There's something about the brushes in Illustrator that never works in sharp corners. I've had the same problem trying to make a perfect dotted line & it works well as long as you use it in right corners, but it deforms the dots in sharp corners. I've tried a couple of things to make a brush as the one you want, but I can't get it to work properly. I posted this problem here as well & ended up using a dashed line with round corners to obtain a dotted line.
Seems to me that the best thing you can do is to just copy the center stroke & make it as thick as the outlines of your drawing & then use the blend tool to fill the space up with additional strokes. If you do the math correctly, you can end up with equally wide strokes as gaps between the strokes.

As Ill Sans suggests, the best way to do this is with the blend tool.
• First, draw the paths and make them as thick as you need
[one tip i found by accident is that regardless what measuring system you use for stroke or text – or whatever – you can force it to mm or inches just by typing it. So if you want a 10mm stroke just type "10mm" into the size field and Illustrator will make it 28.346 pt/10mm. This makes it easier to calculate stroke widths for blends etc.]
• To accurately copy the example you post, you are best to keep the circles complete at this stage and make the stright paths separate so that they can be layered. The complete circles also blend more consistently.
• Next, outline the paths
• Change the stroke and fill colours to give you outlined "donuts" or curves
• Release the resulting compound paths
• Select one of the "donuts" you are left with and Blend (after you have adjusted Blend Options)
• Expand the blend
• Delete the parts of the circles you don't need – in your example, you just delete one quarter of each circle
• To the same with the straight paths (you may need to flip the direction of one path to avoid a "horizon" effect)
• Join up the lines if necessary.

I have probbaly missed something crucial but I made this in about ten minutes using this method.
Sorry if I missed the point.

I was able to get it working with pattern brushes:
here's a tutorial
hope that makes sense...

also, check out the illustrator help under the help menu. There are good instructions for creating a corner tile for pattern brushes.

josh

Not entirely flawless if you look at the inner corner of the loop...
I tried making a pattern brush and an artistic brush, but neither seem to be perfect.

Thanks so much for all your help. I will give it a go tonight and get back to you. Thanks!