It's been a while since I uploaded this project. Since then these Kinematics have been implemented in a couple different firmwares including Reprap firmware and Klipper. There have also been a few printers built using using these kinematic equations (some of them with different belt paths) that I would like to list to help any future builders. The have done far more work on this than I ever have, so take a look.

The Muldex build has a different belt layout, but operates in a similar manner. It's a great machine with fantastic documentation.

https://github.com/3dprintingworld/MULDEX

Next is the Core IDX printer by Gilly. It's a modified take on a similar concept. 

https://www.thingiverse.com/thing:6224372

Finally BCN3D recently announced their industrial 3D printer the Omega I60. Its an awesome looking machine that I hope to see in person one day.

https://www.bcn3d.com/bcn3d-omega/

One final thing to note is that I also just updated the kinematic equations in my original posting. I did not have the correct equations for the X1 axis, so I apologize for the confusion. Once I posted this I sort of forgot about it. It wasn't until a couple das ago that I noticed my mistake.