Common sense tells us that if we have a curved slot and a straight rod, the straight rod can’t possibly fit through the curved hyperbolic slot. However, this umbrella can fit through a curved slot regardless of the reality that it appears impossible. The rod is angled and rotated across space thanks to a three-dimensional shape with a hyperbolic cross-section, allowing the device to function properly. Therefore, it is possible to get the straight rod to go through the slot if the slot is precisely shaped like this hyperbola.
If you want to make your hyperbolic slot, you can follow the instructions here.