3 for the position shown 2 4 1 3 A D C B 1.88" 2.22" 201˚ 1.55" 1.64" 1 2 ϖ 61˚ Problem 3.8 The purpose of this mechanism is to close the hatch easily and also have it remain in an open position while the owner removes items from the back. This is done by the use of an air cylinder, which helps to support the hatch while it closes and holds it up in the open position. The mechanism is an inverted slider-crank linkage, where the car acts as the base link. There are two identical linkages one on each side of the car. Assume that the angular velocity of the driver (link 2) is a constant 0.82 rad/s clockwise and the angular acceleration is 0. Compute the linear velocity of point D 2 , and the angular velocity and angular acceleration of link 3 for the position shown
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- 42 - 1 2 ϖ C A 12.50" B D 12.60" 42.30" 40.91" 2 3 4 145˚ 35.74˚ 4 Problem 3.9 The wedge mechanism has three links and three sliding joints. Link 2 slides on link 3 and link 1.
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