I know about the "whitworth" 3 plate method for making a flat surface but even if you used the side of another of the same material there's no assurance that the two sides would be parallel. This is a property I expect out of gauge blocks for instance, I don't just expect their surfaces to be flat, I expect them to be parallel so that they have a consistent distance from each other too.

Assuming you have a flat surface and nothing else, how does one go about making that? Is there a technique to go from there to make a part with parallel flat surfaces?

I suppose a related question is how you get flat 90-degree surfaces?


2 Answers 2


It's less about how to make them and more about how to measure it.

It actually is a valid method to freehand something and repeatedly check it against gauges until it matches. Since that's so time-consuming and skill-intensive you don't want to do that except to make things in the initial stages, and usually only to make gauges or tools that will obviate the need to repeat similar processes in the future.

So the trick isn't actually how to make "the thing". The trick is how to make the first gauge when you have no gauges to verify it with, and how to verify that all subsequent gauges are good.

The reason that 3-plate method is so important is that it lets you make the first gauge without needing another gauge to verify it. From there the process is mostly using that first gauge (and any other gauges you may have accumulated) to verify if your new gauge is good or not.

Do you know how to measure if something is parallel?

You place it on a surface plate and run a probe along the top face at a fixed height and see if it is actually the same height everywhere. Nowadays, you probably use an indicator mounted to a transfer stand (which will measure the variance in height):

enter image description here


Or even a coordinate measuring machine (which will measure the actual height):

enter image description here


However, these bely what you actually need: You do not need to measure (i.e. quantify) the height to do this. You do not even need to measure the variance in height.

In the most primitive approach, your hands can feel the resistance decreasing, increasing, or staying due to the height decreasing, increasing, or staying the same as you run it along the surface. Therefore, you need is a base, a vertical beam, and a sharp horizontal point that can be mounted on the vertical beam at any height. A so-called surface gauge:

enter image description here


Now, you could then freehand and continuously check it until it is parallel. But from what I said above you can probably extrapolate that a much easier method in this case is to run a cutting tool at a fixed height similar to the probe. But if you so desired, you could freehand it to shape it. What you can't do is freehand the measurement part.

You use this to build your parallels. The longer you make your parallels (which also requires making a larger surface plate) higher the resolution you can check for parallelism.

Once you have your parallels you can start working on squares. For initial checks, you choose one arm of the square as a reference edge and align it to the parallel and trace the vertical edge. You then flip it and the more square it is the more closely the mirrored vertical edge will overlap/be parallel to the first traced vertical edge. Again, the longer you make the arms the more resolution you will have to check for squareness. enter image description here


Later on you can also do things like mount parallels vertically on a surface plate and run a height gauge on the "unfinished ends" until they read a constant height above the surface plate. At that point your parallels now have ends that are square to the length.

From there you can then mount a horizontal parallel (that does not necessarily need square ends) on top of a vertical parallel (that does have square ends) and run a probe along the length of the horizontal parallel to check if it's height above the surface plate is constant.

enter image description here


Also, from having parallels with square ends, you can now now make devices sit on the surface plate and run up and down vertical from the surface plate to more quickly check for squareness without needing to do something like mount two parallels together. But this is not strictly necessary. It's just really convenient.

enter image description here


At that point you have squares and parallels with square ends. Only then do you start worrying about making a gage block which is parallel, square, and of a particular dimension. Because dimensions are arbitrary. Parallelism and squareness (and by extension cubes), are not.

You would check the that the dimensions of a cube are all equal the same way you checked for parallelism by checking for constant height above a surface plate. And if it was the beginning you could just make any cube, as long as it was a cube and declare that as your unit of length. Because dimensions are arbitrary. Parallelism and squareness (and by extension cubes), are not.

As a result, dimensions tend to be least important thing. Geometry tends to be far more important (parallelism, squareness, roundness, flatness). A gauge block where the dimensions are a bit off but where the ends are parallel parallel is still useful, but a gauge block where the ends are not parallel is useless.

