These notes should be used in conjunction with the two programs NthreadsP and BoxftrhreadP both written by Geoff Carter. The former works from the server, but the latter needs to be downloaded (ignore the "Run" option and select "Save"). However, both are better downloaded and saved for full functionality. Don't just attempt to use the programs, read and understand these notes first to get the best results. If your lathe has a screwcutting gearbox it is even more important to go steadily though the explanations and examples given.
The programs have been written to help with the following situations:
1) If your screwcutting chart is absent - or to calculate a new one.
2) If changewheels are missing the programs will calculate alternative arrangements using just the gears to hand
3) To generate a pitch not on the threading chart 
4) To calculate the missing gears necessary to make a complete set
5) To generate metric pitches on an English lathe without using a 127 tooth gear

Much detailed information can be found in the modestly-priced book: "Screwcutting in the Lathe". We always have copies in stock for immediate delivery. Please email for details.

WHICH PROGRAM TO USE:
NthreadsP is the program for lathes with screwcutting by changewheels whilst BoxftrhreadP is for lathes with a quick-change gearbox (remember, the latter needs to be downloaded before it will work).

BACKGROUND:
Calculations will show that with a set of 20 gears, it is possible to have 380 2-gear arrangements, 29,070 4-gear and 775,200 6-gear: a total of 804,650. By working out all of these possible gear-train combinations you set up gear trains that will generate threads with only a very minor or even zero pitch errors. It would of course be extremely laborious to calculate all these possible pitches by trial-and-error method with a pocket calculator - but a computer program is an idea means of determining the many possible set-ups.

THE GEAR-TRAIN:
The lathes for which the NthreadsP program is written are the smaller British and American types such as Myford, South Bend, Boxford, Colchester, Atlas, Craftsman, Sheldon, Delta, Rockwell, etc.  For lathes that have screwcutting by changewheels (and not a screwcutting gearbox) a typical set-up is shown in gear-train.bmp. Briefly, a gear on the end of the main spindle engages with a tumble-reverse mechanism (two gears on a pivoting arm arranged to reverse the drive) that has an output gear to driving either a "simple" train of gears or (as shown in  gear-train.bmp ) a "compound set" - where two gears are mounted on one or more of the shafts. Idler gears are also sometimes included, to space the gear-train out and make it physically possible to build, but these, no matter how large or small, have no effect upon the final ratio.
The gear on the end of the primary shaft (shown red) is the first DRIVER gear. It drives a gear on the 1^st stud (yellow gear) which is a DRIVEN gear.
The adjacent gear on the 1st. stud in this case a smaller gear is a DRIVER gear (red gear) which drives the final gear that we are interested in on the leadscrew which is a DRIVEN gear (shown yellow)
The intermediate idler gear on the 2^nd stud (shown green) has no practical effect but is needed to space the gears apart to assemble the gear-train without adjacent gears clashing. The number of teeth on the idler gear has no effect on the thread produced.
NB : Depending on the gears required to cut a given thread it will sometimes be necessary to fit the idler gear on the first stud and the compound set on the second.

SIMPLE GEAR-TRAINS:
Frequently the gear-train can be simplified (no compounded gear required). The gear-train then become: Driver (gear on primary shaft) and Driven (gear on leadscrew). One, or both, of the two studs (it makes no difference) will be idler gears.

