Chapter 11. building with gears You can use gears to transfer motion from one rotating axle to the next. For example, you can transfer the motion of a rotating motor to the wheels of a robot to make it drive. Gears can also be used to change the output speed and torque of a rotating axle. A series of gears used to transfer motion is called a gear train. In this chapter, you’ll begin learning how gears work as you experiment with a basic gear train. You’ll then see how the gear ratio controls the performance of the gear train. Finally, you’ll explore each of the gears in the EV3 set and discover how you can use them effectively in your own robots. gearing essentials To begin, create a mechanism with two gears, as shown in the following steps. You’ll use this mechanism to experiment with the essentials of gears. Be sure to try out the other examples as you read on—it’s the best way to really understand how gears work. Before we look at gears in detail, let’s rotate the gears manually and observe what happens: Turning one gear makes the other gear turn. Regardless of which gear you turn, the other gear always rotates in the opposite direction. For every turn of the red dial, the white dial completes precisely three turns. (To see this, have both dials point down at first and then count how many times the white dial goes round as you rotate the red dial once.) The small gear always rotates faster than the big gear. In fact, the small gear turns three times as fast as the big gear. If you try to block the grey axle (attached to the big gear) with your hand, you’ll find that you can still turn the black axle (attached to the small gear) with some effort. On the other hand, if you block the black axle, it’s very difficult to turn the grey axle. You’ll find explanations for each of these observations as you read on. taking a closer look at gears If you look at the gears in our example more closely, you’ll see that the small gear has 12 teeth (we’ll call it a 12T gear), while the big gear has 36 teeth (36T). At the contact point, the teeth of both gears mesh, as shown in Figure 11-1. If you turn the small gear manually, its teeth force the teeth of the big gear to follow, causing the big gear to turn, in the opposite direction. We’ll refer to the gear that we turn manually as the input gear. The gear that follows as a result is the output gear. DISCOVERY #58: OBSERVING GEARS! Difficulty: Time: As you rotate the gears slowly, you’ll see that both dials point in the same direction on several occasions. As the red dial makes one complete rotation, how many times do both dials point in the same direction? Can you explain why this is so? For each tooth of the small gear passing through the contact point, there is one tooth of the big gear that follows. As the small gear (12T) makes three complete rotations, each of its teeth passes through the contact point three times so that a total of 36 teeth pass through the contact point (3 × 12 = 36). During this time, all 36 teeth of the big gear (36T) are pushed through the contact point so that the big gear completes one turn. Figure 11-1. If you look at the gearing mechanism closely, you’ll see that the teeth of both gears mesh. The input gear makes the output gear turn by pushing the teeth of the output gear at the contact point in the direction of the arrow. calculating the gear ratio for two gears As you’ve just seen, three rotations of the 12T gear (the white dial) result in one rotation of the 36T gear (the red dial). You can describe this configuration with the gear ratio. The gear ratio is the factor by which output speed decreases relative to the input speed. The gear ratio is also the factor by which output torque increases relative to the input torque. (More torque makes it easier for a vehicle to drive up a hill. We’ll talk more about what torque means in a moment.) You calculate the ratio as follows: The output has 36 teeth and the input has 12 teeth, so in our example, the formula gives us 36 ÷ 12 = 3. The gear ratio is the factor by which the output speed decreases so that the output gear spins 3 times as slow as the input gear. In other words, 3 rotations of the input result in just 1 rotation of the output. Gear ratios are sometimes written as the number of teeth on the output and the input separated by a colon—in this case, for example, 36:12. If you simplify this ratio to its lowest terms, you get 3:1, which has the same meaning. (Reading from left to right, you see again that 3 rotations of the input result in 1 rotation of the output.) CALCULATING OUTPUT SPEED Once you’ve calculated the gear ratio of an existing design, you can use the ratio to calculate the output speed if you know the input speed: If the gear ratio is 3 and if you rotate the input gear at 30 rotations per minute (rpm), the output gear will turn at 30 ÷ 3 = 10 rpm, which confirms that the speed decreases by a factor of 3. CALCULATING THE REQUIRED GEAR RATIO You can rewrite the previous formula to calculate the required gear ratio for your design if you know the input speed and the output speed you want to achieve: For example, if you want an output gear with a wheel to rotate at 120 rpm while you have a motor rotate the input gear at a constant speed of 72 rpm, you need the following gear ratio: 72 ÷ 120 = 0.6. You can accomplish this ratio with a 20T gear as the input and a 12T gear as the output (12 ÷ 20 = 0.6). Not every gear ratio can be realized with the gears in the EV3 set, so you may want to use one of the gear combinations given in this chapter and use formula [2] to calculate whether the resulting output speed is satisfactory for your design. NOTE Be sure to use the same units for the rotational input and output speeds. (If you measure the input speed as rotations per minute, you should measure the output speed in rotations per minute, too.) decreasing and increasing rotational speed Now let’s look at how the example gear train could be used in a robot. You can use gears to change the rotational speed of an output, such as a wheel, relative to the speed of an input, such as a motor. To gear down, or decrease the speed, the output gear should have more teeth than the input gear so that the gear ratio is greater than 1, as shown in Figure 11-2. This configuration decreases the wheel speed by a factor of 3. As a result, the output torque is increased by a factor of 3. Now let’s look at what happens if you interchange the two gears, as shown in Figure 11-3. The 36T gear is the input driven by a motor, and the 12T gear is the output connected to a wheel. Figure 11-2. Decreasing the rotational output speed by a factor of 3 while increasing the torque by a factor of 3. The gear ratio is 3 (or 3:1). Figure 11-3. Increasing the rotational output speed by a factor of 3 while decreasing the torque by a factor of 3. The gear ratio is ⅓ (or 1:3). The gear ratio is 12 ÷ 36 = ⅓, or approximately 0.333. Therefore, the speed decreases by a factor of ⅓, but that’s the same as saying that the speed increases by a factor of 3. (If you rotate the input at 30 rpm, formula [2] gives you 30 ÷ 0.333 = 90 rpm as the output speed, which is indeed three times as fast.) Increasing the output speed is called gearing up. Increasing the output speed means that the output torque decreases, so it will be harder to drive up a hill. DISCOVERY #59: GEARING MATH! Difficulty: Time: What is the gear ratio of each set of gears shown in Figure 11-4? If you turn the input gears at 10 rpm, what will be the rotational speed of the output gears? TIP You can verify your answer by building the gear trains. Add dials to the gear axles to make it easier to see how much each gear turns. FIGURE 11-4. WHAT ARE THE GEAR RATIOS OF THESE GEAR TRAINS? If you use two gears with the same number of teeth, the gear ratio is 1, and both speed and torque remain unchanged. what is torque? You’ve just seen how you can increase torque, but what exactly is torque? Why can increasing it be useful? To experience the concept of torque, replace the red dial with a weight consisting of two wheels, as shown in Figure 11-5. Now try to lift the weight by turning the grey axle manually. When you do this, your hand has to apply torque to the axle in order to counterbalance the torque created by the weight of the wheels placed at a distance from the axle.