I have figured out a way to make an undistorted 7x7x7 cube mechanism. It uses a 3x3x3 cube expanded to a grooved sphere as the core, but that isn't the important part.

The important part, of course, is how to get the 8 corners to work. Each corner piece is attached the corresponding corner of the core via a metal shaft. These shafts have a small kink sqrt(3) away from the outer corner and can rotate in crankshaft fashion to get out of the way of an inner edge of the 2nd row as a 1st row is rotated. These crankshafts neatly solve the problem of maintaining the position of the corner pieces relative to the rest of the mechanism while getting out of the way of the inner edges which make a traditional 7x7x7 mechanism impossible.

The rest of the mechanism does not need such crankshafts. Pairs of pieces fit in each groove segment and quartets of pieces fit at each groove intersection to fill out the rest of the mechanism. I've worked out the geometry of the remaining pieces and they don't conflict.

But holding the corners in really isnt a problem, its just like using a 5x5. The center is an extended 3x3x3.
The problem is that when you turn a layer, lets say the U layer 45 degrees (does anyone know how to make that degrees symbol?) The "wings" in the "u" layer will have nothing holding them in place.

Your plans sound very clever... Im not one of the people here who make these puzzles, but i certainly AM hanging out to see a 6x6x6 or 7x7x7 one day! Good luck, and if you ever get to making one, dont forget to tell us all...

I'm not exactly sure what the terms "U layer" and "wings" refer to, but I do know what the problem with designing the 7x7x7 is.

Holding the corners and edges in are the problem, because of what happens when you rotate a side by 45 degrees. The edges are handled pretty easily, by extending them inward perpendicular to the only axis in which they problematically rotate. The corners are not handled easily, because they problematically rotate on 3 different axes.

If you just use a 5x5x5 style mechanism to hold in the corners, you can't rotate the layers with the corners. If you try to rotate it 45 degrees, the support for the corner will run into the edge of the middle cubes of the next layer. This is why a crankshaft is needed. The crankshaft lets the support move out of the way while still providing solid support.

Hi Tyler,
To make the degrees symbol here is what you have to do:

First make sure that your numbers lock on your keyboard is turned on. Then while holding down the "Alt" key, type in the number "248" on the keyboard's number pad. When you release the "Alt" key, the degrees will show up.

There are other symbols that can be made using the same method but using a different 3 digit number. Depending on what you are doing, it may or may not work. Here are a few other useful ones:
± 241
≈247
²253
π 227
µ230
Ω234
√251
÷246
≥242
≤243

I know about ascii, i do VB and C++ (borland) programming... I just didnt know the keycode so i didnt bother. My favorite one is ¿¿ heheh. good for spanish projects