How do you make more accurate tools from less accurate ones?

I was wondering, in a general sense how people make more accurate tools from less accurate ones.

More specifically, I was reading about reprap and it said it was possible to make components of itself from other previous repraps. However, the errors in them would compound and make less and less accurate/precise models. Therefore there would be some limit to how many times it could replicate.

But, for instance. A lathe requires an accurate/precise leadscrew to control x axis motion. Using a lathe it is possible to make another leadscrew however this would be less accurate/precise than the one already on the machine.

So for my true question. How do they make more accurate ones than the previous ones. If all the current lathes in the world are +- 1mm then how would you make the next set of lathes that are more accurate/precise than that without a piece of machinery that originally had better accuracy. (sort of a chicken and egg problem) Is there some type of machine or algorithm or something that allows a machine to make something that is more accurate/precise than itself.


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The origins of the screw-cutting lathe for example go back a very long way. Henry Maudsley is credited with a lot of the early work on precision machines. I have read books on how he made the first accurate leadscrews for example, using corkk nuts that straddled multiple threads, and took up the average position of them, increasing precision each time.

Couple with Maudsley's work, you have to look carefully at what Sir Josepth Whitworth, a great pioneer of metrology and engineering did - it is said that, as Whitworth entered engineering, people would talk of a bare 1/16th of an inch (1.6mm) as very good work. By the end of his career, routine measurements, to a precision of 1 millionth of an inch were being achieved.

Making flat surfaces is a key part in the evolution of metrology, and the invention of the the three plate method was important too.

Circular division is a key field, also tied to precision gearing techniques.

It is remarkable just HOW accurate handwork can be. We routinely expect handwork in my field to be < 0.010" without struggling.


Excellent answer to a question that has tugged at the edges of my imagination for some time now. Thank you for the recommendations of Maudslay and Whitworth, along with the three plate method and circular division.

One trifle though: Henry's last name was Maudslay. Henry Maudsley was a psychiatrist.

podarok1 year ago

I just leave this here

Krb6865 years ago
I think the answer to this question that is key is that with an inaccurate tool, knowledge, repeated trials, and accounting for errors, more accurate tools can be made. I have always thought about this question myself as well. Think back to cave men days. How did humans as a whole progress from using extremely inaccurate rocks being pounded together to the accuracy of tools today?

Another thing to consider is crossing different areas of science and engineering. Some technological aspects ALLOW for the creation of more accurate tools. It's all about the building blocks. How did humans create the Empire State Building much larger than themselves? Building blocks. How did humans create computers that calculate linearly millions of times faster than themselves and have transistors merely hundreds of atoms in width ? Building blocks.

A Whole sometimes allows for more than the sum of its parts. Also take for example the discovery of the laser. This piece of technology ALLOWED for more accurate tools.

Check out the most perfect sphere ever created, which has rough spots that vary no more than 3 atoms in width.

MRHint5 years ago
The reprap prints a part for a newer design or upgrade for the reprap or new machine.
maddman6 years ago
i can only answer the question in a rational calculational sense. consider the screw driver not in it's self a complexed machine, but a mere "tool" to utilize in order to complete a more complex task. such as making a machine that would do the screwing instead of you having to screw, once you had the machine made it would most likely if set at the correct mechanical timing could outspeed a person and deliver much more speed and precision than you could with a screwdriver. so in that logical sense a tool could make a more precise version of itself.
kylemp6 years ago
It's amazing how often this question comes up in my mind too..
For example, how do you have a flat and square block, without having a reference??
Finally, after a LOT of thinking I came up with a answer for the screw thing, as long as your guiding it from a thread you SHOULD be able to move at a consistent rate.. Think of the way a die moves down a rod to thread it.. It's using it's previous work as a reference and can cut consistently the same distance.
But it is always a question in my head, how dis we ever get to a point where we can achieve such high precision, and consistently??
But I have always marveled at how we have got there, especially since building 2 cnc's and having a intrest in making all my tools myself
TANZMEISTER6 years ago
I think if you wanted to find out how to create more accurate tools from less accurate ones, a good start would be at the beginning. I'm a huge fan of the book series by Dave Gingery.

His books let you follow development through the industrial revolution so you have a clear path to go from the creation of one tool to another. Hand tools build a foundry, foundry builds the lathe, lathe builds the shaper, shaper builds the milling machine, milling machine builds the drill press, etc.

Following this process, a drill press is (arguably) more precise then hand drilling the same hole. A miter box will give you more accurate cuts then the saw you used to create the box.
I realized that I never mentioned, that Gingery's books are not an analysis, they actually teach you how to create these tools.
aeray6 years ago
Many measuring and layout operations can be self-correcting, or used for self correction, like squaring a square, or straightening a straightedge. Look around this site for examples.
Re-design6 years ago
Operator's skill has A LOT to do with what the tool does.
seandogue6 years ago
Aside from the changeover from humans to automation, which imo changed the game considerably, I think it all had to do with the accuracy a skilled operator brought to the party, along with standardization of metrics and likely, the clever use of the same principle upon which the slide rule uses... (anyone else have one of those vernier calipers that shows the principle in action?)

And good eyes. There was a time when I could accurately, by sight, tell you to ~.05 mm what a measurement was. Granted, after several stupid accidents with lasers, a severe knock to the head with a 1" thick steel bar, a couple chips in the eye from stones I was working, and the added effect of the aging process, that is a definite *was.

There IS a real method by which it happens. I learned it once, but all I have to fall back on now that the memory has faded is what I wrote above, which is just "logicking", rather than actual delivery of a known method.
rickharris6 years ago
The original screw cutting lathe was made by James Watt - He used a common lather called a big Wheel that was driven by several heavy workers taking turns at the large fly wheel that powered the lather - Gradually using then next generation more and more accurate lathes are made until you get to the standard you require

In general working to high tolerances requires you can first measure to that accuracy and that you have a standard with which to compare or all measurements will be different.

Whitworth developed the principle of standards when making guns for the UK army and needing common parts that could be interchanged even down to the level of screws and nut and bolts so he defined a standard for the whitworth thread that is still used today.

It begs the question: How do you make the measuring equipment in the first place: this was Maudsley's great innovation. Whitworth WORKED for Maudsley.

orksecurity6 years ago
The way you make more accurate tools is to either account for the errors during design and manufacturing (ensure that the errors are in places which are noncritical), or to use more-accurate tooling/procedures.

In the case of RepRap, I believe the former applies. The critical measurement is the leadscrews, and those are NOT being manufactured by the previous generation of RepRap. Errors in the piece which mates to the screws can be absorbed either by always driving in a single direction with some effort to minimize backlash, or by shaping the threads which engage the screws so they're a sufficiently tight fit to apply pressure against both sides of the screw threads despite any manufacturing error. Either will ensure that manufacturing error in that component is not cumulative over successive generations.
blkhawk6 years ago
Very interesting and useful concept. So you have in mind replicate tools with less accurate ones but tweak the measurements and make them accurate. Awesome!
Kiteman6 years ago
That is an excellent question!

My first thought would be to ask the nice people at NPL.
Kiteman Kiteman6 years ago
(What you are asking about is metrology)