Hi,
Question in message #38

So is there anything else to take into account to reverse the direction of movement of a stepper BESIDES the coil patterns?

Yes,
Commutation pattern shall always be coilA+, coilB+, coilA-, coilB-, coilA+, coilB+.
A+ and A- may be swapped, or B+ and B-  may be swapped to reverse rotation.
If there is a misconnection somewhere in commutation logic, signal connections, or in motor wiring,
such that commutation pattern become something like coilA+, coilA-, coilB+, coilB-, coilA+, coilA-, coilB+, coilB-
or coilA+, coilA-, coilB-, coilB+, coilA+, coilA-, coilB-, coilB+ ,
that is signal for coil A have been swapped with signal for coilB,
then motor movement will be erratic or unpredictable. 
 
This was pointed out in message #2, but all problems described later,
indicate that such a problem may still exist.
 
Full step driving, Half step drive, or Wave drive is about overlap or no overlap between current in coil A and current in coil B,
pattern of commutation always alternate between coil A and coil B.
 
    Mysil