Here's the basic unit. I made it out of baltic birch plywood starting with a plan in Lutherie Tools a book from Guild of American Luthiers.
Here it is "exploded."
There are three main sections, the base, middle, and top. The base
and middle pairs are both the same size, about 6" wide x 26" (or so); the
top are narrow strips about 2" wide x 26" long. The bottom is held
together with four scrap plywood strips that are about 2" wide that run
cross-grain to hold the bottom together (they're not visible). The
two bottom pieces are separated by a 3/4" space so the router bit can extend
through the plates being jointed. In this photo, the space is filled
with a strip I use when gluing plates (more on this later).
The plates to be joined are placed between the bottom and middle pieces and all held together with the top pieces. The whole setup is held together with wing nuts that fasten to bolts that I epoxied to the bottom of the jig.
Note that the distance between the top pieces is the same width as the base plate on my router. Once all together, one pass with the router joints the plate edges. I then loosen the bolts, insert the filler strip, apply glue to the edges, retighten the wing nuts, then add a few clamps.
To use this to carve radiused forms, I set aside the middle and top pieces, and flip the filler strip in which , I epoxied another bolt (threads cut off) that acts as a pivot (see below) for 1" MDF that I have cut into a 23"-24" circle. I also add blocks on each bolt to allow the MDF to move under the router guides.
The pivot matches a hole drilled into the center of the MDF circle.
I used a band saw to cut
the arches (these are 15' and 25') that will provide the carriage on which
the router will ride. I started with 2 x 4 stock, marked the arch,
then cut it. When it was then sanded to the line, I ripped the 2
x 4 in half, so the set would match. In each end, I drilled holes
that match the spacing and diameter of the bolts epoxied into the bottom
of the jig. 
I then mount the rails on
the bolts and blocks. I made a simple base plate for the router that
fits the rails and allows the router to stay centered between the rails
(it is a rectangular piece of hardboard or Plexiglas or whatever with two
additional pieces glued on that cradle the rails).
To cut the form, I use a 2" straight plunge bit. I start at the end and lower the bit until it just touches the MDF. I then spin the circle (sometimes the circle spins itself) and it carves away. When I complete a revolution, I move the router a bit towards the pivot and spin again. It only takes about 10 minutes the carve the dish, and the amount of noxious dust created is incredible.