Share external USB hard drive over USB between multiple computers

Solution 1:

Nope, USB operates on a tiered-star topology with one and only one host controller.

One possibly feasible solution would be to use USB Bridge cables to connect two of the computers to a third, where the hard drive would be plugged in. You would essentially be creating your own USB network with the middle computer presenting the USB drive as a shared resource.

Solution 2:

No, it is not possible to accomplish this via the setup you are proposing. A USB connected hard drive cannot simultaneously be connected to multiple computers. You can share them via a port device such as this one, but the device can only be connected to one computer at a time.