cybertron,
To aid you in your understanding of machines, I recommend the article found here:
http://en.wikipedia.org/wiki/Simple_machine
Your posts #51 and #53 reveal several points which make your project more difficult...
1. The doors weigh twenty pounds.
2. The mechanism and its motor must fit in a space 2" wide by 18" long.
3. The mechanism can be no taller than 1-1/2"
The weight of the doors is a problem because the mechanism will have very little mechanical advantage. This is because the linkages will be attached to the short square tubes relatively close to the hinges. To lift twenty pounds without bending, the mechanism will need to be stronger than dimensions may allow.
The 2" by 18" footprint for the mechanism and its motor is a problem because the motor will have to be very small to fit in a space less than 2" wide. A small motor which might fit will probably not have the power needed to open the doors. The 18" restriction will prevent a larger motor being mounted off one end of the mechanism (as I previously described for the Worm Drive alternative...).
The 1-1/2" height limitation on the mechanism is a problem because it forces you to use a very small rack and pinion assembly, which (if one can even be found) will probably not have the structural strength to do the job without bending (or stripping gears).
***
There are some things that could address some of the problems which your most recent posts have uncovered:
1. Lighten the doors to reduce the forces on the mechanism and the power required of the motor.
2. Significantly increase the vertical space available for the mechanism so it can be made larger (therefore; stronger).
3. Increase the 2" by 18" footprint for the mechanism and its motor to allow a larger motor to be installed.
***
I have attached two scaled sketches based on the current limitation to 1-1/2" for the height of the mechanism. As shown, the Pinion can be no larger than about 3/4" diameter and the racks no more than about 3/8" tall. Only the approximate length (3-3/4") is shown for the linkages.
Think about what can be done to change the current "givens" for your project so we can have a better chance to make it work.