Illustrator is a 2D drawing program. What others have tried to explain is that for many kinds of "3D" sign fabrication, you could use a program like illustrator to make your fabrication working drawings, just as was and is commonly done via 2D drafting since long before anyone ever saw a desktop computer. They're speaking in the same sense that 2D drafting works just fine as instructions for a crew to build a 3D house.
But generating instructions for driving a three-axis numerically controlled machine is another thing entirely.
If the router head actually moves in three dimensions (X, Y, and Z) as it cuts, Illustrator is the wrong kind of program for that. You need to be using a 3D CAD / CAM program in which you define an actual 3D model that can then be described in the form of driving instructions for an NC device that actually moves in three axes.
Now, if your NC router is really just a 2D router table with a depth adjustment, then you could use a 2D drawing program to draw 2D paths for a stack of incremental heights. This is similar in concept to the elevation contours you see on 2D land plots. But contour lines like that are not going to be generated by merely using graduated fills like you've done in your crab cartoon. And for drawing such contour paths, you would be far better off using a 2D drawing program that provides a decent "contour" feature (Corel Draw, for one example), as opposed to mere offset path and path blend features.
Even if what you're calling "3D" is really just making a stack of 2D cuts at different depths, understand: Illustrator and programs like it would just be for drawing the paths. Such programs are not going to actually drive the the cutting machine. For that, you will need a separate program (which may or may not be available in the form of a plug-in for your drawing program) that translates the paths you draw into plotter language instructions and then sends those instructions to the cutter.
All this is why you need to better describe what kind of device you are actually working with, and what kind of fabrication you are doing. "3D" is a very broad term. I could use a 2D computer-driven router to make a bunch of plywood cutouts that could then be assembled into a stack so as to make a "3D" embossed sign. That is entirely different from creating a file that can be used to drive a 3D computer-driven router, in which its instruction flow instructs the router to smoothly change its depth as it cuts.
This is the wrong site for seeking instructions for that. You need to be reading the documentation of the router and perhaps talking to its manufacturer about the file formats that drive it and recommendations for specific programs that you can license and learn in order to do your modeling and generate the compatible driver file formats.
JET
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