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Gear ratio problem

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garriwilson:
Hey guys!
I need to figure out a gear ratio for a small elecic car.
I'm not asking for the answer, I'm asking how to figure it out.
Ok I have 5 gears:10tooth, 20 tooth, 30 tooth, 40 tooth, and 50tooth.
How do I figure out the combination of THREE of those for speed and then for torque?

Thank you and ask if you are confused.

bens:
Consider a two-gear setup: 10 and 20 tooth.  If you affix the 10-tooth gear directly to your motor and use it to turn the 20-tooth gear, you should be able to intuitively see that the 20-tooth gear will turn half as fast as the motor's output shaft (if the 10-tooth gear is going 1 RPM, the 20-tooth gear will turn at .5 RPM).  What you're doing here is increasing torque at the expense of speed.  Torque is increasing because the 20-tooth gear has a larger radius, so you're applying force farther away from the gear's axis of rotation.  Torque = the cross product of F and r, which in this case has a magnitude of F*r.  If the torque of your motor shaft is T, the 10-tooth gear can deliver a force of T/r10, where r10 is the radius of the 10-tooth gear.  This force, when applied to the 20-tooth gear, generates a torque of F*r20 = T*r20/r10, where r20 is the radius of the 20-tooth gear.  You can expect the 20-tooth gear to have twice the radius of the 10-tooth gear, so using this setup you can effectively double the motor's torque by halving its speed.

If you switch the order of the gears (20-tooth is on the motor's output shaft), you analagously determine that you will double the rotation speed and halve the torque.  Figuring out the three-gear solution is just an extension of this analysis.

ed1380:
IIRC you take teh first and last gear and then find out the ratio by deviding # of teach per gear.

yep.
http://www.societyofrobots.com/mechanics_gears.shtml#gearchains

--- Quote from: Admin ---Gear Chains (more than 2 gears together)
Suppose you have 30 gears (holy squirrels!), all in order, like in the image above. How in the monkies do you calculate the gearing ratio of that behemoth? Easy. Ignore all the gears in between the very first and very last gear. If the diameter of the first gear is 2 inches, and the diameter of the last is 1 inch, you have a 2:1 ratio. The gears in between do not matter. Now what direction does the last gear rotate? Easy, you have an even number of gears, so it is counter-rotational of the first gear. What efficiency do you have? Well thats:

effienciency_total = gear_type_efficiency ^ (# of gears - 1) = .9 ^ (29) = 4.7 %


If instead you used 5 gears, you would have:

effienciency_total = .9 ^ (4) = 65.6 %



--- End quote ---

Admin:
are you allowed to do compound gears?

if you have a compound gear, both individual gears (no matter what teeth they have) will have the same velocity and direction. the torque change however will be calculated like normal.

compound gears have 100% efficiency ;D

paulstreats:
where does the extra energy come from for the velocity to remain but the torque increase?
A large gear with a gear half the size on the same axle would calculate the same as one normal gear turning a gear half its own size surely? just with a reduction on friction

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