You are right. I had not noticed the different orientation.
The machine is mostly used for jewelery molds cut from wax. It uses a 50000 rpm spindle with 4mm dia tooling. Because there are no cutting forces it just uses open loop NEMA 24 steppers and they reckon a tool could last 12 months!
I'll find out a bit more in terms of the dimensions. I think the A & B would be positive in the direction of the arrows.
They are not happy with their current Windows solutions as they can't get all axes moving smoothly at the one time. They'd like to migrate to Linuxcnc with a Mesa card and have asked for help. Initially I made the same mistake as Tommy, then I realised we don't yet have a Linuxcnc kinematics for XYZAB.
On the other 5 axis thread I linked to, Dewey Garrett said he'd be happy to merge other kinematics models into the core code so it would be good if we could use this opportunity to build an XYZAB-trt module.
But I have no clue about matrix algebra. I figure once the formulas were resolved I could code it in C.
I have not looked at Vismach yet but there is a a good start in the bridgemill sim and I thought I could manage that side of it for a proof of concept.. Long term, I wanted to build a model using STL's of the actual machine.
So in answer to your question, I need help with the maths to start with.