I have some ~36" 4x4 pieces that need to have round corners with a radius equal to the width of the board. (Each end of the 4x4 will have a 1/4 circle connecting the top and bottom of the board.) The curve would lie in the plane of one of the long sides - that is, if you if you looked end-on at the "ends" (3.5" x 3.5" profile), it remains square, but looking at the front or back (36" x 3.5"), you'd see half of a capsule shape (with curves cut in each end).
Todo: insert picture here. :/
My problem is that the board is too deep to cut with my router unless I cut from both sides - it's tricky to get both sides to line up, even using the template I've cut from 1/8" MDF. I have the same issue with my jig saw as it appears to cut about 2-2.5", and the (planed) board is still about 3-1/4" thick.
I can approximate the curve with my miter saw, making a series of cuts in ~10 degree increments that are tangent to the curve, then hit it with the orbital sander to smooth it out. That works okay, and provides the the most repeatable results, but I feel like there should be a better way.
I do not have access to a band saw.
I tried the router approach but wasn't able to get the result I was looking for. I finally went back to the miter saw, going in 2-5 degree increments. It worked pretty well, just have to find my belt sander now. :)