Fabric Between Moving Rods w/ Kangaroo+GH

I'm really new into GH (with only couple days of experience) so please excuse my messy/ overly complicated definition of this rotating flower mechanism I'm trying to model. Not sure if that could be simplified, but that's not the question I have. 

I'm trying to figure out how to put non-stretchy fabric between these rods/arms so that when this "flower" is completely open, the fabric is tight, but when the "flower" closes, the fabric will relax and just hangs. 

I've been looking at Daniel Piker's mesh relaxation, but that only seem to apply if the anchor points are stationary? I also looked into Giulio Piacentino weaverbird, but not quite understanding if that would help as it seem to apply only to subdividing/ getting mesh. 

Could it be something about catenary curves?

Any advice on how to do this with GH , Kangaroo, or whatever else? :D

Thanks!