A while back I made a Longworth chuck from the Woodworker’s Guide plans. I used #4 stoppers from my LHBS, and because they have a 3/8″ holes in them I used 3/8″ bolts along with 3/8″ slots. This eliminated the need for the threaded rod 1/4″ > 3/8″ bushings. The other change in design was to use a wooden faceplate with a 1″ x 8TPI hole.
The 3/8″ sizing worked fine until I wrecked the wooden threads when an oak bowl popped out and got caught between the tool rest and chuck. My mistake.
For version two of the chuck I wanted to use 1/4″ bolts for each button because the 3/8″ bolts made the chuck a bit heavy, and also the larger diameter of the hardware forced me to use larger stoppers. I still didn’t want to screw around with lamp rod bushings so I follow this person’s advice and used lab supply stoppers. These have a smaller hole which will accept a 1/4″ bolt after a bit of a push. I selected the #3 size, and they cost me $0.28 apiece from my local American Science & Surplus store.
In addition to not needing any bushings, the holes on the lab stoppers are centered much better as compared to the homebrew supply stoppers. At the homebrew store I had to dig through the big to find 8 good ones whereas the lab supply stoppers were all the same, nicely centered. I’ve noticed the difference in how true work runs when fixed into the chuck.