If you're going to do great gears on the map, you could make them 'real' and have the whole world operate by clockwork or steam or such. Or the moving could just 'happen' and the great gears of the underworld are an imagined reason for the mobility.

I'm reminded both of Xanth, and of Dr Dolittle. Yours is unique though - I like it a bunch.

If you need movement, then stationary a while, then movement again, look up interrupted-gear mechanisms. Cool stuff.