The ideas for the Cabin have evolved considerably.
The new idea that was just stated in the 2011 update was to move the Cabin in both the forward and sideways directions by means of an array of fixed wheels that engaged in rack like features on the base of the Cabin as shown in this animation .
Since then this idea has been expanded into movements in the vertical direction.
My initial idea was to put vertical rack features at either end of the cabin which would engage with an array of gear wheels. The profile of the rack is cycloidal and the "teeth" of the gear are small wheels. This is to make provide a rolling contact between the wheels and Cabin to eliminate the requirement for lubrication and minimise wear. This follows the design philosophy of minimising the cost of owning the Cabin. A downside to the use of a cycloidal profile is that it will only provide a constant velocity with one specific gear wheel size, in this case 12 teeth.
The idea of using vertically moving Cabins as an alternative to lifts (elevators) is expanding and the contact wheels can have elastomer tyres to minimise noise and vibration.
The following animations show:
I am now considering a helical gear with an involute profile . The advantage of this is that the size of the gear is no longer fixed and can have a few as three teeth. The point of contact is in a single vertical plane, and I propose that the gear will have an elastomer tyre, shown in red, along the tooth.
The key insight comes from the table comparing the capacities of various transport modes. We see that there is a substantial potential carrying capacity of Cabins on a conveyer belt. Expressed as passengers per hour per square metre of cross-section this is outstanding.
The problem is how to get the Cabins on and off such a conveyer without massive and complicated machinery.