Welcome to the forum.
I think that on some old Craftsman routers the inner part of the collet was the motor shaft. There are several manuals available here, maybe look up your model and see if that's the case. Don't forget to pull the bit out a little (maybe 1/8") before tightening. A bottomed-out bit can cause tightening issues.
Yes, the collet is the end of the armature. I I have possibly solved the problem. As another responsedee said that I may be using metric bits. I tried all of them and some tighten some do not so upon micing the shaft some are 10 t0 20 thousandths under .250 so that is most likely my problem, I thank all so much and I will be active on this sight.
Have you tried cleaning the collet? Accumulated dust, moisture, oil, etc. maybe the whole problem, the slits in the collet have to be clean. Try using some simple green with a Q-Tip and a toothbrush. Then blow it out if you have an air hose or. I don't have a compressor so I put a vacuum hose on the exhaust port of my shop vac.I have a vintage craftsman router, I love tis router! I have not used it in several years but it is perfect for certain jobs. I cannot get the collet to tighten around the bit? Is there any way to fix this? can the collet be removed from inside the shaft? I tried to find parts but they are no longer manf, Help?