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After I just made that post, I realized a giant omni-wheel robot would be fun to drive . . .You will need three or four big geared down (low speed high torque) DC motors, some big omni-wheels rated for the weight you expect, encoders on each wheel, wood+steel frame, and some motor drivers. All this will be controlled by a microcontroller....
Do the wheels really require encoders? It seems that they could be run open loop since the pilot and bombardier working together would presumably be correcting for minor inaccuracies in the system -- just like in a real plane. Of course, this assumes that the inaccuracies in the platform motion are reasonably small.
Would you recommend 3 or 4 wheels/motors? Given the slow speed and controlled conditions I'm thinking that 3 wheels may be adequate and would help to keep the cost down.
I found several sources for wheels that seem capable of handling the load. Do you have any pointers for motors such as you described? Is there anything special about mounting them for omnidirectional use?