# Relationship between gear pitch and diameter

I found a reference that states the relationship between gear pitch and the outer diameter of the gear is OD = (No. teeth + 2)/pitch. Is that correct?

If it is a “standard” gear this is correct.

The standard addendem is (1/DP) or (1*module)

The OD is 2 addendems larger than the Pitch Diameter so that means the OD = (N/DP) + 2*(1/DP) = (N+2)/DP

Be careful about using this with smaller gears because they are often enlarged to make the teeth stronger. Even with larger gears, they are sometimes modified to mate with other gears (to make them quieter, stronger, or whatever).

Joe J.

P.S. Your question was not dumb.

Thanks for the information. I want to add a castor coupled to an encoder to measure distance. The castor I’m looking at is a 6cm omni wheel. Since the castor is so small I have to gear it down before the encoder, at a ratio of 3:1, so that the shaft speed at the encoder is less the 300 RPM max for the part. I was planning on using a 24 tooth gear on the castor shaft and a 72 tooth gear on the encoder. The finest pitch I saw was 48, so they would be roughly 0.5" and 1.5" diameter each. Is this a resonable plan or is there a better way to do it? The shaft on the castor would be 1/4" and the gear on the encoder would be mounted directly to the shaft on a locking hub.

There is an excellent section on the Standard Drive Products website regarding gear and drive components and the engineering behind them. Follow the link… http://www.sdp-si.com/D190/D190cat.htm

Though this is perhaps a tiny bit off topic… I’ve made a couple of webpages for Westside Boiler Invasion’s KIP program (Knowledge is Power!) that are related to gears, how they work, and whatnot…

Here’s a link with some bare-bones definitions:
Gears 101

And here’s a link with some applications, and how you go about solving problems…
Gears 102

There’s also a page on bending stress… mechanics of materials 102.

Matt

just slightly more on topic, SDP-SI has a lot of gears and pinion shafts and other neat stuff. Specifically, if you need a finer pitch they go up to 120 pitch. Check’em out. SDP-SI