From Team 449 Wiki
A gearbox is a mechanical assembly used to convert between speed and torque. Most motors spin at much higher speeds than are desirable, but produce very little torque, so a gearbox can be used to increase the torque transmitted, which decreases the speed. The product of speed and torque, the power, is a constant.
A simple gearbox consists of gears meshing with each other. When one gear is made to spin (the driver gear), it will make the next gear spin (the driven gear). Consecutive gears will spin in opposite directions. The gear ratio (GR) describes the ratio of the gears as such:
where r is the radius, n is the number of teeth, is the angular speed, and is the torque.
The gear ratio is usually expressed in the form of <turns input>:<turns output> - that is, a gear ratio of 4:3 indicates that for every 4 turns of the input shaft/gear, the output shaft/gear turns three times. A gear ratio in which the first number is larger than the second is "geared down," and increases torque at the cost of decreased speed. A gear ratio in which the second number is larger than the first is "geared up," and increases speed at the cost of decreased torque.
A gear train consisting of more than one pair of gears in series can be described with a single gear ratio, equivalent to the product of the sequential gear ratios.
Here's an example:
In the picture above, the red gear has 14 teeth, and the blue gear has 28 teeth. So, the first gear ratio is 2:1. The green gear has 42 teeth, so the second gear ratio is 1.5:1. If we drive the red gear, the total gear ratio is 2*1.5=3:1. Note that, in this case, the final gear ratio is equivalent to simply driving the final gear with the first gear directly, as if the second (middle) gear were not present - in this case, the middle gear is called an "idler" gear. Gear reductions of this sort are called "single-stage" reductions.
In order to get higher gear ratios, a multi-stage reduction is needed. In a multi-stage reduction, multiple gears are present on the same shaft. Since coaxial gears will spin at the same speed, this allows for much larger gear ratios in the same amount of space. Let's work through another example:
In the picture above, the blue and yellow gears are on the same shaft. The red gear has 14 teeth, the blue gear has 42, the yellow gear 14, and the green gear 28. The first gear ratio (red and blue) is 3:1. The second gear ratio (green and yellow) is 2:1. This time, we need to compute both of those, because the total gear ratio is (3*2)=6:1. The reason for this is quite simple. The blue gear spins 3 times as slow as the red gear. The yellow gear spins at the same speed, since it's coaxial. The green gear spins 2 times slower than the yellow gear, which is 3*2=6 times slower than the red gear. This corresponds to 6 times greater torque, since power is still constant. Notice that this takes up much less space than having a 14-tooth gear and an 84-tooth gear. In FRC, this sort of simple multi-stage reduction is most-often used in the drive - for mechanisms, planetary gearboxes offer a more compact solution.
A planetary gearbox functions a bit differently. It consists of a sun gear (green), planet gears (blue), a planet carrier (red), and a ring gear (gray). The gear ratio for a single-stage planetary gearbox is 1+(R/S), where S is the diameter of the sun gear and R is the diameter of the ring gear. The advantage of planetary gearboxes is that stages (a single stage is shown in the picture) can be stacked. Notice that the planet carrier has a gear on top of it. This is because the sun gear of the previous stage is coupled to the planet carrier of the next stage. The reason stacking stages is nice is that it allows for very large gear ratios, which are often needed for small motors.
By far the most common gearbox used on our team is the VersaPlanetary. They have stages with reductions of 3:1, 4:1, 5:1, 7:1, 9:1, and 10:1, and up to 3 stages can be combined. Since the ring gears are all the same, it is easy to swap and add stages. Assembly instructions are available at the link above. Although they are designed for smaller motors such as the BAG, there are adapters available that can allow them to attach to Mini CIMs and CIMs. When doing this, make sure to check to manual to make sure that the chosen gear ratio is safe, as high torques can destroy gearboxes. Also, be sure to place larger gear reductions closer to the motor, where the loads are smaller - the larger the gear reduction, the less strong the stage is. Avoid using a 10:1 as an output stage unless it is the only stage.
Choosing a gear ratio
Main article: Motor#Gearing