Just some suggestions..for what's it worth. Prime bicep builder: If you want a full extension and full contraction for the biceps than you might consider close curl grip pull-ups. Can also apply this to a lat pulldown machine. But the old fashion pull-up/chin would be first choice. Can go very heavy with this exercise, which is the whole point anyway. If you have a set of gymnastic rings (they allow the nature curve of the wrist, forearms, joints for bicep action/reaction..from start to finish) so much the better. At our gym there is a EZ bar grip on the chinning bar that works very well.
The second best bicep exercise (in my view) is the BB curl (heavy.. cheat allowed and encouraged). You will not get a proper full extension and contraction. But really who cares when you can get increased muscle mass to the biceps. And at a fast rate. (An honorable mention is the incline DB curl, which let's the curl start from the natural thumbs forward ((hammer grip)) and ends at the top position in a full bicep contraction..thumbs pointing out)
Might try doing a set of curl grip chins SS'ed with a set of heavy BB curls (2 or 3 cycles). A effective way to work the biceps. If anyone is into tri sets than do the chins, BB curls and last the incline DB curl (2 cycles only). No rest between any of the exercises. If preferring the conventional way, than do the chins and BB curls or incline curls in a arm workout. Good Luck.