Creating a vector stroke?

[dv986]

Hi everyone, I have a question.

I'm having an object who's copy I'm trying to equidistantly enlarge, so that I can subtract the initial object and be left with only a "stroke".

This may sound confusing, so I have attached the image I'm working on. Basicaly I'm trying to recreate it to a vector design. So, I was thinking of making the black area an object, then find a way to equidistantly enlarge it, and subtract it so that In the end I'm left with what you see there as a yellow stroke.

I never really found out how to do something like that, yet I needed it quite often. Could anyone help?