In the February 2012 issue of Popular Woodworking Magazine, I use a simple jig to quickly and accurately make perfect circles. There are a couple of steps before using the jig. The circles are first marked with a compass and cut on the band saw, just outside the lines. The circles need to be marked on both faces of the blank, at least the centers need to be on both sides and lined up precisely. A shallow hole (about 1/8″) is made with a Forstner bit on the band saw on the bottom side of the disc to be. The diameter of the hole matches the diameter of the dowel that sticks up from the face of the jig. I turn my own dowels from a durable hardwood. The ones you buy won’t be round or the right diameter. If I were doing heavy production, I would probably use a piece of brass rod instead of a dowel.
This is one of those operations where you want to come as close as you can when sawing (to minimize the amount of work in the next step), but not too far (to minimize the amount of cussing). The block of wood under the clamp in the video stops the jig from rotating. I sand the first disc to a slightly larger diameter than I need, then set the block to the position of the pivoting part of the jig. The block then is adjusted to zero in on the right diameter for a nice fit.
Read the article for details about how to make the hand mirrors that the round things fit into.
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