Parametric Mitchell Truss Geometry

I have a geometry question - I want to build this model based on the angle (gamma) value, the number of arc legs(symmetric), and the vertical distance between supports. I will then turn lines in to a structural model for optimization. See below:

The Mitchell truss above can be drawn in Autocad very quickly using:

1.) Inscribed circles

2.) Perpendicular lines drawn perpendicular to other lines which intersect the base radial array defined by alpha=90-beta

3.) Perpendicular lines drawn perpendicular to other lines which intersect inscribed circles.

This snippet from autocad shows the process:

My grasshopper file is attached. It is sloppy, and uses hoopsnake, which is probably unacceptable if I can avoid it.

Does anyone have any suggestions on how to tackle this problem? Is there some way to use a circular mesh to generate this? I imagine there is a very easy solution but I am not skilled enough with grasshopper to figure it out. HELP PLEASE!