I just finished an office with nary a straight line in it. I had the designer send me the .dwg, which I then emailed to my local mega shop, which needs to feed their CNC machine constantly. For a minimal amount of money, I had the substrates cut out, all the templates for the solid wood edge run, the plates for a curved modesty panel cut out and the top and bottom of a big curved light bridge cut out. Of course everything fit perfectly. It was the only part of the job that went well.
The quick, cheap and dirty method is to make a set of offsets from your scale drawing. Kind of like the x, y coordinates that they use in geometry. Layout full-scale with these offsets and place a 4 or 6 penny nail in that location. Make a batten out of a good straight grained wood like oak or straight grained fir. 1/2" x 1/2" seems to work without breaking. Bend the batten around your nails and mark your curve. Boat builders have been using this method forever.
From contributor G:
Attach your router to a shop-made trammel/ base that replaces the router base plate. Make the trammel as long as it needs to be for the required arc. Use a screw as a pivot. The trammel/base can be used for different radius just by changing where you put the pivot screw. The router cuts and cleans up the cut in one operation.
From contributor B:
Contributor G has it, as long as it is a true radius. Just screw your router base to a piece of plywood, with the pivot point being a screw or nail, and make a few passes of 1/4" or so progressively deeper cuts until you are through the material. You can use the pieces as templates for making many more parts like top and bottom plates for walls, etc. with a top bearing flush trimmer router bit to follow the template you made. Move the pivot point on the plywood, holding the router to make inside and outside curves using the same point as the center of the cut. Say you are using a 1/4" bit for cutting. If you get the outside of the curve you want, and want to use 3" studs for building a wall, move your pivot point on the plywood, holding the router in 3 1/4" (3" for the studs and 1/4" for the router bit) and use the same swing point that you put the nail or screw in for the outside of the curve. Nails seem to be easier to use than screws because the center is more exact and easier to find than with screws. Easy to do, but hard to explain in words.
If the curve is not a true radius, you probably will need to make templates of the job conditions and work with those.
I have a Bosch router I use for all my arches. I had some long 3/8 threaded rod from hanging dust pipe. On one end of the two rods, I drilled holes in a piece of 1 x 2 oak. The rods then go through the holes in the router base, placed there for an edge guide. Measure from the screw in the oak (used as the pivot point) to the outside of the bit and tighten the thumbscrews on the router. Quick and accurate every time.
As a cabinetmaker for an industrial millwork shop, I make a lot of curved pieces. Trial and error with a thin stick and a pencil used to be my method, but I stumbled on a method in a magazine recently.
The author uses two nails and a string. The downside is you have to have your work piece on its side. Just put a nail at the start and finish points, hang the string across, and let gravity do the guesswork. Adjust the arc with the length of string you use, then trace the string. Works great. For true radius work, 4 words... router on a stick!
I use the same method as contributor B, only substitute the piece of plywood with two battens joined at the middle to form the notch. Put a nail in the middle at the outside of the curve, put another nail at the end of the template at the outside of the curve, put another nail at the other end of the template at the inside of the curve. Place two battens, one along the front and one angling back to the nail at the other end. Screw the two pieces together where they meet. Hold a pencil in the inside corner of the battens, move the battens along the nails, switch your nails and repeat for the other side, using the same battens. This will make a perfect radius of any size on any work piece.
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Comment from contributor H:
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