Fixing an out-of-round vintage Sturmey Archer SBF drum brake
No more sh-sh-shuddering from this early SBF
A front drum brake on a bicycle is a wonderful thing. The benefits are many: smooth and quiet, powerful, yet with precise modulation, low maintenance, weather resistant, sealed from muck and dirt, no rim gouging… I can't recommend them enough. 
But none of this counts for much if braking shakes the Booty out of you and your bike.
This is the situation I faced after installing a new old stock (NOS) 1970s Sturmey Archer SBF in the front wheel of the Bootiebike Moulton Deluxe. A little googling found that the shaking, or shuddering, was caused by the brake drum being out-of-round beyond the acceptable tolerance.
You could perhaps be forgiven for thinking that the sterling old Sturmey Archer company would be expert at making round brake drums. And that a new old stock brake drum would indeed be round. But that wasn't the case here, and I'm guessing it was no coincidence that this example sat around long enough to warrant the NOS description. I've experienced dodgy NOS things a few times before, and can't help but wonder if NOS is really worth the risk. It's also notable that this example dates from 1979, by which time the once-proud Sturmey Archer firm had begun its descent into becoming a shameless producer of junk. (On the other hand, the bearings are as smooth as anything ever made…)
Anyway, the solution to this seemingly major problem turned out to be easy and quick. Simply wrap a strip of emery cloth around the brake shoes and use that to sand down the 'high spots' in the brake drum. 
A big thanks to Mike Perrin and the Greenspeed website for helping here. They're the source of the ingenuity described on this page.
Step 1: Prepare emery cloth
Cut a piece of emery cloth (cloth-based abrasive) and cut it to shape as shown in the photo. There may be a little trial and error to get it exactly right, but I know you appreciate that sort of thing. I used 240-grade, which is what I had handy, but you may wish to go coarser.
Step 2: Wrap the abrasive cloth around the brake shoes
Pushing the brake lever to open a gap, poke the tab on one end of the emery cloth between the cam and the flat contact surface of the adjacent brake shoe. Then tightly wrap the emery cloth around the shoes and insert the other tab on the other side of the cam. Make the emery cloth as taut as possible.
Step 3: Reassemble the brake
Reassemble the brake and reconnect the cable. If backing off the brake adjustment isn't enough to let you reconnect the cable, it may be necessary to shift the cable stop a smidgen. Adjust the brake until the emery cloth is in light contact with the drum.
Step 4: Start sanding
Rotate the wheel back and forth to sand down the high spots on the braking surface. (Adjust the brake a bit if you can't feel the emery cloth 'doing some work'.) You will notice that the level of resistance varies as you rotate the wheel. Continue rotating the wheel several/many times, first one way and then the other, until the resistance diminishes. Adjust again, rotate wheel again. The amount of variation in resistance will reduce as you continue sanding. Repeat until the resistance is consistent over the full rotation of the wheel.
Notes
- Part way through it may be necessary to remove loose grit and/or change the emery cloth. I didn't need to.
- When finished, don't forget to ensure the brake internals are clean and free of grit.