Reuleaux polygons are nifty round-faceted shapes
which, remarkably, have constant widths just like the
circle.
The Reuleaux triangle is the simplest such shape, and has
the
least area per width; folks may be familiar with it via the
'Wankel' engine and rotary drill bits which make nearly
square
holes (other familiar Reuleaux shapes are those of the
British
20p and 50p coins, which despite their distinctive faceting
can
be used in vending machines which check the width of a
coin
rolling through.).
Anyway, spacecraft folks often harp on payload weight as a
key
factor in mission costs, and look for all kinds of ways to make
their precious cargo lighter. As NASA's Mars Rover website
says, "Mobility engineers were tasked with making the
wheels
lightweight, so as not to add any more weight to an already
hefty spacecraft; compact, so that when the rover is stowed
in
the lander they would fit; and capable, so the twin
geologists
can maneuver off of the lander safely and climb rocks up to
ten inches high."
Might all these factors be better served by Reuleaux
triangle-
shaped wheels than by standard circular ones, especially in rovers with tread-coupled wheels? The
Reuleaux
rollers would maintain the same constant clearance as
circular
wheels of the same width; assuming wheels of uniform
density, the Reuleaux would weigh 2(pi - 3^.5)/pi -- less
than
90% -- as much as the circles; and they would also be that
much more compact, the better to fit in NASA's cramped
overhead bins.
Of course the Reuleaux rollers would require kinda tricky
ellipsoidally floating axles to roll smoothly, which might add
back a little of the saved weight, but they still seem worth
a
look (who says you can't reinvent the wheel?...).