Kinematic model for a 5axis mill with universal (nutating) head

I'm a bit confused as to the arrangement of your table rotary, if it rotates in the XZ Plane then it would rotate around the Y-axis which would make it a B-rotary and not an A-rotary.
Also looking at your vismach model I see the machine coordinates pointing with the y-axis (green arrow) along the axis of your table rotary.

I presume the issues you describe are observed on the vismach model and not on the real machine.
Does the TCP mode work as expected?
Does the jogging work along the tool-z axis when in TOOL mode?

As a general note:
There are really two different models to set up here, one being the kinematic model as described in the documentation and the other being the vismach model seen on the screen.
As a consequence if you see unexpected behavior the problem may be and error in the kinematic model or it may be in the vismach model or both.

Maybe I was a little unclear in my description. How it's shown in the image is correct. The B rotary table rotates around the Y axis (green arrow). The nutating A,C head has the nutating A joint rotating around the X axis (red arrow). However, because it's nutating, I said the A axis lies on the XZ plane.

Based on your original config, I've implemented both TCP and TOOL kinematics on my real machine and they behave correctly/the same on my real machine and in Vismach. I do understand what you mean about the difference between the kinematics and the Vismach model. I saw this initially with my real machines C axis rotating the opposite of my Vismach model. And it's pretty obvious something is wrong when in TCP mode.

Then based on your updated config (and because it's very similar to my real machine), I went through the Juypter file and redid the kinematics to set up a simulation machine in order to get the TWPs working. The kinematics seem to work correctly. Both TCP and TOOL work as expected in Vismach. And it does correctly jog along the tool-Z axis in TOOL mode. After working through your original config and implementing the kinematics on my real machine, I think I have an ok understanding of Vismach, the kinematics, and their relation to my real machine.

With all that said, my math skills are lacking. And I'm not sure if what I have done is correct when it comes to rearranging the equations I need to get the tilted work planes working. I posted what I have done in my previous post. Any help would be appreciated as I'm sure what I have done is wrong.

 

Ok, good.

Next question:
The tool vectors 'Kz = (Kzx, Kzy, Kzz)' and 'Kx=(Kxx, Kxy, Kxz)' you use in the TWP-angle-calculations you posted are those from the transformation matrix you use in the 'Inverse TOOL kinematics' ?

Yes they are. From the Inverse Tool kinematics I've taken the third column to calculate the spindle rotary joint positions for the tool orientation vector, and then taken the first column for the Tool-X vector. 

can you post your remap.py please?

Remap attached