Drawing Solid Links As, Uh, Solid?

Image of Proposed Drawing Idea

I want to be able to draw links in the Linkage program that look about like this (above). But I’m not sure what type of algorithm to design to do it.

My plan is to create a semicircle at each and and a set of lines for the side, for each of the legs of the link. Then I’ll test the semicircle and lines of each one with all of the others to see if the lines or semicircles go behind any others. A little cutting here and there and I should be able to get this to work no matter what configuration is drawn.

Or not. I’ll have to wait and see. But it will certainly look cool if I can do it.