Ripper, While it is true that one gear is usually enough for a lathe that uses an "inch" lead screw to cut English measure threads, the same is not usually true for a lathe that is cutting metric threads. Here is why.
First the job of a threading dial is to determine when the relation of the thread being cut and the lead screw are in the same relative position every time that the half nuts are closed. There is a mathematical relationship between the rotation of the spindle and the rotation of the lead screw that is determined by the gears in the train between them. So this position WILL REPEAT, sooner or later. The threading dial tells you when this is happening.
English measure threads are specified in Threads Per Inch and these specifying numbers are almost always given in either whole numbers or compound numbers (a whole number plus a fraction) with either a 2 or a 4 as the denominator of the fraction. Examples: 32 TPI, 24 TPI, 18 TPI, 12 TPI, 8 TPI, 7 TPI, 5 TPI, 3.5 TPI, etc. There is never a fraction that is not a half or one or three quarters. Since the inch was a fairly long unit vs the mm that we do most metric work in, it was convenient to specify the English system (inch) threads in this manner. A 24 TPI thread would measure 0.04166666" between adjacent threads and that is not a nice number to work with. They could have used tenths, but that would have given us a sequence of 1 TPI, 10 TPI, 20 TPI, 30 TPI, 40 TPI, etc. That would be difficult for large diameter bolts like 1/2". 1/2-20 is a fine thread but 1/2-10 would be very coarse. A finer division was needed and using TPI was a good way to get that.
Most threading dials for English system lathes are based on a FOUR inch distance of travel along the lead screw. That's why they have the numbers 1, 2, 3, and 4 on them. Those numbers are INCHES. Now, if you think about it for even a short time, it is plain that any thread that is specified by a whole number of threads per inch will have to synchronize after one inch of travel. There is always a whole number of threads in a one inch interval. So moving exactly one inch down such a thread will put you in exactly the same point on the thread form as you started from (peak to peak, valley to valley, 27% along the left flank to 27% on another left flank). Rule: Whole number threads can be started at any numbered mark on the dial.
Going just a bit further, it is easy to see that if there is a 1/2 fraction in the thread spec., then at one inch of travel you will be at the 50% point of the thread form from where you started. That is the 1/2. But, if you go TWO inches along that thread, then you will again be at the same relative point. You moved 1/2 of the thread form the first inch and another 1/2 of the thread form in the second inch. These two halves add up to one whole and you are back in sync. Rule: Threads with a 1/2 fraction will sync on any even numbered mark on the dial. It takes two inches of travel to synchronize a thread with a 1/2 fraction and that applies to any 1/2 fraction: 99 1/2 TPI will sync in 2 inches, 2 1/2 TPI will sync in 2 inches, etc. for any other number with a 1/2 fraction.
Finally, although rare, the same idea applies to threads with a 1/4 or 3/4 fraction. It takes four 1/4s to add up to a whole inch and four 3/4s to add up to 3 whole inches. Rule: Threads with a 1/4 or 3/4s fraction will sync only on the same numbered mark on the dial that you started from. It takes four inches of travel to synchronize these fractions with a denominator of 4.
The above is one of the hidden advantages of using English (inch) measure.
Now METRIC threads: the pitch of metric threads is NOT measured in threads per mm or threads per cm or threads per decimeter (100mms), or threads per any metric dimension. Metric threads are measured and specified in the straight forward distance between one thread and the next: they are usually specified directly in mms. This is due to the rather small size of the millimeter. One thread per mm would be around 24 TPI, two threads per mm would be around 49 TPI, and it gets really fine from there. There would be very little use for 3 threads per mm. And coarser threads would be require fractional numbers of threads PER mm. That wouldn't work. You could use threads per centimeter, but it would still get arkward for low numbers. And threads per decimeter (100 mms) would be really large numbers. In short, "threads per" just does not work well for metric measure. SO, they decided to use just mm (or mm per thread which is mathematically the same thing) to specify metric threads. And they wanted a nice, numeric sequence instead of numbers with 5 or 10 decimal places and difficult values to remember. So they went with tenths of a mm (0.1mm) and twentieths of a mm (0.05mm) in determining that sequence of numbers. But this is an entirely different type of mathematical sequence than that generated by using a "threads PER" type of sequence. One is, more or less a geometrical sequence (8, 16, 32, 64 TPI) while the other is, more or less an arithmetic one (0.1mm, 0.2mm, 0.3mm, 0.4mm, 0.5mm, etc.)
While a 0.1mm thread, and a 0.2mm thread and a 0.5mm thread will all synchronize in 1mm, a 0.3mm one will take 3mm and a 0.7mm thread will take a full 7 mm. A 0.45mm thread (yes that is used) will take 20mm to synchronize.
It is due to the use of two different types of mathematical sequences to specify the threads that making a threading dial for an English lathe is a lot easier than making one for a metric lathe.
Another problem is the range of lead screw pitches that are used for metric lathes. I have seen a metric lathes with 3mm, 6mm, and even 7mm and fractional mm (2.5mm) lead screws. WHY would you ever use 7mm????????? Insane, but it has been done. If you take two examples from above, a 0.45mm thread and a 6 mm lead screw, you have a real problem making a dial to use to synchronize it. In some cases, it may be easier to make a threading dial for use with an English lead screw and transposing gears making metric threads.
I know I will get flamed for saying it, but English threads make a lot more sense. A LOT more.
If we are talking about the thread dial that tells you when to close the half-nut, then you don’t need a “set” , one gear will work for all the threads the lathe can cut. The pitch of the lead screw and the gear teeth on the thread dial will determine how many marks you put on the dial, and what positions on the dial can be use for each thread.
If you are talking about change gears that drive the threading gear box from the spindle or you don’t have a quick change box and want a “set” of threading gears, that’s a whole different subject
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