Measuring tape....
Don't forget.
Abs.
Don't forget them either. An 18" arm doesn't mean shit without abs.
If you are going to do biceps work, you would actually warm them up first and then 1) avoid full extension 2) keep the elbows non-moving (or supported) throughout MOST of the range of motion 3) when you get your fist upside your head, hit it (j/k) ~ actually, turn your wrist AWAY from your head and squeeze the bicep as hard as you can, lift and hold (static)
When you lower your arm, this is another great place for *variable* negative resistance. If you had a good training partner, he could add enough resistance throughout the lowering phase. He would have to know just exactly how much resistance to add ( not too much, not too little)~ then at the bottom of the rep (not full extension) you could hold a static contraction with added resistance. After the bicep is on fire with lactic acid, you could start pumping out partial "burns" and fry them.
You shouldn't have to do this twice.
If I could "invent" a machine, I would have fully twisting handles and a foot lever to vary the resistance throughout the range of motion. This is the only way I could see a machine tailoring it's movement to you and your individual build. I don't know how I could get enough resistance (without a partner) for the lowering (negative) portion of the rep.
You could attempt single arm curls in the seated concentration position (to begin with) and then stand up against a wall for the rest of the rep, and for the negative, reach your other arm across and pull down during the lowering phase I suppose...