The original question was how more accurate machine tools are made using less accurate tools to build them.  There must be some famous examples.

Whitworth's surface plate

Cheers

Greg Locock

This certainly isn't a historical example, but I think it's such a good modern example that it's germane to this thread:

There's a series of books authored by David Gingery that details how--using hand tools--you can build a completely functional set of metalworking machinery.  The process begins with making yourself a simple furnace and foundry to sand cast aluminum.  Aluminum sand castings then form the basis of the next project: the lathe.

The lathe is constructed with the knowledge that inaccuracy in most of the parts of the machine doesn't affect the accuracy or function of the finished machine.  Components that require accuracy are generally finished by hand scraping, just like Whitworth's surface plates.  Mating components are constructed with only sufficiently good fit; designed with adjustment to take up slop/lash.  By the time you start to need precisely-turned components to finish the lathe, the lathe is complete enough that it can be temporarily rigged to machine its own parts.

Once the lathe is completed to that point, you're set.  Further books in the series use your manual skills and your new lathe to build a metal shaper, horizontal milling machine, and drill press.  These are then used to go back and make the gears, dividing head, etc., to add screw-cutting ability to the lathe.  At that point, the world's your oyster.

Now, being a modern series, certain short cuts are taken; cheap threaded rod and cold-rolled steel abound.  But the point is nothing that it required for the lathe can't be created with a surface plate and some hand scraping or filing, with some thread chasing thrown in.

It's an interesting project and probably quite closely follows the developmental path of early toolmakers in most regards.  Google search 'Gingery Lathe' for examples.

I hope that's interesting.

Regards

Adding a little to "i278" post concerning lathes about each part being better than before here is a short anecdote about the lathe.
I was told how in the 20's my father was working with a lathe trying to produce a very accurate lead screw for a ruling machine.  When they had made the most accurate lead screw that the lathe could make they installed this in the lathe and instead of a metal follower on the lead they used a hard leather follower to smooth out the imperfections of the lathe's lead screw.  I saw references to this same procedure in the 50's in making diffraction gratings.

The introduction of ball bearings and the development of a good 4 jaw greatly helped the lathe business. Another  big improvement came with the barrel micrometer.  Prior to its’ introduction the caliper and divider were king. Both my fathers and grandfathers tool boxes had at least 50 pairs each of all descriptions.  

One thing that allowed improvements in accuracy was a lot of the designs were made with comparisons to one component of the piece.  In my father’s old books there is a design for a packing gland for shafts up to 1 ½" that every measurement is referenced to the stem diameter.

Accuracy is a always been dependent on one thing, the skill and dedication of the machinist

rhodie,

In your history about accuracy of machine tools, you should not forget the Pratt & Whitney company.

On their history page at http://www.prattandwhitney.com/history.htm they have a copy the book "Accuracy for Seventy Years 1860-1930".  The book has a lot of information about machine tools and measuring instruments.  On page 36 is a drawing of the Rogers-Bond comparator and on page 38 is a "Interferometer capable of measuring to fractions of millionths of an inch".

I believe some of the most accurate machine tools were developed by arms manufacturers to get higher accuracy on the gun parts..hence the invention of rifling....I can't remember who did this first though??

Friar Tuck of Sherwood

There is an excellent text that covers this subject :

“Foundations of Mechanical Accuracy”
Wayne R. Moore - 1970

I believe it is still available from Moore Special Tool.