Helical automated fabrication

[Dave Long]

>                                         You'd actually only have to
> control two of the thirds, if the speed of the third was known; so you
> get 6DOF for the price of 2.

2DOF is right for a space curve, as worked out by Frenet and Serret.

  0  k  0
-k  0  t
  0 -t  0, where k and t are curvature and torsion, is the change in the 
parametric coordinate system as it follows a curve.

Kappa and tau can be used as proxies for energy, so for example your 
lissajous laser scan* is nice because it has much lower peak curvatures 
than a traditional raster scan geometry.

-Dave

:: :: ::

* I know some people who have built an automotive road scanner that 
used a natural frequency of the mount to drive the scan, meaning that 
scanning comes for free when the vehicle is in motion.  Mechanically 
arranging two orthogonal modes should yield a 2D lissajous with very 
little extra work.