This bicep curl, called the supine curl, puts a lot of stress on the biceps while also forcing your core muscles to come into play.
I would start out using light dumbbells until you are sure you can stay on the ball. You can also do these one arm at a time if you like.
I recommend doing 3 sets of 8. Once you can stay on the exercise ball with no problem, increase the poundage once you can complete the 3 sets of 8 reps.

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