3 vs 4 jaw lathe chucks
from http://www.mini-lathe.com/Mini_lathe/Chucks/4_jaw/4-Jaw.htm#4-Jaw%20Chucks :
Benefits of a 3-jaw:
- self-centering
- can hold hex bar-stock
- quick and easy to use.
Disadvantages of a 3-jaw:
- can't hold square bar-stock
- run-out/off-center can't be easily fixed
- can't hold irregularly shaped work
- can't turn off-center
Advantages of a 4-jaw:
- work can be centered to high precision
- can handle square/rectangular bar
- can turn work off-center
- slightly more grip on round stock
Disadvantages of a 4-jaw:
- slower/fiddlier to mount work (dial-indicator required)
- can't hold hex-stock