X is the axis that moves between the left and right side of the StorageBot. This axis also has to support the weight of the other axes, Z and Y.
Like many Makers I sometimes struggle coming up with the best design approach. My first attempt at prototyping the X axis was unsuccessful due to binding issues. When building any rail system mounted to a wooden frame one has to compensate for wide build tolerances. For example: the wood isn't always straight, there may be warpage with temperature and humidity, cut lengths are slightly different, etc. The final solution I came up with was inspired by a rail system that was already used in my house. It so happens I have pocket doors and the rail system used on those doors can also be adapted to the StorageBot.
Pocket door hardware is an inexpensive and simple system for producing linear motion while hanging a lot of weight such as a door (or equivalent on the StorageBot). See the attached pictures on how I adapted this simple system. This is a great example of how being observant to the world around you can provide insights into solving problems.