HOW TO USE THE PROGRAMS:
Examine your lathe and see if it has a gear-train setup similar to that shown in the gear-train.bmp file. If it not, the program may be unusable.
Check  that one turn of the spindle = one turn of the primary shaft: if not, see "Kludge Factor" below.
You may have a quick change gearbox/pre-select gearbox that allows you to run the Boxfthread program instead of NthreadsP. See point 2.0
1.0   Run the program by double clicking on Nthreadp.exe (you should have un-zipped the
program already by using WinZIP) from My Computer, Windows Explorer or use the run bar to open it. You can also create a short-cut icon to the program if you intend to use it frequently.
1.1   Make a list of all the loose gears that you have to hand. The number of teeth on each is entered into the 24 boxes available. Enter 0 in the unused boxes if you have less than 24 gears.  Press "save gearset" to save the gears for your lathe again.
It is only possible to save the gears for one model of lathe.
1.2   Find out what your leadscrew is by measuring it or looking up in your manual. It is critical that you correctly identify whether the leadscrew is Metric or Imperial and what its exact pitch in mm or number of turns per inch (t.p.i) is. Enter this in the box for the leadscrew, check to see that you have ticked the first box if you have a metric leadscrew.
1.3   Decide what thread you would like to produce, tick the inch-thread required or metric-thread required buttons accordingly and enter the pitch for metric/BA or the t.p.i. for BSP, UNC, UMF, BSW and BSF.
1.4   Enter a maximum error. This should be as low as possible; the best thread is the one with the minimum pitch error. Press the Calculate button.

If you have too many results gradually reduce the error until only the best results are shown. If you have no results, increase the allowable error and press calculate again.

If you can, choose a "simple" gear-train answer in preference to a "compound".
1.5   Once calculated you can write down the results or cut and paste by right clicking the results box. Left click "select all", right click again, left click "copy" and paste to another application such as a word processor or spreadsheet.
1.6   To look for another thread go back to point 1.3. If you have finished, press the stop button.
2.0  Instructions for BoxfthreadP are as follows:

Run the program as described in 1.0 by running BoxthreadP.exe . 
2.1   Proceed as point 1.1, then work out the gear ratios for the gearbox part of the lathe (see.
BoxfthreadP calculations) and make a reference table for yourself to relate the lever positions to the ratio. Press "Edit quickbox" to enter these ratios. Start by entering the number of ratios to consider in the top box and then type a ratio into each box starting on the top lhs and working down. Press "save current data" and "press to stop". Restart the program, press "edit quickbox" and check that all ratios are correctly typed and positioned in the white boxes. Check that all gears are correctly entered in the main window as per 1.1 above.
2.2   Proceed as point 1.2
2.3   Proceed as point 1.3
2.4   Proceed as in point 1.4. If you have many gear ratios the number of results will frequently be high; to save, copy and paste the results to another application as per point 1.5.
Depending on the speed of your computer, and how many ratios you have, BoxfthreadP may take a little while to do each computation and require some patience.
2.5   To look for another thread go back to point 2.3. if you have finished, press the stop button.

THE CALCULATIONS (NthreadP):
These are the calculations upon which the program is based and also for assistance with some calculations required by the user:
FOR AN IMPERIAL (inch) LEADSCREW
TPI produced = DRIVEN/DRIVER  x  DRIVEN/DRIVER  x  LEADSCREW TPI
It does not matter in which order you place the driver or driven gears.
FOR A METRIC (mm) LEADSCREW
PITCH  produced = DRIVER/DRIVEN  x  DRIVER/DRIVEN  x  LEADSCREW PITCH
It does not matter in which order you place the driver or driven gears

EXAMPLE 1: (Imperial leadscrew, imperial thread required)
Leadscrew turns per inch :  8 (1/4 inch pitch)
No. of teeth on primary shaft gear (driver) : 50
No. of teeth on 1^st stud driven gear: 80
No. of teeth on 1^st stud driver gear: 32
No. of teeth on leadscrew gear (driven) : 60
TPI = 80/50 X 60/32 x 8 = 24
This will produce a 24-turns-per-inch thread

EXAMPLE 2:  (Imperial leadscrew, metric thread required)
Leadscrew Turns per inch :  8 (1/4 inch pitch)
No. of teeth on primary shaft gear: 48
No. of teeth on 1^st stud driven gear: 50
No. of teeth on 1^st stud driver gear: 36
No. of teeth on leadscrew gear (driven) : 44
TPI = 50/48 x 44/36 X 8 =     10.185 TPI
Convert to millimeters : Pitch in mm = 25.4 / TPI   
                                                               25.4 / 10.185 = 2.494 mm pitch
This equates to a 0.25% error against a 2.5-mm pitch.

