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Much has been written about making gears while little has been set down on measuring them. Measuring a newly made gear to insure that it meets specs is relatively easy. You know all the target numbers and only need to verify them. If you used a 12 DP cutter, then it will at least be close to the tooth form for 12 DP. You can calculate the various values and just check them. Verify the tooth thickness with a gear caliper or mike. Then use pins sized to touch at the pitch circle and verify the pitch diameter. OD is easy: may require some calculation if there are an odd number of teeth and you want to check to tenths, but it can be done. All of the above can be done with precision. There appears to be an unworn section on the gear Ken pictured so this "new" assumption can probably be applied there.

However, if you have a worn gear and no information on it, no specs, then you have a delema. If you are stuck with a gear that is worn all over like badly worn section of Ken's gear, then you must use approximate measurements and made assumptions. What if you measure the OD? It is obviously worn quite a bit. Without the unworn section, you would not know how much. So it will not be easy to get a DP from the OD and teeth + 2 formula. The number you get will be low. Suppose you get a calculated 15.5 DP. Is it a 16 DP? Could there be enough wear to make it an 18? Probably not. But perhaps an unstandard 17? Perhaps. But 16 DP = module 4.987 so could it be metric module 5? With that much wear, how could you tell? You could measure other features and see if they are even numbers in either inches or mm. But this is far from certain. Other measurements like PA will be equally unsure.

Is my example just a single coincidence where the DP comes out close to a module value. Well, no. Any gear in the DP sequence 1, 2, 4, 8, 16, 32, 64, etc. will have the exact same close ratio to a standard module gear. And a 5 DP = module 15.959 so other sequences of DPs will also be close enough for confusion. 20 DP is especially close to module 4 and gears of the two, if the same PA, could probably inter-mesh.

If you have a heavily worn gear, you are are going to have to make some assumptions, some guesses. Fact of life.

Paul A.

Make it fit.

You can't win and there is a penalty for trying!