Originally Posted by
jonainmi
The narrow flats are making it really hard to grab a hold of the drive side, and the nondrive side has nothing to grab onto, because of the threads.
PB Blaster is generally thought of as one of the best for dealing with corrosion - spray that first, then tap both cups sharply to help it penetrate.
There are two ways to approach this. If you can find someone with a tool that will fit your fixed cup flats then try that first by using the bb spindle and nut plus washers, as shown below (credit to Miamijim for 2nd pic)
The other option is to grab the threads on the adjustable cup with a pipe wrench or large vise grips or ideally a good machinist's vise. You can grind some flats on it to help.