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Gears
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Gears were introduced in 3 as a way to convert torque and speed. Like chains and sprockets, gears can be used to carry power (torque) from one place to another as well as to reverse the direction or axis of rotation.
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CHAPTER 9 Power Transmission
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Fig. 9-12.
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Gear box.
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Try This: Normally, a box of gears is used to perform large power conversions. Figure 9-12 shows one such gear box. Note that there may be two gears on one shaft. The input is the tiny 8-tooth gear at the right of Fig. 9-12. This meshes with a 40-tooth gear, giving a 5 to 1 reduction in rotational speed and, ignoring losses due to friction, a 5 to 1 increase in torque. A 24-tooth gear on the same shaft meshes with another neighboring 40-tooth gear, for a 24:40 or 3:5 step. This pattern repeats once more, so the output shaft shows a speed reduction of: 40 : 8 40 : 24 40 : 24 5 : 1 5 : 3 5 : 3 125 : 9 9-1
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A 125:9 ratio requires 13.9 input revolutions for one output revolution. If you used a 40:8 ratio at each of the three steps, you would have a 125:1 nal ratio. That s a big reduction in speed and increase in torque. These same gears can be stretched out to carry torque from one place to another, as shown in Fig. 9-13. In this case, there is not much adjustment from the input to the output. Each step from a small gear to a large gear slows down the motion (and increases torque), but each step from a large gear back down to a small one does the reverse. This chain is then: 40 : 8 24 : 40 40 : 24 24 : 40 40 : 24 5 : 1 3 : 5 5 : 3 3 : 5 5 : 3 5:1 9-2
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CHAPTER 9 Power Transmission
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Fig. 9-13.
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Gear train.
Fig. 9-14.
Gears around a corner.
Only a ve times torque increase, since each 3:5 cancels out a 5:3. Using this same type of gear train, you can carry torque around a hinged joint, as shown in Fig. 9-14. Turning the input shaft ve times causes the output shaft to rotate once, no matter how the joint is bent. If you hold the input shaft steady and bend the joint, the output shaft still rotates a little bit.
CHAPTER 9 Power Transmission
Fig. 9-15.
Gear elbow.
Can you gure out how far the output shaft will turn if you bend the arm 908 Note that 908 is the same as 1/4 turn. Lock one of the gears near the output so it can t rotate. When you turn the input, the gear train bends at the joint (Fig. 9-15). Can you nd the levers in this system How many times do you need to turn the input shaft to get the arm to bend 908
Backlash
Gears are more precise than pulley belts, but they still introduce errors. Since their teeth don t mesh together perfectly, there is a little bit of slack in any system of gears. You can feel this yourself using the mechanism from Fig. 9-14. Lock both the input and output shafts so they can t turn. Now carefully ex the joint. The gears, even though they don t rotate, provide enough slack to let the joint move. This slack between the gears creates backlash. Backlash comes into play when the gears are moving in one direction and then reverse their rotation. The slack in the gear train lets the gears reverse without any resistance until the teeth all mesh tightly again, and then there is a jolt. Another problem with backlash is a loss of precision. Sometimes you want to position something accurately. Any slack in your gears introduces an error into this position. To x these problems, gears can be preloaded. Preloading is where you apply tension to the gears, holding them against each other to take up any slack. One way to do this is with a split gear, or spring-loaded scissor gears. This is a gear that has been split into two halves, like two gears side by side on the same shaft. A strong spring is mounted between the halves so they are
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