I have a vehicle with 4 wheels. Say I replace the wheels with large helical gears (pinions). If I set the vehicle on linear helical racks, it should be able to travel in one dimension. Say I replace the racks with a similarly toothed ground surface, could the vehicle travel in 2 dimensions (without rotating the body of the vehical)? I think it would be possible with opposing front and rear wheel drives. It should operate like a "screw" in the second dimension. Would the ideal helix angle be 45 degrees (to support movement in both directions)? How will speed, Torque, and service life be affected?
No, it cannot work as you are imagining. Such a vehicle can roll to the left or right under its own power, and it could be pushed diagonally along the grooves by an external force, but it can't "screw itself" up and down. All four wheels must always turn in the same direction.
Actually, after giving it some thought, you could have two sets of grooves in the surface at right angles to each other. If one pair of wheels meshed with one set of grooves, and the other pair mated with the other grooves, then you could get the kind of motion you're thinking of. But friction would be a huge issue for up-and-down motion.
Is this theoretical. If so I will bow out, but if not, Airtrax Sidewinder Forklift already does this. See the video. https://www.youtube.com/watch?v=vAiwLRGsNrE