[How do I?] Do 20 TPI

Is it my imagination, or does the 'Thread Per Inch' chart show the 120 tooth gear to be larger in diameter
than the 127 tooth gear?

Two factors of 127/120 multiplied by 20 tpi gives 22.4 tpi.

OK, I give up, could you please explain the last paragraph?
 
OK, I give up, could you please explain the last paragraph?
If one drives the 120 gear, which is pinned to the 127 gear, the output gets a 127/120 boost over having
both gears 120 teeth. But if one does that when what is intended is to drive the 127 tooth gear which is pinned
to the 120 tooth gear, you get twice the mismatch with the intended drive ratio.

So, 20 tpi becomes 20 *(127*127/(120*120)) = 22.40138 tpi

The implication is that the illustration has the '120' and '127' tooth labels incorrect, though the pictures
show the larger and smaller gears in the 'right' positions for inch threading according to the table.
 
It confuses me that the charts show a metric end gear setup for both inch and metric charts; for inch threads the spindle and QC box should mesh with an idler in between, not the compound gear train shown.
You are correct John, very strange to see compound gearing on both metric and imperial threading charts. It appears this lathe has an inch lead screw. Also the 100 gear pictured larger than the 127 gear. There is a mistake there someplace, and I am guessing the inch threads do not use compound gearing at all, and that you use either the 100 or 127 as an idler, which does not affect the ratio at all.
 
Took pictures of the side gears. Looks like the plate is wrong all together, the gearing is 40/127/40. I just got lucky that the threads I previously did were right on. When I get back in the garage tomorrow afternoon I will try C-3, maybe the gearing on C goes 16, 18, 20, 22, 23, 24, 26, 28. The reason I am including 23 because looking real close at the picture when I did C-5, it is not quite 24, and I don't have 23 thread gauge to verify.

20170925_224707.jpg 20170925_224735.jpg 20170925_172907.jpg
 
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I think your threading chart might have the labels for 120 & 127 reversed, as the chart for my lathe has that gear reversed between metric and inch threads, while your chart has the numbers go the same way for both, but the image shows the gear is reversed (as visually it shows the smaller gear on the other side).

Here's my threading chart (similar to yours, just some of the gears have different counts):
IMG_0474 (1).jpg
 
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Took pictures of the side gears. Looks like the plate is wrong all together, the gearing is 40/127/40. I just got lucky that the threads I previously did were right on. When I get back in the garage tomorrow afternoon I will try C-3, maybe the gearing on C goes 16, 18, 20, 22, 23, 24, 26, 28. The reason I am including 23 because looking real close at the picture when I did C-5, it is not quite 24, and I don't have 23 thread gauge to verify.

View attachment 242627 View attachment 242628 View attachment 242629

Your geartrain isn't configured either as the diagram shows it should be for TPI, or as I think it "should" be, with the 120/127 gear reversed.

If you are going to try what your chart says (at least, how I read it), 20 TPI is C, 4 for the handles, the 120/127 gear and the top gear stay the way they are in your picture, but the bottom 40 gear needs to be flipped around and shifted closer so it engages the 120 gear instead (I can't tell from your picture what shifts to get it to engage).

But from looking at the metric charts, I think you need to also flip the 120/127 gear, so the smaller gear is on the inside, the top 40 gear then engages the inner 120 gear, and the bottom 40 gear engages the outer 127 gear.
 
On second thought, from comparing your and my lathes threading charts, you may want to consider just flipping the 120/127 gear, and then tightening up the gear train, so both your top and bottom 40 gears engage the 120 gear...
 
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The chart has to be done wrong. If pos a1,a2,a3,a4, are all multiples of each other, then the rest of the chart has to be the same for each column. You just said that 5c, is 23, which is a multiple of 5b (11.5). Try using 3c, and see if you get the 20 TPI there.

I think we all agree, that the gear train diagram is wrong for standard threads, and should be as set up in you last photos.
 
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