# planetary gear ratio calculations

I have been trying to figure out what the gear ratio for a planetary gear is when the sun gear is held stationary and the input and output
are the Planet carrier and Ring gear. I think the reason I can't find anything that talks about that specific scenario is because it is always a 2 to 1 ratio and for that reason probably never be used. Is that correct or does it change with different size Sun, Planet and Ring gears?
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Chris W
KE5GIX
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Chris, The size of the planet gears is irrelevant. The ratio is the sun gear to the ring gear.
Think of a normal series of 3 gears. Input = 3" in diameter driving a 2" gear driving a 3" diameter (output). The ratio is 1:1 Change the middle gear, Input to output ratio never changes.
Dave
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Hmmm....it's been a while. It's easy to show that that the planet will count twice as many ring teeth as it counts sun teeth. And then the ratio starts looking like 2 X # sun teeth / # ring gear teeth. But the extra piece in the formula that I have often forgotten is the 1 extra turn per revolution as the planet carrier circles the sun. ,,,,But I am too preoccupied at present to look up this formulation, which features a "1 plus" in there somewhere....
Sorry
Brian W
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On Sun, 24 Feb 2008 19:27:25 -0600, Brian Whatcott

[Second try...] This URL http://auto.howstuffworks.com/automatic-transmission1.htm
offers this formula for your case: 1/ (1 + S/R) for the gear ratio for S = # of Sun teeth R = # of ring teeth.
Example: sun has 20 teeth, ring has 40 teeth. Ratio as given above: 1/1.5 or 0.667 to 1 (a speed up gear train)
Sometimes expressed as (1 + S/R) or 1.5 speed multiplier (!!!!)
Brian W
Brian Whatcott Altus OK
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I guess I wasn't clear in my question. In a planetary gear there are three different parts of the gear that can rotate about the center of the assembly, the sun gear, the ring gear and the planet carrier. In order for the assembly to be useful, one of the three has to be held stationary. So far the 2 replies have addressed the configuration where the planet carrier is held, and the configuration where the ring gear is held. What I want to know is what happens when the sun gear is held stationary. From what I have read so far, my guess is that regardless of the gears, that ratio will always be 2 to 1. Can anyone confirm that?
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Chris W
KE5GIX
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Hi Chris, I pointed you to a URL with an animated diagram and formula of the sun gear fixed case. Take a look.
Brian W
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Brian Whatcott wrote:

Sorry I should have looked at your link. I had already read one page from that web site on the topic and figured your link was to the same page, but it is not. That is a much better page than the one I had found earlier, it very concisely gives formulas for all three configurations. Thanks.
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Chris W
KE5GIX
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