In most mechanical applications, gear trains are used. There are lots of information about the gear pairs in Mechanical Base. If the bunch of gear pairs is used in machinery, gear trains are obtained. Just take a look at the below example.
In this example, there are two spur gear pairs are designed to transmit power from the input shaft to the output shaft. According to the used velocity ratios between two gear pairs, there is a proportional difference of torque between the input shaft and output shaft.
If you remember the velocity ratio calculations done in spur gear pairs, it is only the proportion of rotational velocities between the pinion and bigger gear. So, there is an inverse relationship between the torque change and velocity ratio.
If the velocity ratio is bigger than 1, this means that the rotational speed of the input shaft is bigger than the output shaft. And pinion is attached to the input shaft. But, the torque value of the output shaft is bigger than the input shaft.
We can apply this relation between gear pairs to gear trains. In a typical gear train, there are sets of gear pairs are used. As also stated that the velocity ratio is also equal to the ratio of the number of teeth of pinion and bigger gear pairs.
In the calculation of gear train ratio, if we multiply the teeth numbers of all the driving gears in themselves and driven gears in themselves, and if we proportionate these values, we can find gear ratio.
The equation above states everything actually.
In the gear train example above, the gear that is assembled to the input shaft and the smaller gear that assembled shaft 2 are driving gears. Other gears are driven gears. You can do the calculation to find out the train value.
If you multiply the input torque with the train value, you will find out the output torque of the output shaft.
The gear train thing has actually a very basic principle in sense. You just need to define the driven and driving gears inside a system.
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