Welder's Mask Algorithms
Here you'll find algorithms for all 81 of the Welder's Mask cases. Each of the solutions to the cases is 2gen, i.e. the only twists used are F moves and R moves. Each case can be solved optimally in at most 6 twists.
This step is supposed to be intuitive. Let these algorithms serve as a tool, not a tutorial.Sorry in advance for any errors. If you find one, please let me know. (This table was made without a skewb in hand.)
How to Find Your Case
Finding your case is easier than it seems. Each case is identified by four characters.
First character
Permutation of the UFR corner

Second character
Permutation of the UBR corner

Third character
Orientation of the UFR corner

Fourth character
Orientation of the UBR corner

All in all, the combinations should read like so: AA11, CA23, BB31, etc.
Below, there are nine tables, each with a subset of cases pertaining to piece permutation. The columns 1, 2, and 3 represent the third character, and the rows 1, 2, and 3 represent the fourth character.
AA
 1 
2 
3 
1 
Solved! 
R F R' F' 
F R F' R' 
2 
R' F' R F 
F R' F' R 
F' R F' R F' R 
3 
F' R' F R 
F R' F R' F R' 
R' F R F' 

AB
 1 
2 
3 
1 
R F' R F 
R' F R' F' R 
F R F' R 
2 
R' F' R' F R 
R F R' F R' F 
R F R F' 
3 
R' 
F R' F' 
R' F R F' R' 

AC
 1 
2 
3 
1 
R F' R' F R 
F R' F R' F 
F R F' 
2 
R 
R' F R' F' 
R F R F' R' 
3 
F' R F 
R F R' F' R 
R' F' R F' R F' 

BA
 1 
2 
3 
1 
F' R F R' F' 
R F' R' 
F' 
2 
R' F' R 
R F' R F' R F 
F' R' F' R F 
3 
R' F R F 
F' R' F R F' 
F R' F R 

BB
 1 
2 
3 
1 
R' F' R' F' R F 
R F' R 
F' R F' R F 
2 
R' F R' F R 
R F R F 
F R F R 
3 
R' F' 
R' F' R F R' F' 
F' R' 

BC
 1 
2 
3 
1 
F' R F R' F' R 
R F R' F R 
F R F 
2 
R' F' R' 
R F' 
F' R F' R' F R 
3 
F' R' F R' F' 
F' R F R F' R' 
F' R 

CA
 1 
2 
3 
1 
F' R F' R' 
F 
F R F R' F' 
2 
R F' R F' R 
F R' F' R F 
F' R' F' R 
3 
F R' F R F' 
R' F R 
F' R' F R' F R' 

CB
 1 
2 
3 
1 
F' R F' R 
F R F' R F 
R' F' R' F' R 
2 
F' R F R F 
R F R 
F' R' F R' F R 
3 
R' F' R F' R' 
F R' 
F' R' F' 

CC
 1 
2 
3 
1 
F R F R F' R' 
F R 
F R' F R' F' 
2 
R F' R F' R' 
R F 
R' F' R' F' 
3 
F' R F' 
F R F' R' F R 
F' R' F' R' 
