TCP 5-axis kinematics

I have an offset of Dy in my machine, as shown in the picture. I want to compensate that with the Dy offset, which is usable in xyzac-trt-kins. So, in some way, I want to compensate the mismatch between axis C and Axis A, as they do not intersect each other, but without using inverse kinematics such as trt-kins.

I want to use forward kinematics such as trivkins and compensate my mechanical error. I have an xyzac machine. So, when rotating A, Z and Y would have to compensate the tip of the tool. Just like it is already implemented in trt-kins.

Maybe I have a wrong understanding of work offsets, but to my understanding, work offsets are not able to compensate for not intersecting axis of A and C. I made a sketch, that maybe helps understanding my problem.

In this simple example: For the tool being able to mill each side, it has to compensate its length according to the position of the A axis. Just like trt-kinematics is already doing when staying at XYZAC=0,0,0,0,0. I want to use this feature in simple forward kinematics.

I am not all too familiar with the code behind the kinematic modules, but to my understanding, X would just stay the same and every entry in Y and Z, which takes the rotation of C into account, could be ignored.

Sorry for my bad explanation.

@Aciera: Yes, that is exactly what I want to implement.

    Good morning sorry for the english, but I have to translate it with google Thanks to everyone for the ideas on using LinuxCNC that can be found here. I managed to set up the 5 axis kinematics on my home made cnc, but I can't to solve a problem, using the test file made available by plopes 9000, i can't understand why when xyzc interpolation happens, something is wrong, the two squares are deformed, I attach photos help thanks