127:100 should do nicely.

I did it by first working out what 5.08 needs to be multiplied by to get a whole number, in this case 125

5.08 x 125 = 635 : 4.00 x 125 = 500

Looked up an online calculator to see what numbers 635 wa sdivisible by and one was 127

635/127 = 5 so divided the other side by the same 500/5 to get 100.

In Hindsight I could have done 5.08/4 = 1.27 OR divided both sides by 4 and got 1.27:1 and in both cases simply multiplied by 100 to make the 1.27 a whole number.

As above, the exact ratio you need is 508/400 or 127/100.

If you go to: https://r-knott.surrey.ac.uk/Fibonacci/cfCALC.html

you can enter the 127/100 as (126 + sqrt(1))/100) and press the right pointing arrow

Then fill in the ‘find the best fractions with denominators from’ part to go from 22 to 127 as your post.

Hit the ‘Find’ button. It will warn you that there are more than 100 to run through.

It wil then display them.

The first few on the list are:

127/100
80/ 63
160/126
47/ 37
94/ 74
141/111
113/ 89
146/115
155/122
108/ 85
33/ 26
66/ 52
99/ 78
132/104

Edit: I need to make it clear that anything other than the 127/100 is an approximation, in a similar way that an imperial to metric translation gear for screwcutting that is not 127t is an approximation. But often the approximation will be good enough.

To get the 125 I simply divided 1 by 0.08

127 just stood out as an easy change gear to get and the only number that works on the other side as you can’t divide 500 by 127

127 is one of those prime numbers that you can’t divide anything else into but I suppose you could go for approximations using a 63T gear like you find being use on some lathes for screwcutting if you don’t need 100% accuracy. Mate that with a 50T

127/50 and 127/25 will work as long as you can add in either an additional 2:1 ratio or 4:1 ratio somewhere in the gear train. Examples such as 40:20 or 80:20 would do as long as you can assemble the gears together without some sort of clash. The easiest way to avoid a clash is to keep two gears on a single axle close to each other in tooth count. That is why compound gear sets such as 100+127 or 120+127 on an axle are common when a lathe only has change gears and no gearbox. So a 127+25 is possibly not a useful combination.

Martin C

A 3 gear train is no better than a 2 gear train in terms of gearing combinations but a 4 gear train has millions of combinations. With a 4 gear train you would be able to get a ratio closer than manufacturing tolerances but it still wouldn’t be ‘perfect’ like a 127 tooth gear would be.

On 23 November 2023 at 21:16 SillyOldDuffer Said:

These are all closer to 508/400 than 63/50 (error 0.7%).

I do not want to be rude to anyone, but even the hint of 63/50 as an option is misguided.

We have mentioned it again and again here: just because 63 is approximately half of 127 has no mathematical relevance to this issue.

In the model engineering world, 63t gears seem to be the Sirens – luring people down paths that should never be trod.

In the partial fraction approximations for 127/100 above, the first one after that figure is 80/63, thus 127 is a numerator, 63 is a denominator.

All that is necessary to dispel the myth of 63 is to look at a lathe geartrain that uses a 63t gear for imperial to metric translation. The 63t gear is used as a driver; when a 127t gear is used, it is the driven gear.

On 24 November 2023 at 07:15 DC31k Said:

On 23 November 2023 at 21:16 SillyOldDuffer Said:

These are all closer to 508/400 than 63/50 (error 0.7%).

I do not want to be rude to anyone, but even the hint of 63/50 as an option is misguided.

We have mentioned it again and again here: just because 63 is approximately half of 127 has no mathematical relevance to this issue.

In the model engineering world, 63t gears seem to be the Sirens – luring people down paths that should never be trod.

In the partial fraction approximations for 127/100 above, the first one after that figure is 80/63, thus 127 is a numerator, 63 is a denominator.

All that is necessary to dispel the myth of 63 is to look at a lathe geartrain that uses a 63t gear for imperial to metric translation. The 63t gear is used as a driver; when a 127t gear is used, it is the driven gear.

