Swiss ball leg curls are also known as supine hip extension with leg curls – SHELC for short. You probably don't do these because you think they look easy. You're in for a shock when you try them!
This exercise has been invaluable for a large number of my online clients. Most of them train in their home gyms and we need to build workouts around the equipment they have available. This is generally limited to barbells, dumbbells, and bodyweight exercises. They just can't fill up their garages with all the machines you see at Globo-gym.
While barbells and dumbbells do a phenomenal job training the body in almost every movement pattern, they aren't ideal for complete hamstring training. The hamstrings have two functions:
Barbells and dumbbells are perfect for training hip extension with movements like Romanian deadlifts and good mornings. However, they don't provide a good choice for knee flexion (leg curls). The ball allows you to train this function of the hamstring without needing a ton of space or having to spend thousands of dollars.
This exercise is excellent because it works the hamstrings in knee flexion, but if done properly, requires you to maintain hip extension (the other function of the hamstrings). This allows you to get the hamstrings into a shortened position and challenge them in this range.
When doing these think, "Heels in and hips up." Hold the peak contraction, squeezing your glutes hard for a two count and lower under control. I most often program these for 3 or 4 sets of 12-15 reps, with 60 seconds of rest in between. The hammy pump this delivers is incredible!
Once you've gotten really good at these, you can progress to doing one leg at a time. The single leg version certainly isn't too easy!