5 axis spindle XYZB table A

I have a cartesian XYZ machine which spindle can rotate over Y axis ( and has a table what rotates over a translated X (Ly Lz) axis (A).

My problem is I don´t understand so well how to express the relation between the origin of the workpiece space (that I supposed is the G54 touch) off and the X rotation axis.

Could you guide me to a start point in order to make the kinematics of this machine?

Unfortunately, unless you use a specific kinematics file, LinuxCNC simply doesn't know where the rotary axis is in XYZ space.

There is some (rather detailed) info here: linuxcnc.org/docs/devel/html/motion/5-axis-kinematics.html but I don't think it helps you very much.

Do you actually want TRT [strike](which is not often used with a 4-axis machine).[/strike]

I see you have a 5 axis

This sounds a lot like this machine:
Which uses "maxkins"
linuxcnc.org/docs/html/man/man9/kins.9.html

This is a schema of the machine

Unusual...

If you have a 3D model you can easily make a Vismach model to test out kinematics:
linuxcnc.org/docs/2.7/html/gui/vismach.html