Kinematics for XYZAB mill

3. The kinematics module using switchkins assumes the G5x coordinate frame has its origin at the rot_point offset which is given in the original machine MCS coordinate frame. This is done by setting the G54 offset to the rotation center point at the start of the Gcode in the example NGC file made by Aciera in the XYZAB sim config.

The work offset (eg G54) does not influence the rotation center. You can set your work offset anywhere you like. The rotation center is defined by setting the 'rot-point' values that define the offset of the rotation point from machine zero. Without the 'rot-point' offset the center of rotation is the machine reference point. 
I'm not very familiar with the internals of the trajectory planner but I believe, as you say, that it does indeed calculate everything in machine coordinates, so it strips the offsets from the input and adds them back to the result.
 

I suggest that for a clearer picture of how offsets are applied in respect to the kinematics component you add an 'rtapi_print' statement to the kinematic component so you can monitor the values of 'pos->tran.(x,y,z)' which is the coordinate position used in custom kinematics.

As far as I'm concerned sure.
But from what I understand about the build process for documentation an asciidoc format would be preferred to a PDF as that is automatically built in the LinuxCNC build process. While I can export the jupyter notebook in asciidoc format all the math is spit out as 'latexmath' which in turn does not show in the auto built documentation (I think). So looking at other mathematical documentation (like Rudys trt-kinematic docs) the math formulas seem to be cut out of the pdf as images and then pasted into the asciidoc document and that is a lot of work for which I have not had time or motivation. If there is a less time consuming way to add it to the documentation please advise.

This is the raw export as asciidoc:
 

Note how the math from the python output is not included as latexmath at all so that would have to be reentered manually which is real pain.