13T modified (217-6921) v.s. 14T: Gear Ratios


I have a question about the 13 tooth pinion (217-6921) that has the pitch diameter and outer diameter geometry as the 14 tooth.

I’m trying to understand what the gear ratio of 217-6921 is if I use it with 20DP gears.

In previous threads I saw people say the 13T is not the same ratio as the 14T despite having the same pitch diameter. This intuitively doesn’t make sense to me — doesn’t pitch diameter determine rotation? —, but then if they’re the same, why would anyone use the 13T instead of the 14T and then why would vex even make the 13T model? — the only thing I could think of was relatively prime gearing… .

Here are the engineering drawings.

I read a couple old threads but didn’t see a definitive answer; maybe I didn’t search well enough.


I’m pretty sure the 14t uses profile shifting (edit-looks like the 13t does instead.)
Go down to changing the center center distance.


It’s also known as addendum shifting/modification too for anyone doing a search/google.

For a 13T gear you’ll do the ratio calculation as 13T/20DP and for it’s pitch diameter/meshing you’ll do 14T/20DP.


It’s the 13T that uses profile shifting. In the image below, the gray profile is standard 13T 20DP 14.5 deg PA. The black profile is the 217-6921 13T with 14T c-c spacing.


They aren’t the same. The pitch-shifted 13T can be dropped in to an existing gearbox designed for a 14T pinion and instantly get about 7% additional gear reduction. Maybe you thought you wanted that L3 ratio SDS swerve module, but it turns out to be too hot. Swapping in the pitch-shifted 13T pinion drops you back close to the L2 gearing with just one gear replacement rather than two.

Also for reference the 8T, 9T, 10T, 11T, and 13T are all shifted so make sure you pay attention to the table on Vex/WCP’s site!

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This table reminds me of two reasons in addition to interchangeable gear ratios on existing mechanisms that someone would want to sell pitch shifted pinions.

Here is an image of an 8T 20DP pinion with 10T pitch diameter (black profile) compared to a what would be a standard 8T 20DP pinion if it could handle the size of the motor shaft (gray profile).

Making the pitch shifted 8T gives you all the reduction goodness of the 8T, but it can fit on a Falcon spline. Also, look at how beefy the pitch shifted teeth are. All the undercut is gone. Those pitch-shifted teeth should be much more robust.