What is this sorcery? Nice engineering for sure.
The best I can come up with is each cup has a ball that is released one at a time giving the appearance the same ball is “moving” between cups. But how?
One possibility is there are a set of magnets for each cup. A weak magnet hidden in the hands holds the balls in all the cups when the arms lift. There is a hidden rotating gear under the miniature table the cups and balls rest on that has a stronger magnet attached we can’t see.
When the stronger magnet moves under a cup via gear rotation, it locks the ball to the table. This leaves the other two balls fixed to the cups and one on the table when the arms lift the next time. Turning the crank again moves the strong magnet away from the cups releasing and allowing the weaker magnet in the hands to hide them all again. The process then just repeats for each cup.
This has to be the solution…