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# ch06 - Solutions to Chapter 6 Exercise Problems Problem 6.1...

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- 222 - Solutions to Chapter 6 Exercise Problems Problem 6.1 : Design a double rocker, four-bar linkage so that the base link is 2-in and the output rocker is 1-in long. The input link turns counterclockwise 60 ˚ when the output link turns clockwise through 90 ˚ . The initial angle for the input link is 30 ˚ counterclockwise from the horizontal, and the initial angle for the output link is -45 ˚ . The geometry is indicated in the figure. A 1 B 1 O 2 A 2 B 2 O 4 90 ˚ 45 ˚ 30 ˚ 60 ˚ Solution: Invert the motion and solve the problem graphically. Draw a line from O 2 to B 2 and rotate it clockwise 60 ˚ to locate the position of B' 2 . Draw the perpendicular bisector of B' 2 B 1 and locate the intersection of that line with the line O 2 A 1 . This will locate A 1 . The solution is given in the first figure. Measure the lengths os 0 2 A 1 and A 1 B 1 . This gives the linkage shown in the second figure. The link lengths are: r 1 = 6" r 2 = 3.72" r 3 = 7.29" r 4 = 4"

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- 223 - A 1 B 1 O 2 A 2 B 2 O 4 90 ˚ 45 ˚ 30 ˚ 60 ˚ B' 2 Basic Construction A 1 B 1 O 2 B 2 O 4 90 ˚ 45 ˚ 30 ˚ B' 2 r 1 r 2 r 3 r 4 A 2 Final Linkage
- 224 - Problem 6.2 : Design a double rocker, four-bar linkage so that the base link is 4-in and the output rocker is 2-in long. The input link turns counterclockwise 40 ˚ when the output link turns counterclockwise through 80 ˚ . The initial angle for the input link is 20 ˚ counterclockwise from the horizontal, and the initial angle for the output link is 25 ˚ . The geometry is indicated in the figure. A 1 B 1 O 2 A 2 B 2 O 4 80 ˚ 25 ˚ 20 ˚ 60 ˚ Solution Invert the motion and solve the problem graphically. Draw a line from O 2 to B 2 and rotate it clockwise 60 ˚ to locate the position of B' 2 . Draw the perpendicular bisector of B' 2 B 1 and locate the intersection of that line with the line O 2 A 1 . This will locate A 1 . The solution is given in the first figure. Measure the lengths os 0 2 A 1 and A 1 B 1 . This gives the linkage shown in the second figure. The link lengths are: r 1 = 4" r 2 = 2.77" r 3 = 3.21" r 4 = 2"

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- 225 - Basic Construction Final Linkage Problem 6.3 : In a back hoe, a four-bar linkage is added at the bucket in part to amplify the motion that can be achieved by the hydraulic cylinder attached to the link that rotates the bucket as shown in the figure. Design the link attached to the bucket and the coupler if the frame link is 13-in and the input link is 12-in long. The input link driven by the hydraulic cylinder rotates through an angle of 80 ˚ and the output link rotates through an angle of 120 ˚ . From the figure, determine reasonable angles for the starting angles ( ± 0 and ² 0 ) for both of the rockers.
- 226 - Solution Determine reasonable starting angles for each crank relative to the beam member. Use 40 ˚ for the input rocker and 70 ˚ for the output rocker. This is shown in the figure.

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