I want to recreate something I did at college, namely, a circular plug which I can replace with a different wood. I cannot work out how to get the angle of the saw to make the plug wedge shaped to fit the hole. Hope someone can help. Pickles.
If you have a matched set of a reamer and a tenon cutter this is easy (folks like Lee Valley sell such sets). You can create pair as well; searching for Windsor chair-making tools will lead you to a few approaches. A lathe can also make a taper and hole can be drilled straight and widen by diagonally drilling or by filing with a rat hole file.
http://www.popularwoodworking.com/techniques/joinery/chair-joinery-tapered-tenons-tapered-mortises shows Chris Schwartz wielding a reamer and tenon cutter to fit legs
If you are taking a dowel of some sort and want to make it, for example, 1/2" at the top but more like 3/8" at the bottom then this is how i would do it.Using a bit (like in the picture) to make a plug like i was talking about. I would use a table router. You would need to put a board on the guide of the router table to make it easy. The way i described would work it is just the setup you need to be worried about, and play it safe! I would take a dowel and run it by and then cut it off at the top with the table saw. Hopefully this helps!
You didn't say how large your plug was, but I'm thinking 2" or larger in diameter. This is something wooden boat builders do every day. This is no different in cutting out a transom for the back of a wooden boat.
In this wooden boat the rear of the boat starts to narrow at the transom (that flat board at the rear of the boat. That means the front surface of the transom is larger than the aft surface of the transom. (Hint, same as your plug...)
The key lesson here is: To make woodworking easier take the time to mark up ALL CUTS on all visible surfaces of your workpiece.
Again, you carefully mark the edge line of BOTH surfaces, top and bottom of the work. Obviously for your plug, one circle will be a smaller diameter than circle on the other side of the workpiece. Cut out your 'plug' to the larger diameter. Now place the workpiece on your bench, with the smaller diameter facing up. Use a hold down to keep the work from moving. Use a sharp chisel to pare off the edge to the top line, leaving the bottom edge untouched. Much easier than leaving blood on a power tool.
Good for plugs from 2" to 8' in diameter!
Do note, on that transom shown in this photo, the bevel angle varies huge around the workpiece... you've got it easy with a 'plug'.
One more comment... with this method, you are not limited to circles.. you can draw any shape you want... rectangles, square, butterfly dovetail insert, etc....