I am interested in how high-precision screw threads can be made from lower precision parts. As I understand it, one can make threads on a lathe in the following way:

  • The workpiece is rotated by some motor, at a not-necessarily fixed speed $\omega$
  • The feed rate is set proportional to $\omega$ using gears and the leadscrew

This is illustrated by the diagram below:

Limitations of Precision

It seems like this method limits the accuracy of the machined threads to the accuracy of the leadscrew in the lathe. I would like to know how one can machine threads of higher precision than the leadscrew of the lathe.

It seems that this is possible according to the section making accurate screws in this page, where it is written that:

To produce a screw of a foot or even a yard long with errors not exceeding 1⁄1000th of an inch is not difficult. Professor William A. Rogers of Harvard observatory has invented a process in which the tool of the lathe while cutting the screw is moved so as to counteract the errors of the lathe screw. The screw is then partly ground to get rid of local errors.


So to summarise, my question is:

Suppose you have a lathe, with a not-necessarily-accurate leadscrew. How can you manufacture a leadscrew of higher precision using this lathe?

Or alternatively: what might be the method described by "Professor William A. Rogers"?

  • 1
    $\begingroup$ I'm not a machinist so I can't help but it has occurred to me in the past that if we couldn't make better machines using the machines we've got then we could never have made any progress! $\endgroup$
    – Transistor
    Jul 17, 2022 at 14:29
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    $\begingroup$ I assume by "lead-screw accuracy" I assume you actually mean "lead-screw precision" (i.e. deviation in pitch). Also, it is worth looking into how you make a longer leadscrew than the one you started with. However, perhaps the error in both these questions is the assumption you need to use a lathe to cut a more accurate or longer leadscrew. Convenient for custom threads, but perhaps not for the leading edge. There are more methods and machines to cut threads than a lathe and it is within the realm of possibility that you cannot turn a more accurate leadscrew than the one your lathe came with. $\endgroup$
    – DKNguyen
    Jul 17, 2022 at 19:47
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    $\begingroup$ practicalmachinist.com/forum/threads/… $\endgroup$
    – DKNguyen
    Jul 17, 2022 at 19:48
  • $\begingroup$ You're right- I mean precision (I'm looking for the property that turning the leadscrew a fixed rotation gives a consistent linear movement). My broader interest is in how one can "increase precision" from low precision tools- you've answered another question of mine before on how flat surfaces and the 3-plate method help lead to this. In this case, however, I'm interested in how one might manufacture a lathe, since it seems to be the "mother" of all other machine tools (i.e., it seems like using a lathe you can get everything else). $\endgroup$ Jul 28, 2022 at 8:53
  • $\begingroup$ The description in the last section might be helpful. Not as clear as I would like but clear enough to be helpful. gracesguide.co.uk/Jesse_Ramsden What is described might not actually be the screw cutting machine itself. It almost sounds more like a marking tool in which case it is nearly analogous to John Whitworth's measuring machine which is shown and described in this video: youtu.be/T-xMCFOwllE?t=449 $\endgroup$
    – DKNguyen
    Aug 6, 2022 at 4:11

1 Answer 1


One combines multiple imprecise measurements to a more precise one.

In the case of this screw cutting, the method alluded to here might involve cutting the same part with different portions of the imprecise screw(s), probably in both directions. The result is a superimposition of all the material removals as dictated by the different parts of the imprecise screw, and removing some of the machine slop if done in both directions. This sacrifices other metrics such as the shape of the cut for pitch.

A similar combination approach might involve a flexible (technically everything is flexible to a degree...) force transfer member. For example if the nut were made of a less rigid material, but covers more threads, it essentially depends on combining more turns to produce the same force result in a turn. Naturally, "flexible" also means easier to affect from (undesired) outside forces such as the work part and so would be able to cut significantly less per pass.

Another possibility is two that complement one another. Though they don't alone meet a tolerance, due to features of manufacturing processes, the deviation of one tends to negate the deviation of the other. Unfortunately this is not that simple for pitch. For something where tool wear is a larger factor, a fresh tool portion can be associated with a worn tool portion to average to add to a mid-wear equivalent.


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