Re: Polar Coordinates CNC?

The application would be the same as any other - i.e. router/plasma
application (4'x8' as practical size for discussion purposes).

I would think that Linear moves in polar space would be roughly the
same and no more complicated than arc/circular moves in cartesian
space - would they?

I think that a polar machine could be a more cost effective approach
given that you eliminate many of the most expensive components of the
system (the long axis). Parallelism is eliminated as a requirement
which generally requires you to do "special" things to tie the
parallel sides of a large gantry style machine together either via
encoders or long belts if using multiple drives. You lose a certain
amount of rigidity with a gantry machine that either must be made up
by stiffer slides or beefier components on the gantry itself. All of
these result in a large heavy gantry which of course requires a
larger motor(s) to drive. It looks to me like a lot of these issues
can be avoided on a polar based machine as there is a single pivot
point and therefore single drive point. A very large machine would
have to either have an extremely heafty arm or would have to be
supported on the outer end of the boom. So significantly larger
sizes likely are not practical.

I think the biggest problem with a polar machine is one of
accuracy... i.e. the accuracy will "expand" as you go out from the
central pole. That's ok as long as you can get sufficient accuracy
in towards the pole/pivot point. This factor would also likely
dictate the largest practical size. As a test application I was
thinking of a 4x8 application using 2 quadrants. 4' x 1.414 (2*sqrt
(2) ) makes a boom of 6' able to cover the entire area of a 4'x8'
sheet.

Why hasn't this been done before? I don't know - I expect that the
cartesian basis of g-codes themselves have preselected this to a
degree. A Polar router has some similarities to a hexapod in my mind
in that it requires ongoing trig conversion for each axis/movement.
But it's obviously been handled for hexapods which I think are
significantly more complicated than the polar option. So it seems
doable...

Lee Wenger
Denver, CO