Four-jaw chucks have four advantages over three-jaw chucks.

1-They can be used to hold irregularly shaped parts.

2- With the use of a dial indicator they can be used to center parts with a great deal of accuracy (concentricity)

3- They can be used to deliberately hold a part off-center (eccentric)

4- They can clamp the part tighter. This is a valuable asset when machining cams, crankshafts, and similar parts.

A four jaw chuck has independently adjustable jaws. It can be used to center parts that are not round. The square part shown in the video is far off center. Each jaws is adjusted accordingly and the part is verified to be on center. After a cut it can be seen that all four sides of the square are tangent to the cut.