Summary

Need a linear motion? This Thing gives a simple solution, driven by a very low cost 24BYJ stepper motor. If necessary, limit switches can be mounted. Stepper controll by an ATtiny85 and a ULN2003 driver. Some lubrication does not hurt.
Rack and pinion are based on the enclosed openSCAD script of Dr Joerg Janssen.
A rack length of 20 cm can be realized by rotating the rack on the bed 45 degrees around the z-axis.

https://youtu.be/2h2Gol47aHI