The geometry of clamping a 90 degree corner - A question

[Glen Blanchard]

It has been quite a while since I had a geometry class, and I am sure I should know the answer to this question, but I’ll ask anyway.

Let’s say I am gluing up a drawer or a box, and want to be sure it is square. Furthermore, let’s say that I have a corner clamp of some kind that will assure a true 90 degree corner. How many of these corner clamps do I need to use to assure a square assembly? I know I don’t need to use four such clamps, as if three corners are exactly 90 degrees, the last corner must also be 90 degrees. So I surmise that three such clamps would do the trick. Would two work? My logic tells me that if I placed corner clamps on opposite corners of the box, I would get four 90 degree corners – but have used only 2 clamps in the process. Does this sound right? What about using just one clamp? If I am certain that I have one 90 degree corner, do the other three corners have to also be 90 degrees? I am unable to conjure up a mental image whereby one corner of a box is 90 degrees, while the other 3 are something other than 90 degrees. Am I nuts, or does that all make sense?

[Hoa Dinh]

Before I attemp to answer, I need to know something: what kind of joinery do you use at the corners?

[Glen Blanchard]

Before I attemp to answer, I need to know something: what kind of joinery do you use at the corners?

Let's say mitered or butt, but would it matter?

[glenn bradley]

When I square up a frame, box, carcas, whatever; I use corner clamps if possble. K-body clamps help keep things at 90* but . . . measuring between opposing corners is the sure bet. If the upper left corner to the lower right corner is 12" -and- the upper right corner to the lower left corner is 12", the box is square.

[Jim DeMarco]

Two opposing corners should do the trick, as long as the lengths on the two opposite sides are identical.

[Glen Blanchard]

When I square up a frame, box, carcas, whatever; I use corner clamps if possble. K-body clamps help keep things at 90* but . . . measuring between opposing corners is the sure bet. If the upper left corner to the lower right corner is 12" -and- the upper right corner to the lower left corner is 12", the box is square.

Indeed. I know that measuring will confirm square. But let's say that you had nothing with which to measure, but you had some 90 degree clamps. How few clamps could you use to assure square?

[Hoa Dinh]

Let's say mitered or butt, but would it matter?
It does matter. For butt join, I can get away with two clamps, or even one if I'm careful and the project is not too large.

Miter join slips. I need 4 clamps.

This assumes one "layer" of clamps. If the project is tall, I may need more than one layer.

-- Hoa

[Dan Cameron]

If opposite sides are the same length and straight you will have a parallelogram.
ONE clamp will make the parallelogram a rectangle.

Dan

[Charlie Velasquez]

You are not nuts... at least with respect to this example.

If you know you cut the opposite sides of the box/drawers equal in length, then it will form a parallelogram. If one corner of a parallelogram is 90 degrees, then the opposite corner is 90. And since adjacent angles of a parallelogram equal 180, then all the angles are 90's... at least in theory. In real life it never seems to work that way for me...

[Tom Jones III]

Simply using geometry and treating this like a homework problem will not always lead to a square glue-up. The wood can bend or sag, sometimes pieces are not always the exact same size. Often the joinery that we think is 90* is not so when we apply clamps we force the glue-up to conform to the joinery.

I suggest you start with the minimum number of clamps that you think will lead to a good glue joint using the minimum of pressure required on each clamp. Measure for square in every dimension you can think of and measure each dimension in several places. Add new clamps and tighten existing clamps as required. Recheck for square often.