The Japanese collector, whose name appears as "nothing" below, emailed me his photos of three types of 2x2x2 mechanisms. He asked me to explain them because he has trouble with English (not nearly as much trouble as I have with Japanese!). The pictures are not his, so he asked me not to post them on a web site. I will describe the one he mentions below, that he says is about 20 years old.

It has a ball in the center. There are six brass stems, and at the end of each stem is a contoured disk (think of a steering wheel.) The disks are screwed into the stems with little philips head screws. The cubies have a foot that slides around between the ball and the disks. If I can believe my eyes, it looks like each foot has a notch in it, but the purpose is not obvious. It is similar to the inside of a keychain pyramorphix, except the disks are round instead of triangular, and the cubie foot looks sturdier. This puzzle looks like the mechanism would move very smoothly.

Another photo is the inside of a Rubik's Pocket Cube.

The last is a 2x2x2 with a spherical magnet in the center. The cube is black with a white line that you match up. The line is interesting; it looks like an integrated circuit line running along the surface of the cube.

Thank you, sir, for sending me the photos. We need to translate your name into phonetic English. We need a better name for you than "nothing".

The "popeye cubik puzzle (2x2x2)" is ball mechanism.
I think it is rare because the current "Pocket Cube (2x2x2)" is no ball mechanism.

There is the photo of "popeye cubik puzzle (2x2x2)" on following web site.
http://www.virtualpuzzlemuseum.com/2x2x2puzzles2of8.htm

I do not know what mechanism of Face cube(2x2x2) is.
Please let me know.