Knot Geometry - connecting curves tangentially

hello everybody. I'm trying to produce a knot like geometry. I have six circles, (three base circles and these have been each offset)

I am trying to connect parts of these curves to produce one single line (a bit like a mobius strip, only a little more complex)

please can someone advise me how to evaluate these curves to extract the points I'm searching for. The final aim is to be able to move the three base curves to modify and but maintain the geometry.

I have attached the file, i have drawn polylines to demonstrate where the lines should be to give an outline of what i'm trying to achieve.

many thanks you wonderful helpful people !

cheers

jp

ps sorry about the horrendously simple definition, i had high hopes, which were quickly dashed at the first hurdle!!