The carriage and the lift system are the most delicate parts of the entire project.
The carriage must be lightweight but strong enough to support the load, the lift system must run smoothly and the positioning must be precise.
There's plenty of ways to do this, steel rods and linear bearing, rail and linear guides... but looking for a more DIY solution i found that truck curtain rails work very well. It surprised me, but using two of these rails and 4 of the original slides i'v been able to make a carriage that slides pretty well. There's only a little play on the tilt, but nothing to worry about.
Here's a prototype of the carriage, you can clearly see the 4 slides.
The final carriage and fork:
The lift system consists of a string (actually a braided fishing wire) attached to the carriage that rewinds on a motorized spool on the base of the robot. A steel rod on the top of the rails allows a vertical lift of the carriage.
The motor used for rewinding the spool is a stepper recycled from an old laser printer. Why a stepper? Because it permits a precise positioning without a closed loop control and has a high holding torque to maintain the fork lifted. In this case even the detent torque (the maximum torque by the motor when it's not powered) is enough to maintain the fork lifted. So it's possible to lower the power consumption by turning off the motor when the fork needs to stand still.
Here you can see a video done during the test of the lift system to count the number of steps necessary to fully lift the carriage.