How about this idea for getting the equivalent of four motors on a horizontal 
two joint articulated arm using three motors...

Put two motors at opposite corners with the third on a line bisecting the line 
between the other two. Directly opposite the third motor, use a weight or 
spring.

That would have four cables connected to the end of the arm and give the same 
control authority over the full envelope (which is non-square) reachable by the 
end of the arm.

With three motors at 120 degrees to each other it's impossible to move the end 
of the arm outside of the triangle framed by the motors. With three motors and 
a weight at 90 degrees it's possible to move the end of the arm anywhere within 
the square that the arm can reach.

Since it's a torch instead of a cutting tool in direct contact with the 
workpiece, there's no forces that could kick back and pull the weight.


Then there's the issue of the non-quadrilateral shape of the maximum operating 
envelope. How does LinuxCNC handle that?

Aaaannnnd I just had another thought. Two motors and two weights... but that 
wouldn't work too well when needing the arm end to move out towards one of the 
weight's corners as the weights are passive and wouldn't move differentially. 
Pretty much the same issues as a two motor and one weight system. With a 
vertical string plotter a quadrilateral envelope can be covered with only two 
motors, but cable slack on the long side is a problem in the lower corners and 
close to the motors, with a corresponding lack of control authority. Thought 
discarded as interesting but unworkable for horizontal use. ;-)

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