I don't think that you should have any problems, Bald Eagle, especially if you shut down the 'puter correctly before final dismantling.
I use computers on board ships, where they're subjected to all sorts of motion & vibration, both when running & shut down, so I can't envisage problems with the machine itself.
The only thing that might require locking is the scanner, but if this was supplied without any specific securing arrangements, then you should be OK.
Just pack the equipment safely; in original packing if you've got it. If not, then stout boxes & plenty of polystyrene blocks/bubble wrap will do the trick.