Yet more topology

Once again - a topological puzzle. This puzzle is in some respects is similar to Reefer Madness. I must admit I had help with this puzzle.

Had I not asked a classmate for some assistance I'd have never completed it, because I thought that our assignment was to remove the string from the center hole, allowing the two beads to be on one line. I tried different techniques,

and thought really hard, and then came to the conclusion that it was impossible. I was right. It was impossible. It was also not the assignment at all.