How To add robot arm model into linuxCNC

You should just need to convert the image to a G code path. Do you have any sort of CAD / CAM software?

The first step would be to trace the bitmap into a curve / spline / path (depending on the software used) as the bitmap image is not a useful starting point for CAM.
Gcode-tools in Inkscape seems like a good starting point, though Fusion360 is another strong contender.

Why do you need to? The DH parameters in the Vismach model are correct.

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What does the G-code say? it looks like a linear move in the Z axis.

Your picture does not make it clear what " it works like this" means. Or what you think is wrong, or what you consider "correctly"

You haven't even said which G-code file you are running.