Elevator door mechanism

ct13

Hi there...
I've tried searching all over the place and haven't quite found what I'm looking to implement in a building:

- Basic sliding door as in Death Star Final Duel (#75093) (IRL architecturally I think this is usually called a "pocket door")
- Door will open using the drive force from the elevator raising/lowering rather than using additional motors/sensors
- Door will slide open when elevator goes up or down and into floor position
- Door will slide closed when elevator goes up or down and into floor position

I've tried doing a little with Stud.Io but I've never really tried to model anything with gears and I'm not certain about how they will mesh. (Never mind the whiplash problem.) See below and apologies for the terrible colors and piece choices but it basically conveys what I'm trying to attempt. In case it isn't obvious the sliding door is 180 degrees rotated with gear rack on bottom facing down and sliding across a technic lift arm's smooth surface.

I'm pretty sure that the gear rack protrusions from the lift itself will not actually be strong/stable enough to provide the force needed to slide the doors open. Any thoughts, ideas or has anyone ever tried to do something similar in their own MOC before?