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Schematic of a double speed reduction system
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the gear reduction shown in Figure 6-2 The D1 / D2 is the first gear reduction ratio, and D3 / D4 is the second gear reduction ratio
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In the previous example, you looked at a speed reduction of 10 With the double-speed reduction system, you have a lot of options for choosing gear diameters The product of the first and second stages in the speed reducer must be 10 For example, you can choose the first gear reduction to be 4 and the second gear reduction to be 25 In this case, you can use the same 15-inch-diameter gear on the motor shaft, and then the second gear should be 6 inches in diameter This is smaller than the 10-inch-diameter wheels used in this example The third gear could be a 2-inch-diameter gear, which would mean that the last gear should be 25 times larger or 5 inches in diameter These gear sizes are much more manageable than trying to do this entire gear reduction in one step
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As a general rule, the greater the gear reduction, the more gears you will have to use to achieve the gear reduction In the real world, you may not find the exact gear and sprocket diameters you want This may be because the actual sizes do not exist For example, if you are using sprockets instead of gears, it is rare to be able to find a sprocket that has a diameter 10 times greater than the driving sprocket You will usually have to choose components that are close to the values you want Thus, the speed reduction will be a little lower or higher than what you want
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The output torque is also a function of the gear ratios, but the torque and gear ratios have an inverse relationship When the speed is reduced, the torque on the output shaft is increased Conversely, when the speed is increased, the output torque is reduced Equation 7 shows the torque relationships from Figure 6-1 The direction in which the torque is being applied is identical to the rotational directions
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T1 and D1 are the torque and the diameter of gear 1, and T2 and D2 are the torque and diameter of gear 2 If D2 is greater than D1, the output torque is increased From Figure 6-2, the output torque is shown in equation 8
In the previous example, where we were looking for a 10-to-1 speed reduction, this will increase the output torque by a factor of 10 During the robot design process, the power transmission must be considered at the same time while you re selecting the motors The number of gears, sprockets, and pulleys and their sizes can have a significant impact on the overall structural design of the robot To simplify the overall power transmission design, you should choose a motor that has the lowest RPM so that the number of components in the power transmission (or speed reducer) can be minimized
Force
The robot s pushing force is a function of the robot s wheel diameters and the output torque on the wheel, and the coefficient of friction between wheels and floor By definition, torque is equal to the force applied to some object multiplied by the distance between where the force is applied and the center of rotation In the case of a gear, the torque is equal to the force being applied to the gear teeth multiplied by the radius of the gear Equation 9 shows this relationship, where T is the torque, F is the applied force, and r is the distance from the center of rotation and
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