a.k.a. TomZ Constrained Cube, Tom's Constrained Cube
Purchased from Mefferts, 2012.
(plastic 2.2" square;
TomZ Constrained Cube 90,
TomZ Constrained Cube 180,
TomZ Constrained Cube 270,
TomZ Constrained Cube Ultimate)

Locks in the center allow the corresponding face to only rotate a particular number of degrees. Below is a photo of the 180 degree cube, and also a photo of a second 180 degree cube which came with its blue face set to 90 degrees. The ultimate cube has a mixture of degrees on its faces, including 0 degrees.



Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/quarter.htm