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So my approach (which may be wrong though) would be to start end the kinematic chain with a matrix for the skew (also called 'shear') which has the form:
 

The inverse looks the same with the shear elements (ie lambda and mu) negative

So I'm adding a Tsudokama RZ-160 rotary as a full 4th axis.   I'm replacing the existing TPC-JR with a standalone drive and wiring everything direct.  I have a good handle on most of this, however I'm left with the choice in the title.  The encoder is an absolute encoder wired directly to the drive.  The drive then either passes along the serial absolute position OR has outputs for a simulated incremental encoder.  I know how to wire the incremental, it's the same as my other 3 axes, and can get wired directly into "Axis 3" on the 7i77 board.  However, the RZ-160 of course does not have homing switches (that I'm aware of), so repeating the same location with the incremental encoder output through a power cycle may prove challenging.  At the very least, I'd have to break out an indicator and indicate in the 4th if I understand correctly.  With the Absolute encoder, in theory, I'll always know where the rotary table is at.  I don't know that that is accurate, and it may only remember location within 1 rotation of the motor, which is 1/60th a rotation of the table.  Is that accurate?  Can the PSO /PSO output be wired into the 7i77 SSerial port easily?  Is it worth it?How would you set up your 4th axis given this choice?  My drive is a Sigma II Yaskawa drive (SGDM-04ADA, same as what is in the TPC-JR), the servo is a Sigma II (SGMPH-04A1A-TF11).

Thank you

For an easier start on how to use jupyter notebook and ipython to derive the kinematic linked above you can directly load the notebook used to create it and the documentation to study/modify:
github.com/Sigma1912/LinuxCNC_Demo_Confi...0Kinematics%20.ipynb
This contains all the python code blocks that handle the math.

I want to make a machine with two 7i92 (configuration 7i92_5ABOB_Enc), at first I decided that one would stand on the machine and collect signals from the rulers and sensors, the second in the control cabinet and output step/dir, i.e. it turns out that feedback from the ruler goes through the computer, but then I came across information that mesa is not just an input/ conclusion, it almost recycles g-codes, i.e. hypothetically, the encoder feedback control loop can be closed inside mesa, and it is not advisable to break it, is this the case, or does the circuit in any case go through the core, and in mesa only the encoder counter and the step generator?

timo wrote:

Just a side question: Why do you need a separate Controller for the manual operation?

Isn*t everything possible to do in the LInux CNC. Slaving axis, Using MPG to move the axis manually?

 I think all of the functionality is available in LinuxCNC, however I developed a little touchscreen GUI for the existing ELS and I really like the ease of use when using the lathe in manual mode.

The path for python is missing in the ini

linuxcnc.org/docs/stable/html/remap/rema...emap:embedded-python

Yeah, was a bit sick at the start of the year and had 6 months off work, not much happened at this time, just me thinking about this new build.

Very busy otherwise, I work full time, and I cut steel signs, and I run a small mowing business, and I work for my brother in his fabrication workshop, AND I'm still building my own house.

New build is coming along nicely.
Machine is built, most mechanical fitout complete, and started on the wiring tonight.
Pics to follow