There aren't many adjustable workholding chucks that are perfectly true to
the center axis.
The more moving parts, the less accuracy.. generally.
Variations in the overall (in)accuracies of individual parts will dictate
the accuracy of a chuck (lathe, drill, etc).
Collets are generally considered to be much more accurate than adjustable
chucks. The adjustability feature of chucks is more for convenience.
Turning a simple part such as a bushing with a shoulder, will most likely be
most accurately machined/turned, when the bushing dimensions are cut to
desired sizes, then the part is cut off.
This is a common practice for very good/excellent concentricity.
Having chucks with soft replaceable jaws allows the user to bore an
axis-concentric hole/bore in the jaws for a particular sized workpiece, and
re-bored for a different size for best accuracy.
The jaws themselves, the guides that position the jaws and a scroll that
engages the jaws for adjustment, are all involved in the overall accuracy of
adjustable lathe or drill chucks.
The jaws typically aren't identical in adjustable chucks (the gear-type
teeth that engage the scroll differ from jaw 1, 2, 3 etc), so it's not as if
one could build a very accurate chuck with only a couple of sets of jaws.
The big difference in accuracy between chucks, is cost. Accuracy and quality
control are more expensive.
China and India typically make consumer grade products that looky-like a
real item, but quality control and accuracy generally aren't priorities..
just filling up the cargo containers for the next shipment is what matters.
Accuracy of chucks from other locations will vary, depending upon the cost
and the intended application that they were manufactured for.
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