This is a process that took me a while to figure out. Here's the step-by-step to make it easy.
Note: This will only work for files made in Inventor Pro, I still have not figured out how to get files from the student version into Illustrator.
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Step 1: Export From Inventor
This step is easy. Once you have a model drawn up in Inventor, just right-click on the face you'd like to export, click "Export As", and choose DWG.
Step 2: Convert to 2004 Format
Now, for this next step you have to use a program called Autodesk Trueview. This is a free program that you can get here from Autodesk's site. Open the .dwg file you just exported in Trueview, and hit DWG Convert, a button in the top left of the window. Select the file you want to convert, and set the conversion settings to 2004. For some reason, Illustrator just can't open .dwg files that aren't in this format. If you're going to use the file in VCarve, this is the last step of conversion.
Step 3: Set Up Illustrator
Once the file has been converted, open up illustrator. Open a new window to the size you want and make sure that the units are set to whatever units you made the original model in. Now drag your file into the program.
Step 4: Drag Into Illustrator
Select "Original Size", and scale it 1:1 in the units you drew it up in. Hit enter, and the outline of the face from your model should now be in Illustrator. I use this for easy laser cutting, and now you can too.