Not to be rude either, but the 63T gear does not come originally from being approx. half of 127. It comes from the metric translation ratio of 160/63, which when one is divided into the the other, gives a ratio of 25.399, as close as dammit to the magic 25.4mm to 1.0 inches metric conversion figure achieved by 127/50.

And before you think, ah but a 160T gear is even bigger than a 127, the 160 is usually broken down into pairs of compounded smaller gears. Or the 63T is dispensed with and replaced with a compound train of smaller gears. EG Myford using a 21T (63/3) gear for their metric conversion gear. Unlike 127, the number 63 is not a prime number, being divisible of course by 9 and 7 as well as 3 and 21. So 160/63 can be broken down into 7/4 x 9/40 or 3/4 x 21/40 or 7/8 x 9/20 and so on and suitable standard gears selected to give those ratios. (Courtesy of M Cleeve, see next par). Cleeve also points out that using the 63T (ie 7 x9) as a driving wheel , the error is a mere one thou per 8 inches, which is not enough to matter. Whereas using the 63T incorrectly as a half of 127, the error is a more worrying 8 thou per inch.

No need to re-invent the wheel with this metric-imperial gearing stuff. Machinists have been doing it forever in relation to lathe leadscrews. Martin Cleeve’s excellent little Workshop Practice Series book “Screwcuttng in the Lathe” devotes a whole chapter to the mysteries of both the 127/50 conversion ratio and the 160/63 plus charts of approximation gear trains using standard change gears, with surprising accuracy in the realm of 1 in 8000 etc. He also includes a two-page chart of standard gears that compounded twice give a full range of “approximations” to the magic 127/50 translation ratio, with an accuracy ranging variously from 1 in 300 to 1 in 130,000 or so. The 63T gear is used in some of those options.

Which may not be of help to the OP in search of a simple two-gear solution but it would be worth studying the first principles of the arithmetic involved by reading Cleeve or Machinery’s etc to get a handle on things. YouTube probably will not suffice in this instance (or many others once you get beyond beginner level.) But Cleeve also suggests using a 127/50  combo in gears of a smaller DP than the rest of the train, so the overall diameter is smaller while maintaining the correct ratio. Those gears can be compounded on the same stud as a larger DP gear. Minilathe gears come to mind as a ready source. Or stock gears from HPC etc in small DP/Module.

I vaguely remember Neil Wyatt did an article in MEW some years back re the ins and outs of the 63T gear for metric translation to imperial and vice-versa, which I am sure explains it better than I can. Maybe it was posted on the old forum site??

Personally, in the OP scenario, unless there is an absolute imperative to make metric helixes, I would stick with milling imperial helixes on an imperial leadscrew and work out the relatively simple gearing from first principles. Plenty of information about on how to do the arithmetic, if you have any of the old books on milling or a Machinery’s Handbook. We all had to do it at tech college as a third year apprentices, so it can’t be too difficult. We were no  brains trust, that I can assure you.

The ready availability of 4mm leadscrew charts does not seem to me to justify the faff of setting up the translation gearing just to save doing apprentice-level imperial arithmetic occasionally.

Tis all black magic I tell Ye!

My understanding was that he wanted to add additional gearing to what is shown in a 4mm pitch chart so that he can get usable pitches hence the request for how to gear the 5.08:4 ratio.

As Hopper says just applying a 1.27 multiplier to the pitches won’t give you usuable sizes as it would be a bit like having a screwcutting chart that gives 1.27mm pitch from the 1mm pitch set up.

By including the 5.08:4 gears in the train you would get 1mm pitch from what was sown for 1mm pitch on the table for a 4mm screw.

On 24 November 2023 at 23:37 Hopper Said:

Good idea, simplest is always best, but he would end up with a chart of totally oddball leads.

To use my Adcock and Shipley mill for spiral milling with 6mm leadscrew I made 127 and 100 gears,these provide and exact ratio,I do not see any point in using approximate ratios,the 127 gear can be quite large but they can be used when made choosing a dp with smaller tooth size, and use steel to make them, a finer dp should be adequate for most applications. The 127 wheel was made by using differential indexing.