Henry Maudslay invented the "three plate method" for producing high-precision surface plates, apparently required to produce replaceable parts with high precision. For example, this website claims that:

To ensure all parts could be produced identically, Maudsley introduced the requirement of a true plane surface for measurement.

In another example, in this video at 6:30, the presenter describes a way to get two "coplanar" surfaces by bonding granite surface plates with epoxy, which apparently helps achieve high precision using a machine tool.

My question

How does an extremely flat surface help with the following?

  1. Producing replaceable parts (like screws, bolts etc.)
  2. Achieving high precision with machine tools
  • $\begingroup$ High-precision mass production methods vary widely by product type. Surface plates are only applicable to a certain subset. $\endgroup$ Apr 28 at 13:45
  • $\begingroup$ I would like to know what that subset is, and exactly how surface plates make it possible to produce the products in that set. EDIT: to be clearer, in the quoted text, it is claimed that using a "true plane surface for measurement" helped ensure "parts" could be produced identically. What are some examples of such parts, and how does the surface help ensure they are identical? $\endgroup$ Apr 28 at 14:23

2 Answers 2


See this answer for how flat surfaces are the origin of all other mechanical measurements: https://physics.stackexchange.com/questions/615177/how-do-you-make-more-precise-instruments-while-only-using-less-precise-instrumen/615295#615295

The answer basically boils down to the fact that:

  1. When you have nothing, the only thing you can measure against is itself.
  2. That means you need to exploit symmetries such as flatness, parallel, squareness, and roundness that can be verified by self-referencing.
  3. Flat surfaces are the only self-referencing geometry you can make from scratch (i.e. without other measurement tools to verify geometry.
  4. From that the other self-referencing geometries can be made and thus originates all mechanical measurements.

How does an extremely flat surface help with the following?

Producing replaceable parts (like screws, bolts etc.)
Achieving high precision with machine tools

Forget the screws and bolts. Start simpler. How do you check if a cube you made is actually a cube? Or a rod that you made is round? Not just round, but cylindrical rather than conical? If you can't do that, forget checking something complex like a screw.

Imagine yourself going through the motions of measuring the geometry of something and it becomes real obvious real fast why you need flatness. If I have a stack of gage blocks on a surface plate as a height reference to measure the height of every point on the faces of my "cubes", what happens if the plate is not flat? Obviously my height reference now varies depending on where I use it on the surface plate. A measurement reference that changes is no good. You need flatness to check that the height and by extension through heights at multiple locations, parallellness.

Same holds for objects sitting on the table of a mill or grinder. If it's not flat, distance from the tool head to the surface varies depending on where you are. And if the rails the tool head rides on is not also flat and parallel to the table, the same problem occurs. But how are you going to make flat and parallel rails without a flat surface?

All the same issues apply for the rail that the tool head on a lathe rides on: needs to be parallel and straight relative to the axis of rotation of the workpiece or else you never know where where the tool head is.

And how do you check if a rod is round? Spin it on a lathe chuck and see if the highest point varies in height above the table (technically you can't trust the lathe to be aligned either so you adjust the lathe to find the achievable minimum deviation in height is ala symmetry of rotating around an axis). Checking that the height above the table for the circumference at one point along the length of the rod is easy, but how do you do it at other points along the length so you can make sure it's not just round by a straight cylinder and not a cone or some shape that randomly varies in diameter along the length? Well your table now has to be flat again and parallel to the rotational axis.

What if you're a caveman with no lathe? Well then you can make a surface plate from scratch and roll the object along a flat surface and see if the height changes. But that only works if the surface is flat. (Also, it won't weed out lobed shapes. A circle has a constant radius and diameter, but lobed shapes have constant diameter but non-constant radius and can be so slight that appear round but aren't and that can really matter).

You could say that having a flat surface lets you physically "construct" cartesian coordinates since the straight lines on cartesian coordinates. Of course, cartesian coordinates also require squareness and parallelness but you can construct and measure the tools for these through the clever use of flat surfaces.

  • $\begingroup$ I had to think about this (excellent) answer quite a bit, but I can begin to see how surface planes enable the rest of precision manufacturing, even if they are not directly used. If I understand correctly, although one can use a lathe without a surface plane, in order to make the lathe, you would need one. Some other references that helped me a lot were this video on 'the origins of precision', as well as understanding the history of the Gauge block (also covered in that video) $\endgroup$ May 2 at 14:29
  • 1
    $\begingroup$ @statusfailed Yes. You can basically free hand anything with enormous effort and skill and the repeatedly check it with measurement tools until you get it. Even with a lathe with digital readouts, you can take cuts but when you measure the dimensions or geometry it won't be round, straight, or cylindrical, the faces may not be square, and the dimension may not be what the readout said. The cut taken is not the same as where the tip of the cutter is, and the hole drilled is not the diameter of the drill. So being able to measure and verify is real important. Otherwise you are flying blind. $\endgroup$
    – DKNguyen
    May 2 at 14:33
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    $\begingroup$ And you need measurement tools to set up the lathe as well so it actually is as true as you can get it (like adjusting aligning the chuck and tailstock). $\endgroup$
    – DKNguyen
    May 2 at 14:37
  • 1
    $\begingroup$ You can also take a second pass of the same cut or drill and still remove material because of the first cut removed more material resulting in tool deflection or heat expansion followed by cooling. $\endgroup$
    – DKNguyen
    May 2 at 14:51

There are basically 2 ways you can make parts fit together.

  1. Make the parts crudely, and then file them down and test the fit until everything works.

  2. Make the parts with precise tolerances, so that the parts fit every time without modification.

#1 is obviously much simpler. You can create very nice mechanisms this way without any precision measuring tools. But it has a serious drawback. All the parts of your product (lets say a musket) are now "unique" and not interchangeable with the same part from another musket. The more industrial things got (wars, large factories, etc), the more of a problem this became, creating a need for products with parts that could be simply removed and replaced without fitting by a craftsman.


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