I am surprised about all this talk about edge flipping algorithms.
Once I learned the concept of mono-ops, I immediately proceeded to
invent a very simple, and quite obvious, edge monoflip. You can do it
by manipulating only the front and the horizontal center slice
(hereinafter referred to as the "slice"). A virtue of the procedure I
am going to describe is that you can think of it in geometrical terms
and explain it that way. The result is that it is easy to remember
and invert, and you do not need any notation.
Hold the cube with the two edge cubies you want to flip in the U face.
Have one of them, the current "target", in the UF position. You can
think of its "socket" as moving with the F face. Now turn the target
cubie over to the left side.(F') Then move it to LB position by
turning the slice. Next flip its socket over to the right.(FF) Now
put it back in its socket by giving the slice a half turn. Finally,
return it to the U face. Don't worry about the fact that you have
changed the orientation of the cube, as that will be fixed when you
reverse the process for the other edge you want to flip.
Conceptually, this is a 5 move sequence. Since two moves are slice
moves, you have to count it as 7. If you want to count quarter-turns,
it would be 10. In any case, it is simple. (Singmaster has published
even shorter monoflips.) But to me the most important thing is that
it is obvious on inspection that it has to do what you want. The way
I look at it, you are using the slice for manipulation and storage.
You remove the target from between its neighboring corners and put it
back with the opposite orientation. (Is this as obvious to everyone
else as it is to me?)
The same way of looking at things allows you to create edge monoswaps.
Just put the two edge cubies you want to swap in diagonally opposite
corners of the slice and give it a half turn before putting them back.
You can arrange it so that they will or will not be flipped. Such
moves are their own inverses.
Using the D face for storage and manipulation, you can also easily
invent monotwists and monoswaps for corners in the U face. For all
such moves that I have created, it is apparent to me what needs to be
done and why it will work. No memorization of obscure move sequences
with magical effects.