How do I wrap line segments around circle?

Thank you so much for the replies! I've spent hours trying to figure out how to do this but I'm just stumped. These techniques are just way over my head. If anyone is interested in helping me out I'd be happy to pay for some time. 

defaultg,

Depending on the actual properties of your HVAC panel, any of the approaches suggested by Bobby can be the most efficient one.

If the properties of your HVAC resemble those shown in the photo, I would suggest an elaboration on the first one, basically simply drawing the HVAC panel in steps, taking advantage of the symmetry round the shortest white top line (and the centre of the empty bottom part), and at the same time incorporating the complications, including the overlapping of the opposite line growths outwards from the centre, the fact that the identical line growth for red and blue is quite different to the dual one for white, and the separation of the thicker end lines that would otherwise form parts of the last (red/blue) lines.

The following images show possible steps in creating such a HVAC panel, which can be made (with reduced opacity) on top of a locked template or sketch, in any case starting out with a (circular) filled background (and a nostroke/nofill counterpart) and the outer boundary of the HVAC as a stroked circle, ever working with stroked paths until you have established the right widths and angles before switching to filled paths, mirroring the dividing paths while drawing them, creating the end lines and the general lines separately, and finally recolouring; if your HVAC panel has no thicker end lines, steps 6) - 9) and 13) can be skipped.

Click/RightClick to get closer, Click again to get closer still

There's a few possible ways to create that effect.

You could create thin rectangles to cut through the circle shape using Pathfinder operations, Center align rectangles across the circle, rotate them to desired positions then cut through the circle shape. It's a slower, manual process but easy to control the results.

Another approach: create a blend using small rectangular dashes and apply it to a circular path. Create the initial blend (and specify the steps needed in the blend). Then select the resulting blend and the target path. Then go to Object>Blend>Replace Spline. This approach is fast if you need even spacing for the blended objects.

An Art Brush applied to a target path is another possibility. I would create an open circle as the target path. Then I would make note of its path length in the Document Info tab (click on the Objects option in the flyout menu). I would create a new flat rectangle shape in the same length as the target path and make all the line cuts through it. That finished compound shape would be dragged into the Brushes pallette and turned into an Art Brush. Select the target path and apply the desired Art Brush to it.