  • $\begingroup$ how do you get the the height gauge though? $\endgroup$
    – Jake
    Jul 17, 2022 at 16:24
  • $\begingroup$ @Jake You don't need a "height" gauge. The actual measurement of the height doesn't matter. What matters is the height is the same and in the most primitive approach, your hands can feel when sliding the probe around whether the resistance is increasing or decreasing due to the height getting higher or lower.. The dimension is the least important part of a gauge block. The geometry (parallelism, squareness, roundness) is far more important. See edits. $\endgroup$
    – DKNguyen
    Jul 17, 2022 at 17:14
  • $\begingroup$ This was super useful thanks! Scribing using a surface gauge was what I was looking for! $\endgroup$
    – Jake
    Jul 18, 2022 at 18:22

Here's a possible answer and a source at least. I should also note that I just read this and am not an expert. I'm likely getting some details wrong here so please refer to the original source. That said I'll do my best at an explanation to help myself grok my answer to this. Hopefully bring wrong on the internet will encourage someone else to give a better answer. With that warning out of the way:

In Moore Tool's "Foundations of Mechanical Accuracy" they first describe the 3-plate method. Later they describe a technique for creating a straight edge which is a rectangular prism (in their case a square prism).

Procedure: Try to create a straight edge that's as close to the end result as possible using whatever methods you have. Now pick one side and denote it as side 1. Scrape side 1 flat in reference to your reference flat (which can be made using the 3-plate method). You can do this by putting machinist blue or some other paint on the straight edge and rubbing side 1 against the flat and using the technique of scrapping to scrape the height points away. This is a whole art form unto itself but there are lots and lots of explanations of this technique available.

Now that side 1 is flat rest side 1 on your reference flat and scrape it parallel to side 1 using a height gauge, and flat using the rubbing technique. This is somewhat more involved than just flat scraping and relies on some pre-existing way to accurately measure very small deviations height locally. The indicator is then moved across side 2 by sliding a rigid mount across your reference flat, since side 1 is flat, deviations from side 2 being parallel should show up. You'll have to make a lot of such measurements.

Now you have parallel flat surfaces but not a straight edge as defined by Moore. Turn the straight edge over by 90 degrees to reveal an unscrapped surface and call this side 3. To measure squareness place the "knifes edge" (2 knife edges maybe? I can't tell from the pictures) against the bottom of side 3 and position the indicator somewhere against the side 3. Now rotate back to side 1 or side 2 leaving your indicator in the same position. Place the indicator base against the bottom of side 1/2 and you can see the error in squareness of side 3. Additionally use rubbing to ensure that you scrape it flat, not just locally square everywhere.

Now you can follow the procedure used to create side 2 in reference to side 1 except use it to create the final side (call it side 4) opposite side 3 with side 3 as the reference.

The ends of the prism are not square or flat but other faces are all relatively square and flat.

TL;DR You need an indicator of some kind to follow the method laid out in Moore. I'm not clear on how you would make that but it's worth noting that the indicator really just needs to show +/- and give you some idea of degree, it doesn't need to provide an actual measurement in any known units. It doesn't even have to be linear. It does have to repeat well however and it should always make clear the +/- direction of relative movement and should have almost no slop in the measurement. How you make that device with only a flat surface I'm not clear on.

  • $\begingroup$ A good video on scraping: youtube.com/watch?v=S9N3Q8Qww2A $\endgroup$
    – Jake
    Jul 17, 2022 at 2:38
  • $\begingroup$ And a follow up by Stefan on making a straight edge!! youtube.com/watch?v=S9N3Q8Qww2A $\endgroup$
    – Jake
    Jul 17, 2022 at 2:47
  • 1
    $\begingroup$ Your first indicator is just a sharp metal point mounted at a fixed height and your sense of touch as you push it along. And if you don't trust your sense of touch you can apply ink and have the probe score the high spots. $\endgroup$
    – DKNguyen
    Jul 17, 2022 at 17:56

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