Animating a rubber belt

I’ve been looking all over the Internet on how to make and animate a rubber belt. Basically what I want to achieve is that when I rotate the gear, the belt should also rotate and carry the block up and down. The block would also slide along two poles. The picture down bellow describes what I want to achieve.

Array and curve deform modifiers to make the belt. Transform constraint to make the gears turn, and copy location constraint to make the belt follow the target
untitled.blend (119 KB)

Thank you so much. This is exactly what I needed.