Flush Routing to Fit
For a long time I struggled with getting a perfect flush fit between thin plywood and a lumber frame. I never seemed to be able to get the fit I wanted when putting a back on a cabinet or bookshelf. Then I discovered bearing-guided flush cutting router bits. Now I cut the plywood back oversize by maybe an inch or so, glue and nail it to the frame, and trim it flush after the glue dries.
In use, the bearing runs along the frame, and the cutter bit trims the edge. The bit depth should be only just enough to trim the excess off. Any longer and you are likely to gouge the frame slightly.
This method can also be adapted to making multiple identical copies of a fairly complex part from thin plywood. Make a master from 3/4 plywood to the exact shape and size you'll need. Clamp the thin blank to this master, and trim it flush. You'll need to devise some means to clamp the pattern and the blank down while routing, but that will depend upon its shape and size.
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