Joining curves: David Haig's method

Above and below: David Haig’s Monogram rocker illustrates how curved components can be integrated with the technique described here. Photos: Daniel Allen

Words and process photos: David Haig
Diagram: Graham Sands

When I designed my first Monogram rocking chair back in 1990, the point of greatest difficulty for me was how to attach the curved steam-bent back-leg/arm to the side of the seat. I wanted it to slice cleanly through without a break, so that the curve would look as far as possible uninterrupted, as well as ending up in exactly the right configuration to meet the back end of the rocker part below the seat as well as the underside of the arm above it.

I’d studied Sam Maloof’s jointing system, and realised that, strong and sculptural as it was, it couldn’t work starting with a single steam-bent curved element, hitting the seat edge at a compound angle. Maloof joints need to have at least one 90° angle and also a large chunk of wood to start with, to allow for shaping above and below the joint. There was far too much curve involved in my case to even think about using a solid wood block, and the wastage would have been hideous.

So I went for the most direct if unsophisticated method; I just cut a curved slot in the edge of the seat to match the squared up profile of the curved steam-bent arm/b-leg. I thought that with a snug fit, with fine V-chisel slots cross hatched on the faces, epoxied, and reinforced with a wood plugged No.12 dome head screw the piece should hold in place. I carved and blended in the curved cross-sectional shape just above and below the slot and voila! None of those joints have ever come apart and it’s neat and clean looking.

Matching curves

But the key here was this ‘snug’ fit. How exactly does one go about creating a curved slot on the edge of a seat (or any other edge) that will perfectly match the curve of the piece you want to fit into it?

Well, the first ones were nothing more or less than trial and error. I knew that a router using a ring guide should be able to produce a curved slot using a template made so it could be attached to the seat edge at the right spot and angle. So I measured the offsets carefully and then just shaped and filed the profile of the plywood template until it would produce an acceptable fit. It was good enough, and there I left it for many years.

Then, in 2007, I wanted to design a project for a ‘curvature’ course at the newly established Centre for Fine Woodworking here in Nelson, and after a bit of thought came up with my Hoop stool project. It was a good way to introduce steam-bending, laminating and also kerf-bending to students all in one project that would also end up an attractive and useful piece of furniture.

Again though, at the heart of the design was the cutting of very accurate curved slots into the ends of the kerf-bent and laminated seat to exactly fit the hoop-shaped legs into. In other words, a similar problem to the one I had encountered years earlier in my rocking chair.

The pivot jig solution

My first thought was how to avoid the rather hit and miss trial and error business again, and what I came up with initially worked quite well, but imposed a design limitation that was awkward to get around. I conceived the hoop shape at the top of the legs as a true radius, and so was able to use a router on an adjustable pivot to set up exactly matching slots for use with a ring-guide that would attach to the end of the seat. I just needed to dial in the exact dimension to allow for the cutter diameter offsets, and alter the pivot length (or radius) accordingly. I even made up a quite elaborate adjusting pivot jig for my router which enabled tenth of a millimetre adjustments to be made with ease.

The design difficulty was making the top portion of the hoop-shaped legs as an exact radius, as the matching slots could only be cut as an exact radius too, as they pivoted from a single point. On the hoop shaped legs, it meant that the radii had to fade out to a different gentler curve below where they joined the seat, and anyone who has tried blending exact geometric circles into basically parabolic curves will know that the transition point is a little awkward, and more so where a change of thickness is involved too.

The ring guide router technique

In 2010 I co-taught a course at the Centre for Furniture Craftsmanship in Maine with Peter Fleming, head of the furniture department at Sheridan College in Toronto, Canada.

He showed a technique that produced perfect negative/ positive shapes, such that any shape could have its negative (a slot or a housing) produced. This was a big step up from relying on my radius-cutting jig, as it allowed complete freedom to make whatever shape you needed. (Inlay sets use exactly this technique, but on a miniature scale, with very small diameter cutters, unsuitable for furniture-scale parts.)

Firstly, you need to make a thin (10mm or less) template to the curved shape that you want the eventual leg, or whatever to be. This will both shape your final piece and provide the template shape for making the slot cutting jig (photo 1).

You then attach it by screws on top of a piece of ply (or MDF) which is marked out with the outline of the edge you are going to cut the slot into. You set it at whatever place and angle you have decided it needs to join at (photo 2). The bottom piece for the template doesn’t need to be thicker than 10mm.

You then use a sharp 10 or 12mm plunge- cutting straight sided bit, with a ring guide collar, close to the diameter of the bit (so a 12mm bit could use a 16mm collar). Block up (use double-sided tape) each side of the router base to the same thickness as the curved top template so the router will stay flat as it cuts (photo 3).

Run the cutter against both curved edges right through the ply base template, to produce two slots each side, which should also run about 20mm above and below the outlined profile of the edge (photo 4).

