General Approach to RAVEL Solving
I move cubies into position starting with the front layer.
Then, layer by layer, front to back, I move cubies to their home.
As I move more and more cubies home, it becomes more and more difficult to continue without displacing homed cubies.
But with a bit of thought, I'm able to proceed using ad hoc methods.
However, on the last layer when only a few are not yet home, I need to use established algorithms.
The Cycle 3 algorithm
This algorithm cycles the positions of three cubies leaving all the other cubies in place.
The space between the three cubies doesn't matter so long as they form a right angle: cubies 1 & 2 on the same row, cubies 2 & 3 on the same column.
Drag the green cubie right to the apex (blue position).
Drag the red one down to the apex position.
Drag from apex left to where green started.
Drag from apex up to where red started.
The numbers in the image show the sequence of moves.
Remember: (right, up, left, down)
To cycle in the opposite direction, (down, left, up, right).
What if cubies do not form right angle?
- Move the cubies into right angle position (remember the moves).
- Do the Cycle 3 algorithm.
- Finally, manually undo the moves of the first step.
How to undo a series of moves
You do the moves in the opposite direction, in reverse order.
To undo (left, up, left, down), you would do (up, right, down, right).
Swap Two Cubies
Often you can finish solving the RAVEL using just the procedures above.
But sometimes pairs of swapped cubies remain. I don't know of an algorithm for swapping pairs that works for all sizes of RAVEL.
I have managed to solve some examples by just flailing away, trying anything.
I found a procedure to do a pair swap on RAVELs where one of the dimensions equals 4.
The picture shows the sequence of moves to swap the red and green cubies.
Drag the position marked "X" in the arrow direction in the sequence of the arrow numbers.
The vertical dimension must be four.
Of course the procedure can be adapted for RAVELs with horizontal or depth dimensions equal to four.