EXAMPLE 3: (Metric leadscrew, metric thread required)
Leadscrew pitch: 2 mm (metric leadscrew)
No. of teeth on primary shaft gear: 80
No. of teeth on 1^st stud driven gear: 80
No. of teeth on 1^st stud driver gear: 36
No. of teeth on leadscrew gear (driven) : 48
PITCH = 80/80 x 36/48 x 2 = 1.5 mm                   

EXAMPLE 4: (Metric leadscrew, imperial thread required)
Leadscrew pitch: 2 mm (metric leadscrew)
No. of teeth on primary shaft gear: 32
No. of teeth on 1^st stud driven gear: 36
No. of teeth on 1^st stud driver gear: 25
No. of teeth on leadscrew gear (driven): 28

PITCH = 32/36 x 25/28 x 2 = 1.5873 mm       
Convert to TPI : TPI in mm = 25.4 / 1.5873 = 16.002 TPI
This equates to a 0.0125% error against a 1-mm pitch.         

EXAMPLE 5: (Imperial leadscrew, imperial thread required, simple gear-train solution)
Leadscrew Turns per inch:  8 (1/4 inch pitch)
No. of teeth on primary shaft gear (driver): 40
No. of teeth on 1^st stud driven gear: idler
No. of teeth on 1^st stud driver gear: idler
No. of teeth on leadscrew gear (driven): 80
TPI = 80/40 x  8 = 16
This will produce a 16-turns-per-inch thread using a simple geartain

KLUDGE FACTOR:
Some lathes have their gear-train configured in a different way. In an attempt to make the program work with these a "Kludge Factor" is included where (for a variety of reasons) the primary shaft does not run at spindle speed. The Kludge Factor is, in essence, a factor that will be required on some lathes to obtain useful results. The BoxfthreadP version does not have the kludge factor facility but this can be multiplied into your gear ratios if using the BoxfthreadP version of the program.
     
KF =  Spindle speed/First driver speed (Change this to first driver/spindle in later version)
or: KF =  No of teeth on primary shaft gear/no of teeth on spindle gear (may not be true for all lathes)
or: KF =  Actual TPI produced/TPI calculated by NthreadsP with KF of 1
or: KF =  Pitch calculated by NthreadsP with KF of 1/Actual pitch produced
You can work out the Kludge Factor from any of the above formulae - and it should always be the same.   
On lathes with a two-speed primary gear drive use the BoxthreadP program with 2 ratios.

THE CALCULATIONS (BoxfthreadP):
If you have a gearbox in addition to a typical gear-train enter the number of ratios,
and the ratios which you will have to calculate, as follows.
Ratio = No teeth on Driver gear/No. teeth on Driven gear x  No teeth on Driver gear/No. teeth on Driven gear etc
or: Ratio = Speed of gearbox output shaft/Speed of gearbox input shaft
or: Ratio =  TPI calculated by NthreadsP/Actual TPI produced
0r: Ratio = actual pitch produced/pitch calculated by NthreadsP
See also "sample sets for common lathes"; please send more to Geoff Carter for others to use
To use the program results work backwards from the answer to find the lever positions
For most lathes the input gear to the quick-change gearbox is usually the "leadscrew gear" - but this will depend on the make and model of lathe.

FILENAMES
The following files relate to the 2 programmes
NthreadP.doc   This document
NthreadP.exe  Application
nthreadp.txt  Save gear set file (used by NthreadP and BoxfthreadP)
Geartrain.bmp Drawing of typical geartrain
BoxfthreadP.exe Application
quickbox.txt  Save gear ratio set (used only by BoxfthreadP)..