I think I can see that idea, in my head. The only down side to it, is that I live in a small town, and unless I want to build it the size of a tractor, from actual tractor parts... Let's just say that gears, racks, pinions, etc are just not available out here...unless you want them to literally be 10" diameter for the pinion.
I think you're right, though...that would be a very simple arrangement. I see two possible down sides...
1) The racks will "stick out" at a virtually common point, on each of the 3 corners. There is the potential for interference...but that exists with allthread, too. The two corners will have to be *slightly* askew, in order to not interfere. Not sure how that'll affect the geometry, but I'm hoping it'll be negligible.
Worst case scenario would be when they're fully retracted "out" of the machine, at which point they'd be almost horizontal. Move them back in, and you have a "scissor" arrangement, on the exterior of the machine.
2) The angles of the struts will change, across a 60 degree arc...if the motor and pinion are mounted at the corner, and the whole corner "pivots," this might solve the problem. I don't think it's a problem, in reality.
I wonder if I could do something similar, with parts I can get locally? Hmmm...
-- Chuck Knight