Trig and the art of making dovetails

My recent purchase of a router table brought with it a variant on Nintendo brain training, a Nintendo DS game which seems to be selling out this Christmas in the UK.

The problem stems from the imperial vs metric debate. Incra, who make the table fence, provide lots of templates for cutting dovetail joints. I decided to try and write a program which would print out the cut positions for both halves of the joint, using metric cutters. I was led to a guy who'd done this some time back, for an old version of Windows. He'd done the maths so was ahead of me. Our email correspondence informed my calculations, especially where maths and materials intermix on the accuracy stakes.

The basics are shown in . One male, one female cut, within a boards thickness/depth d. Simple! Nearly.

The input parameters are the stock width s, thickness d, the cutter diameter (max cutting diameter) w, the acute angle of the cutter theta and optionally the number of 'cuts' n. My initial code was in Python, quick and easy to use. I eventually came up with a series of routines which worked, all based around a forumulea connecting them all.

s =w(1+n) -2dtan(θ)

I hacked around with this until Thomas pointed out a restriction. The router fence moves the cutter in 'steps' (constrained by the mechanical mechanism in the fence). So if the step size is significant wrt the cutter there will be a misfit. this shows the next position of the fence relative to the first, and the misfit, corrected by changing the d dimension. This starts to get interesting. According to Incra, the step distance minimum is 0.001 inches. According to Thomas, the thickness of the stock should be an integer multiple of the step distance (call it m), and the cutter angle, related using δ = m/tanθ. This gives an increment of 0.004inches as the step distance, i.e. the constraint on the wood thickness. Now even with the best of tools, I doubt this is attainable for many woodworkers.

The other problems are

• Centring the pattern across the stock width
• Catering for patterns where the smallest cut is not a single pass by the cutter
• Finding a way of presenting this to make it easier to use.

Who said maths was boring!