Help: How to run X and A axis with different feed rates simultaneously?

Hello All, I am at a beginner level in linuxcnc and cnc programming.

I have to build a simple winding machine, as depicted in the attached image. (I wish to perform side by side winding of the mateial without any gaps or overlaps)

the X axis is supposed to control the layup slide back and forth.
the A axis is supposed to rotate at a constant speed in the same direction until multiple layers are wound.

here is a simple working example of the gcode i prepared.
g91
o100 repeat [5]
g1 x80 a3600 f360
g1 a720 f10000
g1 x-80 a3600 f360
g1 a720 f10000
o100 endrepeat
m2

*please note that this is just a representative code, which performs the desired motion for me.*
however, since the feedrate is calucated in a compound manner, giving priority to the x-axis, adjusting the rotational speed so as to have a side-by-side layup of material is difficult.

secondly, since the A axis isnt rotating conitnously, it generates a momentary pause (due to deaccelartion and re-accelartion when a line of code ends)

Q: I am looking to eliminate both of these problems, but i dont know how to make it possible in the gcode.
I wish that A axis would keep rotating indefinietly without any pause at a given certain feed rate. and the X axis to keep moving back and forth independently at a different given feedrate.

i can use a spindle setting instead of A axis, the example gcode for it looks something like this:
s100 m3
o100 repeat [5]
g91 g0 x80 f360
g91 g0 x-80 f360
o100 endrepeat
m2

However, i wish to know if this is possible to with X and A axis, what would the gcode look like.

Any help is much appreciated.

Seems to be very similar to a lathe.
When the a axis gets an encoder and the x axis is "slaved" to this.
Pitch should be adjustable.

Leaves the back and forth movement to be taken care of.

Is it a dedicated winding machine? Or you need to solve it just with G-code for a standard x-y-z a Machine?
Greetings Timo

yes it is a dedicated winding machine. I could go with just X and Z lathe config. However, the problem still remains. the Z axis would then take feed in mm/min right? and not be a rotary axis.
nevertheless, can you help further?

hello, the question is interesting but the fact should be taken into account, the feedrate for the linear axis is understood by the configuration as mm/min, but for the rotary axis it is understood as deg/min. so depending on the transmission on the A axis the example shows that the same feed is for both x and A, mechanically the two speeds should be matched. of course it also depends on the thickness of the wire you are winding, so I would personally try to solve the problem by exporting gcode from a program that supports constant rotary operation, I know it can be done in ``deskproto'' and maybe I would try to define a stepover via the definition processing tools (for example, the endmill 1mm tool replaces a 1mm wire in practice, stepover 1mm as well), I would subsequently edit such a gcode to support cycle repetition. it is essential that the CAM program outputs adequate A and X feedrates to synchronize the movement.

that is, I would try it with a configuration for 4 axes, it can probably be done as a lathe config with ``spindle synchronized motion'', but I have no experience on that topic.