Kinematics for XYZAB mill

Thanks to dngarret this sim config has just been pushed to 2.9 as 'xyzab-tdr'

Awesome work team! Aceira, thanks for your hard work with the kinematics.
And thanks to Dewey for getting this amazing enhancement into the next production release of Linuxcnc. I'm always in awe of Dewey's work.
 

Hi Aceria,
These seems to be some problem with the kinematics when using the x-ioffset and z-offset and I am not able to pinpoint it and propose a solution.
I am the original author of switchkins and the idea behind switchable kinematics was that you could switch between machine kinematics without any physical motion of the machine.

Doing the following sequence of actions results in machine motion during kinematics switching
1. Start the xyzab-tdr config
2. x-offset = -20, z-offset= -10, rotation center point = (-50,-50,100)
3. home the machine and switch to MDI mode - still with identity kinematics
4. T2M6G43H2 - this will add a tool with length of 30mm to the Z axis
5. G0x20y20z20
6. G0a90
7. Switch the kniematics to XYZAB kins using the pyvcp button OR M428 and then switch back to identity and watch the machine go for a ride in the vismach window. This can also be observed in the machine coordinates

Now if the x-offset and z-offset are kept to 0, this movement does not happen.

In the forward kinematics, dz seems to be taken into account but dx does not seem to be.

While in the inverse kinematics, dx and dz both are taken into account.

Can you help me take dx and dz correctly into account in the formulas?
Regards,
automata

Automata, thanks for reporting this!
I totally agree, looks like I got a bit overzealous when i cleaned up the math in the comp and just ran the demo code to test. I just quickly tested with an earlier version and it works fine there. I'm just headed out the door for a repair job but will be back later with the patch.

[edit2]
On closer inspection it seems that I only got a sign in the forward kinematic wrong when I manually cleaned up the math. The fix has just been committed to the source.
Thanks again for the report.

 

 @automata
As a side note:
Since you came up with the idea of switchable kinematics I was wondering if you had any experience with 5axis machining in general. I have created another sim config with a rotary/nutating head and I'm working on a G68.2 'tilted-work-plane' remap but I'm lacking the 5axis machining background. 
See here: forum.linuxcnc.org/20-g-code/47984-tilted-working-plane#263422

Hi Aciera,
Thanks for the prompt feedback and correction. 
Can you help how you derived the math? Maybe something along the lines of this excercise  linuxcnc.org/docs/html/motion/5-axis-kinematics.html
I am trying to make a general purpose template to derive any 5 axis kinematics.
I have explained homogenous transformations in this presentation ( drive.google.com/file/d/13wTPaD_pGiWHewh...dYj/view?usp=sharing ) and want to add to it how to work on 5 axis kinematics from that perspective.
1. Considered rotation point center in XYZ i.e., x-rot-center, y-rot-center, z-rot-center. Here we have also implicitly considered that A-rot-center =0 degrees and B-rot-center = 0 degrees
2. Now the G54 offsets are set such that the work coordinate system zero coincides the kinematics calculations zero point. 
3. For forward kinematics what are the reference frames and transformations that are considered? 
4. How would we derive the inverse kinematics?
Regards,
automata