Awesome project! What you've built is a Cable-Driven Parallel Robot, and since you are using gravity to keep the cables in tension it is a suspended cable-driven parallel robot. Using the four cables you are able to move a point in 3D space. I happen to know this because I wrote my phd on the accuracy of these types of robots and their kinematics. At that time Jean-Pierre Merlet was probably the most famous/prolific researcher on this topic (https://www-sop.inria.fr/members/Jean-Pierre.Merlet/merlet_e...). You may also have heard of a company in Germany trying to commercialize this technology on a slightly bigger scale: https://redcablerobots.com/en/. There is also a conference on these types of machines in Europe: https://cablecon2027.sciencesconf.org/ the original being organized by Andreas Pott (another high impact sholar on this).

I have not worked in this field for many years but had a fun time learning about a very wide array of topics.