You can then cut out the whole piece in between the two slots with a jigsaw, so you are left with a hole with two curved edges facing each other (photo 5). Those curved edges are the critical bit. The hole you’ve made will be wider than the original curved shape you have copied by the width of the cutter plus the gap between the cutter and the template, on each side...plus extra top and bottom too as the second ring-guide’s diameter is much bigger than the first and must be able to cut clear all around the edge you are cutting into, so allow enough clear space top and bottom too.

It’ll probably look far too big but fear not, this is how it should be at this stage, which is where the clever stuff happens. Firstly, keep the same cutter in the router bit (this is why you need a reasonably hefty cutter as it is now also going to cut the slot in your edge) and check to see exactly what size slot that bit actually cuts...they are not that accurately made at times, especially the ones milled from a solid block of carbide steel...ostensibly the same diameter as the collett, but in practice nearly always made a fraction smaller.

So the new ring guide you will now need to fit to actually cut the slot, using the curved template, must be twice the diameter of the original bit plus the diameter of your first ring-guide. This was my little eureka moment (though I’m sure its well enough known in some circles) as it removed the need for measuring offsets etc, and it’s a formula that works whatever sized bit or ring collar you use, as long as you stick with the original cutter bit.

The problem was finding or making the second ring-guide of the correct diameter for the actual slot-cutting, which tend to be relatively large. Unfortunately most routers have a lousy selection of ring guide sizes, but you can buy quite comprehensive sets that are generally made to go with auxiliary router base-plates, and these are a bit tedious to take on and off and not always easy to centre. So if you don’t want to go that way, you will have to find or make up a new ring guide out of ply or similar material, that you can slip over the first ring guide, to increase the diameter to what is required (photo 6).

This means cutting out circles slightly oversize and then minutely adjusting their diameter, (you can use a circle cutter in a drill press, or make it on a lathe if you have one) making test-cuts using your slot cutting jig in scrap wood until you can produce a perfectly snug fit. A strip of carefully place double-sided tape can hold the new collar in place on the underside of the first ring collar’s base plate.

Sadly, going off theoretically correct measurements alone does not in practice necessarily produce that perfect fit, but it gives you a very close starting point. With a technique that requires several machining operations and new jigs coming between the two pieces you actually want to join, it does not take much for tiny inconsistencies to add up to a poor fit. So, as in so much fine woodworking, a degree of fettling is often required to finally achieve that elusive perfect fit. Having paired up a cutter with the two ring guides that will produce a perfectly tight slot, make a careful note of the combination. It is now a valuable resource, because if they work for fitting one shape into an edge, they should work for any shape.

If you use a 12.7mm cutter and 15.9mm ring guide, (or 1/2" and 5/8"), it requires a 1" and 5/8" diameter second ring guide collar (41.3mm)... e.g. twice the cutter’s plus the first ring guide’s diameter. However, in practice my carbide fluted 12.7mm cutter is only cutting 12.4, so it actually requires a 40.7mm second ring collar guide. Imperial measurements are in some respects easier with this technique, as you can break increments into 1/8" bites and have more chance of finding off the shelf collars that are the correct diameter, which saves a lot of time and energy.

Attaching the slot-cutting template to an edge also requires some care and thought, and its best to make the whole template piece a lot bigger than you think you’ll need. I usually use a substantial pine block firmly screwed to the underside of the template and aligned exactly with either the top or bottom face of the edge you are going to cut into (photo 7).

This enables the template to be clamped in place wherever needed and the block helps keep it rigid. The pencilled outlines on your template should be used to align the under- block correctly. The block also helps stiffen the template so there’s no bend or give in it. If the oversized slot means you cut into the under-block a little for the first cut, no harm is done and it can actually help having those cuts to assist with precise alignment of the template onto the edge you are cutting into (photo 8). Just make sure your clamps are not in the line of the cut..it is surprising how cleanly sharp router bits will cut into malleable iron or steel...but only once!

Also note that the under-block can have an angled face which allows the curved slot to be cut in at angles other than 90° to an edge (photo 9).

If you are cutting the slot into endgrain, it will pay to have the edge profile already done, as it is hard to shape it afterwards without damaging around the edges of the slot. Depth of cut depends on what you want, but this method will produce a nice flat bottom to the slot in end grain. Take the last cut carefully so as to avoid tear-out. I generally remove waste in about 6mm increments, taking the router cut in a clockwise direction, but just 2 or 3mm on the final pass.

The example illustrated here is just to show that a tapered and curved piece can have a housing cut into an edge to fit very accurately, in a way that would be very difficult to replicate with chisels or handwork (photo 10).

The technique can be applied in myriad ways, but the two-stage copying process is the same. The selection of finished works shown here illustrates some of the ways I’ve used it in the past. I’m sure you’ll come up with many more.

David Haig MNZM is an award winning furniture designer maker who lives in Cable Bay, New Zealand. He teaches at the Centre for Fine Woodworking in Nelson, NZ and also at the Centre for Furniture Craftsmanship in Maine, USA. He has written several articles for Wood Review magazine. Learn more at http://davidhaig.co.nz/