The only advantage to using a three jaw scrolling chuck is rapid fixturing. There are four jaw scrolling chucks available. The four jaw independent chuck can do anything the three jaw can plus mount workpieces off-center, precisely center a workpiece, and work with irregularly shaped workpieces.
One thing that I would like to see is a thin X-Y table that could be mounted to an RT. It would allow you to perform many of the 2D machining operations that would otherwise require a CNC. The DRO on mold mill/drill has an arc cutting feature but it requires a large number of small X-Y steps to make a reasonable arc. I also have a 12" RT on the mill and if I could precisely move the workpiece to the center of the RT, cutting that arc would be a piece of cake.
Years ago at work, I had programmed cutting an Archimedes spiral in G code (we didn't have a CAM program at the time). My recollection is that there were about four thousand lines of G code by straight line interpolation. We later investigated having an outside vendor make the product with a CNC diamond wire saw but their machine was limited to a few hundred lines of code. I rewrote the G code, changing to arc interpolation and the same precision was obtained with only a dozen lines of G code.
In theory, this operation could have been done fairly painlessly with a manual process an X-Y table on an RT.
(I got a Tormach, which ended my quest for the slim X-Y)
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im not a cuemaker nor have I used a cue lathe.
but general to lathes , the 3 jaw tries to center the object and can and should be very close to center. It's never perfect as perfect is infinite.
because a 4 jaw is adjustable it can be dialed in accurately to center.. so the 4 jaw is considered more accurate basically because a 3 jaw is not adjustable.
if something is turned and the chuck is off center it still turns the object round, the problem will surface though, if it is taken out and re clamped, or in machining other parts sometimes you would like to reverse the part and chuck the other end.. that is a test of setup as any run-out is then doubled and shows..
in general a 4 jaw is better for square things, a 3 jaw is faster to setup and go if you aren't particular about it actually running on center. I have both on my big lathe at work and use the 3 jaw a lot more often since I'm not making rocket parts but different kinds of repair work on metal not wood. the thing is heavy its about 100 lbs so I'd only swap it when needed.
an option that can sometimes be valid is to mount the 4 jaw in the 3 jaw. or you could try the reverse but that may not work well at all on a cue lathe setup.
i think the main principle does apply, the 4 jaw is considered more accurate because it can be "dialed in" to center whereas a 3 jaw is basically fixed and near- to center.
a cue lathe has to be long, not that powerful or as rigid and heavy as a machinist lathe the center must be adjusted quite far to make the taper. a machinist lathe usually has some ability to adjust the center of the tailstock but movement is usually quite limited. It can turn tapers by offsetting the cross slide on the apron , the part that holds the toolpost, but them movement of the cutter axially is quite limited in distance, maybe a few inches..
it works best for shorter tapers.. I do that to reform the crown on a pulley when it gets worn flat. commonly a 6" wide belt sander has crowned pulleys to keep the paper running on center of the pulleys. so I sometimes recondition them as they wear flat and make belt tracking difficult.
"stepping over" can be difficult to do accurately. the purpose is different and so is the design.
how or weather this affects the operations of cue turning , well I'm no expert on that at all in any way. I'm interested in learning more about them just out of curiosity mainly. some principles are transferable but not all.
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