the gear and pinion are cut by laser using 6mm plywood (100% laser power, 8mm/sec, 2 repetitions).
To give you an impression of the final device, see the below picture, fully assembled and mounted into my storage system
The idea is to move the two rods (one right, one left) into a hole and lock the storage into position once the whole system has been pushed up. The task of this mechanism is supply to drive the rods, not to hold the whole weight of the compartment. this shall be done by the additional two wooden blocks and shall be safe enough.
This is the drawing; not sure about the scale but the drill in the middle needs to be 10mm in diameter
The vector file (SVG) is attached at the bottom of this side.
Once you got all pieces, you can assemble as shown below. The simple rings are spacers and the one with the two additional holes is used to mount the small rank to the shaft
Here some pictures illustrating how to assemble the complete mechanism
See the function on this video sequence