Generally, it’s best to plan cutting sequences to minimise moving the job. Particularly important when using an ordinary 3-jaw chuck because these don’t reset accurately. Thus, when a rod has to be drilled and turned so the hole and outside are concentric, do both operations without dismounting the work. This guarantees the hole and the turning share exactly the same axis. If job is moved between the two cutting operations, the common axis is lost.
Of course, most complex jobs can’t be done without moving them between machines, or into new positions on the same machine. On a lathe, 4-jaw chucks are often used for this. As the jaws can all be adjusted independently, the operator can accurately reposition the job with a Dial Indicator. With practice this can be done quite quickly so some machinists use a 4-jaw for everything. Otherwise, three jaw chucks are fast, but not accurate when work is moved. Four jaws take time to set up, but can reset work accurately.
If money is no object, accurately made and adjustable 3-jaw chucks are available. They don’t perform better than a 4-jaw, but save time,
For speed and accuracy, collets are the best answer. They’re repeatable without requiring the operator to measure anything. Unfortunately collets are expensive and only grip over a narrow range, so not general purpose. Brilliant for work like clock-making though, and occasionally useful in my workshop. I mostly use ER32 collets to hold milling tools, but they’re also good for work-holding. So I own an ER lathe collet chuck, and some Stevenson Collet Blocks. Blocks can be held by a 3 or 4 jaw chuck, or a bench vice, or clamped to a milling table. Again not general purpose, but they allow work to be reset accurately:
I’m sure other members know other ways of repositioning work accurately after it’s been moved.
Dave