Not having well-lined and deep pockets, I built myself a Longworth chuck so that I could finish the bottoms of several bowls that are otherwise completely turned and finished.
I made a couple mistakes.
1) It is a good idea to be amazingly precise when marking the pivot hole for the arcs. The thing will work if you are merely incredibly close ... but amazing would be better. Be careful marking these holes and even more careful drilling them. THEY ARE the source of the accuracy (or not) of this chuck. The chuck center only exists as a means of locating these holes, the holes themselves locate the important parts.2) Do not fasten the stupid backing plate to the stupid face plate block with a stupid screw through the stupid center while the stupid glue dries. You will need to drill the center later before separating the halves. It can get ugly. I used a hardened drywall screw. It got ugly. Mine works, but the hole I ended up making is somewhat elliptical and this results in my having to give it several 'alignment whacks' to get it to run true. I need to make another. Space multiple counter sinked screws outward of the center by an inch or two and you should be fine.
Do not hesitate to route it for 8 slots instead of the 4 slots in the instructions below. However, no guessing ... don't rely on a reference angle, use a compass to bisect the original angles. This is one step that I got right.
Start here.