Hub brakes are like cinema projectionists. You know they're there, but don't know what they look like and don't give them much thought as long as they do what they're supposed to do. Above is the inside of one of my no-name hub brakes on my Christiania front-loading trike. That white stuff is anthrax spores. I held my breath and brushed it off.
Working on the Christiania is not like working on normal bikes. You don't need any hex keys. But you do need pipe wrenches.
Above are the two main parts of the hub.
And on the picture above here you can see Islay, on loan from a friend. I need a dog, at least intermittently. Islay is a quiet, careful dog, and an Iditarod veteran.
That part on the right hand side of the brake that looks like a cylinder is actually sort of flattish. When the brake lever is held in, the wire pulls an arm on the outside of the hub, which in turn makes that flattish cylinder turn, which then forces the two semi-circular arms outwards.
As you can see, there's not much play here. Problem is, I don't know how much there should be. I oiled the moving parts, which is a big drama as you do not want oil on the brake pads. I changed the cable and cable housing too. But the brake still doesn't work very well. Maybe opening it up again and giving it a good whack with a hammer will help.