If the dirt is particularly stubborn, use an abrasive kitchen cleanser. That will get it off fast and do a little sanding too. Use your selection of brushes to get at all the crannies and do a good job. Whether you have new, clean drives, or old, dirty ones, both need to be thoroughly sanded. The best way to do this is to remove them, separating the upper and lower units for ease of handling.
Many folks try a rotary wire brush for ease of getting at the crevices.
Beware that steel brushes leave traces of steel on the metal that will defeat your paint job. Only sandpaper can be used with a grit no greater than 150. I recommend that you NOT use a machine, because you must be very careful not to go through the finish, only to abrade the surface. All those nooks and crannies must be done by hand. But remember, the better job you do, the longer it is going to last.