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My first experiment with a jigsaw produced a nicely rounded shelf, but it's terribly rough. I am considering reducing the labor needed to properly sand it by getting another toy: a router. A nice side effect of using a router is that the top and bottom edges would not be so square and would be forgiving when someone bumps into them.

jigsawed shelf

Would using a router (once for the top side, and another for the bottom) leave the edge sufficiently smooth so that a bit of hand buffing with 200-grit paper would suffice? Or would I be left with something that is even harder to work with because I would need to sand a round, rather than a semi-flat, edge?

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    Ply isn't the easiest thing to cut cleanly but you've done a decent job with your jigsaw. When I've done similar cuts I've finished the job with an orbital sander without too much effort. The problem with working from both sides is registering the cuts. – Chris H Mar 19 '16 at 11:41
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Tried to make this a comment but must have been to long. So here goes. I think a router would be what you are looking for. There are bits that will cut a 45 and a curved edge. Both will help with the sharp edge. Some bits control the depth with a shaft (cheaper ones) some control with a small bearing. The trick is to figure out the direction of cut to make the cleanest cut, cut two deep and the cut is rough and the router gets away from you. I usually plan on a rough cut to get most of the material off and then a second cut to get a smooth edge. I like carbide bits with a bearing the best but have had good luck with High speed steel on softer wood. A router is great for trimming laminate counter tops so that could be a future project.

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Yes, it will smooth an already straight edge. Meaning, it'll just further smooth what's rough feeling & you'll still need to sand & fill for plywood. But No, it won't fix, square or straighten an edge.

You would have needed to make the cut in 2 or 3 passes (Router's aren't good for cutting over a 1/2" deep per pass) with a Router butting up to a straight-edge or template, you'll have to rasp it & sand it. A Router used on any edge without a template will only follow the edge that's there, regardless of how good or bad it is.

Once you've finished sanding & straightening your Jigsaw cut, then the Router will be perfect for cutting a decorative edge onto any piece. I suggest only using Router bits with the ball bearing guides, the solid steel guides can burn the wood & thereby cause wavy edges. But, that's a pretty fine job for a freehand Jigsaw cut.

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It can be rough putting a decorative edge on plywood. On the other hand, if you can put some facing on that edge, you could use a router to chamfer or round the top edge of the facing and have a super smooth result that you can stain or paint.

You could use a thin strip of wood, steam it or soak it in hot water and gently bend it around that curve and fasten it (glue plus brads). The router would be really nice for finishing it.

To make the initial cut, though, you've done a great job with the jigsaw. If you try the same thing with the router (or even if you want to try to re-do it with a jigsaw), I would look for something you can use as a jig to guide your cut. And example would be something rigid you could attach to the base of your jigsaw (or router) with the blade/bit poking through, then attach to the counter top at an appropriate pivot point (the center of the arc), then you just swing around the pivot point.

Here's an example (not trying to market anybody's product, just looking for an illustration of the concept): https://www.canadianwoodworking.com/plans-projects/adjustable-circle-cutting-jig

If you put a laminate on top of that, a router is exactly the right tool to clean up the edge.

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