Planar Rigid Body Kinematics Homework

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1 Chapter 2 Planar Rigid ody Kinematics Homework Freeform c

2 2-2 Freeform c 2016

3 Homework 2. Given: The pulley shown below freely rotates about point C and interacts with two rubber belts (one horizontal, one vertical). The velocity of point on the drive belt is measured to be v = v î, and the acceleration of point on the load belt is measured to be a = a ĵ. The belts do not slip. Find: Determine the velocity and acceleration of point D on the pulley. y R v x D r C a Use the following parameters in your analysis: R = 0.05 m, r = m, v = 20 m/s and a = -5 m/s 2. Freeform c

4 Homework 2. R no slip v,a Chapter 2: Planar Rigid ody Kinematics Homework Given: End of bar is constrained to move along a straight inclined surface. End of the bar is constrained to move along a straight horizontal surface. End moves in the direction shown with a speed of v and acceleration a. t the position shown, bar is horizontal. Find: For this position: no slip (a) Determine the angular velocity of bar and the velocity of end. Write your answers as vectors. (b) Determine the angular acceleration of bar and the acceleration of end. Write your answers as vectors. L! v,a Use the following parameters in your analysis: θ = 36.87, L = 3 ft, v = 20 ft/s and a = 10 ft/s Freeform c 2016

5 Homework 2.C Given: The compound wheel assembly shown below is driven by a cable attached to the outer rim of the assembly at point. The wheel rolls without slip at point with point C moving to the right with a speed of v C, and the acceleration at point is given by a = a x î + a y ĵ Find: Determine the acceleration of the center point C of the pulley. φ y R r x no slip C v C Use the following parameters in your analysis: R = 0.1 m, r = m, φ = 0, a x = 8 m/s 2 and a y = 3 m/s 2. Freeform c

6 Homework 2.D Given: t the instant shown, the piston has velocity v = v î. Find: Determine the resulting angular velocity ω C of the crankshaft. y L x R C φ v Use the following parameters in your analysis: L = 0.06 m, R = 0.03 m, φ = 30 and v = -50 m/s. 2-6 Freeform c 2016

7 Homework 2.E Given: Link of the mechanism shown rotates with an angular speed of ω 0. t the position shown, link C is vertical, and the coordinates of pin are given by (x, y ). Find: For this position, determine the angular velocities of links and C. Write your answers as vectors. 410 mm 90 mm 0 y x 240 mm C 320 mm Use the following parameters in your analysis: ω 0 = 10 rad/s and (x, y ) = ( 54, 72) mm. Freeform c

8 Homework 2.F Given: Link rotates at a constant rate of ω. t the instant shown, link is aligned with the horizontal line of C and link is vertical. Find: For this position, determine the angular accelerations of links and C. Write your answers as vectors. d d C d 2-8 Freeform c 2016

9 Homework 2.G Consider the four mechanisms shown below. Respond to the questions posed. Feel free to draw directly on these sheets and submit for your homework solution. Use a straight edge when making your drawings. MECHNISM N. 1 Link is rotating in the clockwise sense. Determine the location of the instant center (IC) of link. From the location of this IC, determine the sense of rotation for links and C. Justify your answers in words. C Freeform c

10 MECHNISM N. 2 Determine the location of the instant center (IC) of link D. From the location of this IC, determine the sense of rotation for links D and D. Justify your answers in words. C D v 2-10 Freeform c 2016

11 MECHNISM N. 3 Link is rotating in the clockwise sense. Determine the location of the instant center (IC) of link. From the location of this IC, determine the sense of rotation for link and the sense of translation for the piston. Justify your answers in words. Freeform c

12 MECHNISM N. 4 Racks and are moving in the directions shown with the speeds provided. ssume that the gear does not slip on the racks. Determine the location of the instant center (IC) of the gear. From the location of this IC, determine the sense of rotation for the gear. Justify your answers with numbers and words. v = 0.3 m/s 0.1 m 0.2 m v = 0.1 m/s 2-12 Freeform c 2016

13 Homework 2.H This problem has three parts. In each part, you are asked to use the instant center approach in answering the questions related to the problems. In all cases, the figures are drawn to scale. Please use a straight edge when making your drawings. PRT In the mechanisms shown below, link is rotating in the counterclockwise sense. For the position shown of ECH mechanism: (a) Determine the location of the instant center for link. (b) Determine the directions of rotation for links and D. Justify your answers in words. (c) Which is larger: ω or ω? Justify your answers in words. ω ω D D Freeform c

14 PRT In the mechanism shown below, link is rotating in the counterclockwise sense. (a) Determine the locations of the instant centers for links, E and EG. (b) Determine the directions of rotation for links, E and EG. Justify your answers in words. D G ω E slider F 2-14 Freeform c 2016

15 PRT C Link, having a length of L = 5 in, is part of a planar mechanism. t the instant shown, the velocities of points and are known to be both perpendicular to a line connecting and, with v = 3v = 30 in/s. Determine the location of the instant center for link. v L v Freeform c

16 Planar Kinematics Homework Problems ME 274 Problem II-26 Given: mechanism is made up of links Chapter and 2: Planar C and Rigid a wheel ody pinned Kinematics to Homework C at the wheel s center C. The wheel rolls without slipping on a horizontal surface. Link rotates counterclockwise with a constant Homework rate 2.I of 3 rad/sec. t the instant shown, link is vertical. Find: Given: t mechanism the instant is made shown, up of links and C and a wheel pinned to C at the wheel s center C. Thea) wheel determine rolls without the angular slipping on velocities a horizontal of link surface. C and Link the wheel. rotates counterclockwise with a constant rate of ω. t the instant shown, link is vertical. b) determine the angular accelerations of link C and the wheel. Find: For this c) position: determine the velocity and acceleration of point E on the perimeter of the wheel (at the instant shown, E is on the same horizontal (a) Determine the line angular as C). velocity of link C and the wheel. Write your answers as vectors. (b) Determine the angular acceleration of link C and the wheel. Write your answers as vectors. Write your answers as vectors. r L d E! no slip C Use the following parameters in your analysis: r = 0.5 m, L = 2 m, d = 1 m and ω = 3 rad/s. You may solve the problem using the Method of Instant Centers and/or by adopting a vector approach Freeform c 2016

17 Homework 2.J Given: The mechanism shown below is made up of links and, along with the slider at. The slider is constrained to move in the horizontal direction. Link is moving with a constant clockwise rotation rate of ω. t the position shown, is directly below. Find: For position shown: (a) Determine the angular velocity link and the velocity of the slider. Write your answers as vectors. (b) Determine the angular acceleration link and the acceleration of the slider. answers as vectors. Write your ω L L 1.6L slider Use the following parameters in your analysis: ω = 4 rad/s and L = 5 cm. Freeform c

Planar Rigid Body Kinematics Homework

Planar Rigid Body Kinematics Homework Chapter 2: Planar Rigid ody Kinematics Homework Chapter 2 Planar Rigid ody Kinematics Homework Freeform c 2018 2-1 Chapter 2: Planar Rigid ody Kinematics Homework 2-2 Freeform c 2018 Chapter 2: Planar