Older Clarkson chucks can be quite worn
I have a 2mt version I purchased new and it is accurate. well within about .001"
Also have int40 chucks that came with a machine, they are not accurate the closing nose thread which continues onto the aligning surface that aligns with the chuck body bore is worn, this allows the closing nose to move laterally. In my new chuck the joint is tight.
Also have a second hand but better int40 1'' – 1.25" size collet chuck. this bigger chuck runs out about .002"
Clearly condition is important If there is play between the collet closer and the body alignment will be compromised. There is no taper to bring it back into alignment. The threads help a bit, but not so if they are worn.
My ER40 collet chuck also purchased new is more accurate better than .001" radial at the cutter shank. Being taper to taper wear is compensated.
Regards
John