I made a straightedge from a Corian scrap and glued it to a slightly wider strip of Corian. To use it,
1. Lay a strip of blue painters tape that's longer than the circumference of your next ring face up next to the straightedge and tape the loose end down. Let the roll of tape hand over the end to hold it in place.
2. Stick all the segments on the tape in order and
tight against both each other and the straight edge. This step is really important!
3. Apply glue (I use Titebond Original) to all the segments without moving the segments.
4. Tear off the taped down end of the tape flush with the end segment and tear off the roll of tape leaving about 3 inches of tape as a loose end.
5. Now for the magic. Lift the strand of taped-together segments and flop it over onto it's side. I lay it on the Formica-covered outfeed table of my table saw.
6. Pull the ends together until glue is squeezing out of every joint then secure it with that loose end of the tape. You now have a solid ring that you can safely handle.
7. I go the extra step of putting a hose clamp around the ring until the glue dries. The tape not only holds the segments together until you can get it to look like a ring, it keeps the glue off of the hose clamp.
8. Wash the glue off of the straightedge and the flat work surface. Do this after every ring or the straightedge won't stay straight and the flat work surface will not stay flat. This is possibly the most important single step. Skip it at your peril!
It actually takes longer to read this process than to do it but everything stays in complete control all the time. I glue the whole ring at one time because my segment jig and table saw cut segments with the correct angle.