In previous videos I went over simple machines and bicycle gearing.
In this video we are going to take a more in-depth look at gearing ratios.
In a gear set there is a driver gear or where the torque and motion is coming from and a driven gear that turns as a result of the torque and motion from the driver gear.
So the way a gear ratio works is that you take the driven gears number of teeth and divide by the driver gears number of teeth. So in this example we have a driven gear with 56 teeth and a driver gear with 15 teeth. If we divide the number of driven teeth by the number of driver teeth we get a gear ratio of 3.73. This means that every time the driven gear rotates around once the driver gear has to rotate around 3.73.
In my bicycle gearing physics video I took the driver gear over the driven gear. This resulted in the velocity gear ratio or how many times the driven gear rotates for one revolution of the driver gear. In this example ever time the driver gear rotates around once the driven gear rotates around .268 times. We get this by taking the number of driver gear teeth divided by the driven gear teeth
Now lets talk about torque. If torque is going from driver gear to driven gear the force on each gear is the same. There is a changes in the distance the force is from the center. So to get toque at the driven gear you can multiply the torque at the driver gear times the gear ratio. To prove this we can see that the formula for torque is force times radius. If we take the force times radius of the driven gear and divide it by the force time radius of the driver gear we get the gear ratio. Notice that the force is the same so we are really taking one gears radius over the other gear radius. Doing some rearranging of the formula we get that taking the torque at the driver gear and multiplying it by the gear ratio results in the torque at the driven gear
To finish off the video lets go over gear trains. To calculate the gear ratio of a gear train you can multiply the sub gear ratios. In this example we can take the first driven and driver gear ratio and multiply times the second driven and driver ratio. We get a gear ratio of 13.18

Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.

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