Can you grow grape vines in pots?

.... or do they need solid ground? The reason why is I had a crazy idea of making a mobile grape vine (make a small lattice type fence that you can put in the ground and if you can put grape in a pot you can move the vines to a different location). Would this work? One of the reasons I want to try it is... show more .... or do they need solid ground? The reason why is I had a crazy idea of making a mobile grape vine (make a small lattice type fence that you can put in the ground and if you can put grape in a pot you can move the vines to a different location). Would this work?

One of the reasons I want to try it is because there are a number of locations around the house we think it would look ok but aren't certain so it would be great to be able to move it around. We don't want 3 seperate grape vines.
Update: I would move the whole fence. I was thinking of attaching shelves on the fence to place the vine pots (these really just touch the ground) but if it was moved wouldn't tear or disturb the vines as much... I hope. I'm not sure if I'm making myself clear, hope so.
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