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Gears and Gear Reduction
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We ve already discussed the fact that the normal running speed of motors is far too fast for most robotics applications. Locomotion systems need motors with running speeds of 75 to 150 rpm. Any faster than this, and the robot will skim across the floor and bash into walls and people. Arms, gripper mechanisms, and most other mechanical subsystems need even slower motors. The motor for positioning the shoulder joint of an arm needs to have a speed of less than 20 rpm; 5 to 8 rpm is even better. There are two general ways to decrease motor speed significantly: build a bigger motor (impractical) or add gear reduction. Gear reduction is used in your car, on your bicycle, in the washing machine and dryer, and in countless other motor-operated mechanisms.
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GEARS AND GEAR REDUCTION
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Gears perform two important duties. First, they can make the number of revolutions applied to one gear greater or lesser than the number of revolutions of another gear that is connected to it. They also increase or decrease power, depending on how the gears are oriented. Gears can also serve to simply transfer force from one place to another. Gears are actually round levers, and it may help to explain how gears function by first examining the basic mechanical lever. Place a lever on a fulcrum so the majority of the lever is on one side. Push up on the long side, and the short side moves in proportion. Although you may move the lever several feet, the short side is moved only a few inches. Also note that the force available on the short end is proportionately larger than the force applied on the long end. You use this wonderful fact of physics when you dig a rock out of the ground with your shovel or jack up your car to replace a tire. Now back to gears. Attach a small gear to a large gear, as shown in Fig. 17.6. The small gear is directly driven by a motor. For each revolution of the small gear, the large gear turns one half a revolution. Expressed another way, if the motor and small gear turn at 1000 rpm, the large gear turns at 500 rpm. The gear ratio is said to be 2:1. Note that another important thing happens, just as it did with the lever and fulcrum. Decreasing the speed of the motor also increases its torque. The power output is approximately twice the input. Some power is lost in the reduction process due to the friction of the gears. If the drive and driven gears are the same size, the rotation speed is neither increased nor decreased, and the torque is not affected (apart from small frictional losses). You can use same-size gears in robotics design to transfer motive power from one shaft to another, such as driving a set of wheels at the same speed and in the same direction.
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Gears are an old invention, going back to ancient Greece. Today s gears are more refined, and they are available in all sorts of styles and materials. However, they are still based on
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Gear ratio to
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FIGURE 17.6 A representation of a 2:1 gear reduction ratio.
244 CHOOSING THE RIGHT MOTOR FOR THE JOB
the old Greek design in which the teeth from the two mating gears mesh with each other. The teeth provide an active physical connection between the two gears, and the force is transferred from one gear to another. Gears with the same size teeth are usually characterized not by their physical size but by the number of teeth around their circumference. In the example in Fig. 17.6, the small gear contains 15 teeth, the large gear 30 teeth. And, you can string together a number of gears one after the other, all with varying numbers of teeth (see Fig. 17.7). Attach a tachometer to the hub of each gear, and you can measure its speed. You ll discover the following two facts:
I The speed always decreases when going from a small to a large gear. I The speed always increases when going from a large to a small gear.
There are plenty of times when you need to reduce the speed of a motor from 5000 rpm to 50 rpm. That kind of speed reduction requires a reduction ratio of 100:1. To accomplish that with just two gears you would need, as an example, a drive gear that has 10 teeth and a driven gear that has 1000 teeth. That 1000-tooth gear would be quite large, bigger than the drive motor itself. You can reduce the speed of a motor in steps by using the arrangement shown in Fig. 17.8. Here, the driver gear turns a larger hub gear, which in turn has a smaller gear permanently attached to its shaft. The small hub gear turns the driven gear to produce the final output speed, in this case 50 rpm. You can repeat this process over and over again until the output speed is but a tiny fraction of the input speed. This is the arrangement most often used in motor gear reduction systems.
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