I’m making some workbenches for the woodwork course I’ll be running. Each one has a 1200mm square top. I could simply use a set-square to draw it out, but I find it difficult to keep my marking-out accurate over a large area. Here’s how I mark a perfect square that doesn’t rely on having a set-square. It uses basic geometry that has been used for thousands of years.
Firstly, mark where you want the centre of square to be and draw a circle whose diameter is the same as the length of the square’s sides. This sheet of MDF is roughly cut slightly larger that I need it to be.
Next, draw a line that passes through the centre of the circle.
Then you draw an arc using the same radius as the original circle, with the point located where the centre line crosses the circle edge. Do the same at the other end of the line.
The next step is to draw another line through the centre of the first circle at 90 degrees to the first line. To do this place the point of your compasses (or trammel in this case) where the arc crosses the circle. Using a smaller radius than the original circle draw a small arc roughly where you think the centre line should pass through it. Then draw a similar arc with the centre point where the circle and the other large arc meet. This is the one you can see just above it in the photo.
I like to do the same on the other side, but you can then draw a line that passes through these small arcs and the centre of the circle.
Next draw 2 arcs, radius the same as the original circle, with the centre points placed where the new centre line crosses the circle.
Finally, draw lines to connect the four points where the four large arcs cross.
I can now cut along these lines with my Festool TS55 circular saw along a guide rail. You could, of course, cut out a square on a table saw with the fence set square and to the length you need. However in this case the MDF is too large to fit on my table saw.