One of the better bicep exercises is doing pullups/chins on a pair of swivel rings (360 degrees) or even gymnastic rings. As Charlys69 points out, twist/rotate the hand, wrist and forearm while contracting the two headed biceps. Excellent movement for taking the biceps to the limit. If in doubt, check the biceps on most experienced gymnast. Designed for super sizing your biceps if you give it a fair shot.
Can set up some swivel handles on a lat/cable overhead machine and see what happens. Might also try it one arm at a time for more focus bicep work. Including on rings. Good Luck.