anthony714

A buddy of mine rebuilt a Sturmey Archer 3-speed hub a few years ago on a bike I hardly use and it has always been slightly out of alignment. What can I do to adjust it? Besides the little chain adjustment on the hub itself?

Bandera

Read this:

https://www.sheldonbrown.com/sturmey-archer_3-spd.html

San Rensho 

Agreed. Look especially at the cone adjustment section, then go back and make sure the hub chain is adjusted correctly. You need just the slightest bit of play at the rim.

Gresp15C

I've rebuilt and ridden 3 SA AW hubs. First of all, I would not try anything until after adding some oil and waiting a while. Drizzling oil down the drive side hollow axle will assure that you get some oil to the most important innards. No sense trying to diagnose a dry hub.

So long as nothing is actually broken (possibly due to neglect or mis-assembly in a past life), then the hubs are quite reliable. If it's been assembled correctly, then it only potentially needs lubrication, adjustment of the non drive side cone, and indicator chain. As for the cone, my trick is to leave it on the bike, loosen the NDS fixing nut, and adjust the cone in place, so I can check the amount of play right away. Remember that barely perceptible play at the rim, translates into an extremely small amount of actual play at the axle.

If it doesn't shift right after adjustment, e.g., can't be pulled into low gear, then it's possible that the drive side cone wasn't assembled correctly. That can be addressed without opening the hub, but in my view any sign of neglect or incompetent servicing by past owners justifies opening it up and at least checking for things like broken hair springs, and then re-assembling according to the instructions.