Basic Gear Mechanisms : 21 Steps (with Pictures)

As I mentioned previously, gears can be used to decrease or increase the speed or torque of a drive shaft. In order to drive an output shaft at a desired speed, you need to use a gear system with a specific gear ratio to output that speed.

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The gear ratio of a system is the ratio between the rotational speed of the input shaft to the rotational speed of the output shaft. There are a number of ways to calculate this in a two gear system. The first is via the number of teeth (N) on each gear. To calculate the gear ratio (R), the equation is as follows:

R = N2⁄N1

Where N2 refers to the number of teeth on the gear linked to the output shaft, and N1 refers to the same on the input shaft. The left gear in the first image above has 16 teeth, and the right gear has 32 teeth. If the left gear is the input shaft. then the ratio is 32:16, which can be simplified to 2:1. This means that for every 2 rotations of the left gear, the right gear rotates once.

The gear ratio can also be calculated with the pitch diameter (or even the radius) with basically the same equation:

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R = D2⁄D1

Where D2 is the pitch diameter of the output gear, and D1 is the pitch diameter of the input gear.

The gear ratio can also be used to determine the output torque of the system. Torque is defined as the tendency of an object to rotate about its axis; basically, the turning power of a shaft. A shaft with more torque can turn larger things. The gear ratio R is also equal to the ratio between the torque of the output shaft and that of the input shaft. In the example above, although the 32 tooth gear spins more slowly, it outputs twice the turning power as the input shaft.

In a larger system of gears with multiple gears and shafts, the overall ratio of the system is still the ratio of the speeds of the input and output shafts, there are just more shafts in between. To calculate the overall ratio, it is easiest to start by identifying the gear ratio of each set. Then, starting with the set driving the output shaft and working backward, you can multiply the first value in the ratio (the input shaft's speed) by the values corresponding to the ratio of the next gear set, and use the value obtained from the input shaft's speed after the multiplication as your new input speed for a net ratio. This may be a bit confusing, so an example is provided below.

Say you had a gear train consisting of three sets of gears, one set coming from a motor with a 2:1 ratio, and another set stemming off the output shaft of the first set with a 3:2 ratio, and the next set driving the output of the system, with another 2:1 ratio. To calculate the gear ratio of the overall system, you would start with the last ratio, 2:1. Because the smaller gear on the 3:2 set and the larger gear on the 2:1 set are currently "equal" because of the ratios, the ratio of the input shaft of the second set of gears to the overall system output shaft is 3:1. We do that again, multiplying the ratio of the first gear set by 3 (to get 6:3), and combining it with our net ratio (currently 3:1), to get the overall ratio of the system, 6:1.

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