how do we make ever more precise tools?

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Over time things like machine tools have gotten more accurate, ie I assume early metalworking lathes had a much higher range of error than modern ones.
So how were the more accurate machines made using what must have been a less accurate machine?

In: Engineering
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Good question! In a word, levers. Say I wanted to make a small, precise drawing. But, I’m not very good. I can do a large scale drawing that’s precise, but not small. One thing I could do is attach my pencil to a long lever. We tend to think of levers as a way of gaining a mechanical advantage, i.e. allowing us to push or pull with a greater force. But the way they do this is by reducing distance.

Take a rod 1m long, and attach one end to a pivot. Put a pencil at the free end, and then another pencil 1cm along from the pivot Now, when I draw an arc with the pencil at the end, the pencil near the pivot will make a similar arc. Except the arc it makes will be just a 100th of the size. Any errors I make will also be scaled down proportionately. If I can rig up a similar system with levers to allow me to draw more freely (it involved criss-crossing levers), then I can make accurate, scaled-down drawings. Say I was able to draw accurately to the nearest cm. The smaller drawing would be accurate to 0.1mm.

If you’re interested, there’s a great book on it how we got more precise over the centuries in everything like measuring distance, weight, time, etc. Precision machining enabling steam engines (and better artillery), precision time keeping enabling better nautical navigation, precision measuring to detect gravity waves, etc.

[The Perfectionists: How Precision Engineers Created the Modern World](https://www.goodreads.com/book/show/35068671-the-perfectionists)

Tighter tolerances and better techniques, for one. Cannons (to use an example from the “The Perfectionists” book below) used to be rough sandcasts. The bore in those cannons was… technically aimed the right direction, but not as straight or smooth as is necessary for accuracy. Then boring with a lathe was discovered, and suddenly cannons were axially straight, and much more accurate. This also led into making useful pistons, and a lot of other advances. Everything that followed was better, as a result.

Sometimes there are leaps forward, and sometimes it’s decades of incremental improvements.

In addition to the other really good comments, there’s a couple of “shortcut” techniques that, unintuitively, allow you to get freakishly accurate references surfaces using just hand tools. The most well known is probably the “three plate method”, which lets you make a “perfectly” flat surface using just three roughly identical blocks and a hand scraper.

[https://ericweinhoffer.com/blog/2017/7/30/the-whitworth-three-plates-method](https://ericweinhoffer.com/blog/2017/7/30/the-whitworth-three-plates-method)

Once you have a surface that you *know* is flat, you can use that as a reference to make other very flat things. Then, with clever geometry and engineering, you can build that up to other very precises shapes. By “educated guess, cut, and test” you can then (carefully!) use relatively un-precise machines to make very precise results.