Considerations

Automatic, independent vs manual and all jaws moving together - for any number of jaws
Collet vs no collet.
Automating by turning a screw vs a piston that locks chuck
Indexing of workpiece (hold workpiece at specific angles), vs. indexing of the rotation motion (with CNC), vs. indexing rotation with an indexing (dividing) head [1]

Operation

How to align a workpiece in 4-jaw independent (off-center) chuck using a dial indicator and a sharpened point - [2]
Aligning tail piece to chuck - first use a very straight rod (such as cylinder rod) and then set adjustment screws on tailstock to move side to side. What about up and down? [3]
Indexing chuck - allows you to hold workpieces in a certain orientation, such as a pipe cross - at 90 degrees for 90 degree machining - [4]. This appears solved with CNC lathe/mill combination with multiple heads. Indexing chucks can also be automated so they turn the piece automatically - [5].
Large chuck - [6]

Means that it holds and releases automatically. Simple mechanism is turning the hold with a motor - [7]
More complex is using a piston to close the chuck.