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Squaring an Engineer’s Square

When I am cutting materials by hand for my projects, a lot depended on whether I can mark out the designs accurately, particularly the right angles. I have a cheap engineer’s square (L-square) which I used for my projects, which I later found was not completely square.

There are many youtube videos that teaches you how to check whether the square is actually square by comparing lines drawn when the square was placed first on one side and then on another side on a fixed straight table edge. That is the easy part.

From what I could see, very often the engineer’s square needed to be trued. And the recommended practice was to drag a file over the edges by hand from progressively different locations so that essentially the edges of the ruler would be filed at an angle – to the correct angle. This was a time consuming process, depending on how much the fault to be corrected was.

Since I had a movable gantry cnc machine, I thought it would be a good idea to make use of it for this purpose. A mushroom type grinding head could be used to spin at a high speed by the machine spindle and then made to travel in a straight line perpendicular to one of the L-square’s legs in order to grind off any imperfection in the L-square ruler.

But first, I needed to make sure that my machine itself was moving perfectly square. In order to do this, I squared up my machine first.

This was how I did it. I used Trigonometry in Mathematics for this, particularly the right angle triangle formed when the sides consisted of 3-4-5 units. To fit my machine, I had selected multiples of 113 for my calculation. For the x axis travel, the indicator was made to travel a distance of 113 x 4 = 452 mm. For the y axis travel, the indicator travel was chosen to move 113 x 3 = 339 mm. If the movements of the x and y axes were true, the “Hypotenus” line would measure exactly 113 x 5 = 565 mm. This was confirmed by measuring with a normal steel ruler.

Since the accuracy would depend very much on the human eye reading the markings on the ruler scale, which could also be subjected to inaccuracies during manufacture, the distances to be measured were chosen to be as long as possible to fit the dimensions of the machine table (wasteboard).

Before this, I actually had to calibrate my machine, so that I could be quite confident that what was shown on the computer screen was the physical position of the indicator at the machine table. Using the computer screen movement figures as representing the actual physical dimensions on the machine table, I would then have no need to measure the triangle physically with my steel ruler, thus saving me some time and effort.

Once the cnc machine was deemed square enough, the L-square was clamped in position and the grinding tool was programmed to move slowly to cut away the imperfections. I had to do this slowly so that very thin layers were removed each time. In this way I could be sure that the grinding abrasives would not have dislodged during the whole process of cutting from begin to end making the grinding even.

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