surface scanners

[Kragen Sitaker]

Adam has brought a toy into the office.  It consists of a hexagonal
array of blunt nails threaded through matching arrays of holes in two
parallel sheets of hard plastic, which are separated by a fraction of
the nails' length by spacers at their corners.  The plastic sheets
serve to hold the nails parallel to one another while allowing them to
slide lengthwise.  When the toy is held horizontally with the
nail-heads on top, all the nails dangle through the holes, held up only
by their heads resting on the upper sheet of plastic.  One can raise a
solid object up beneath the toy until it contacts the blunt tips of
some of the nails, sliding them upwards, as now their tips rest on the
object rather than dangling in space.  The extent to which each nail is
displaced is determined by the relief of the object on which it rests;
thus, the nail heads above the plastic sheets duplicate the relief of
the object below.

A clear plastic shield stands above the sheets to prevent the nails
from falling out when the toy is inverted.

If a cheap means were provided of sensing the approximate displacement
of each nail, such a device could be a useful tool for digitizing
three-dimensional shapes.  Some possibilities, none of which,
unfortunately, seem particularly cheap:

- fashion the nails of plastic, with a resistive strip running down two
  sides of each nail, connected to form a complete circuit at the top.
  Grid wires connected to brushes contacting these strips would apply a
  voltage and measure the current, and thus the resistance --- lowest
  when the nail was lowest, increasing to higher levels as the nail was
  raised.
- time-domain reflectometry: apply a voltage pulse to a metal nail
  where it passes through the grid, and measure the time until the
  reflections return from the ends of the nail.  Unfortunately, the
  results will be badly contaminated by changes in the nails'
  capacitance caused by their neighbors' motion.
- the audio equivalent would be more accurate, but far more expensive.
- make the nails of transparent plastic graduated in cloudiness from
  quite clear at one end to quite opaque at the other.  Apply light via
  fiber optics; observe the amount transmitted or scattered by each
  nail.
- run wires one way on the transparent plastic shield and another on
  the plastic sheets through which the nails run; applying an electric
  charge on one wire of the sheet will induce charge polarization in
  the nails it is nearest, which polarization will give the nails an
  electric field which decreases as distance from the nails increases.
  Measuring this charge at the shield in various positions should give
  an estimate of the distances of various nails along the first wire
  from the shield.
- various physical properties of the nails could be graded in the same
  way I suggested for opacity; magnetic permeability, electret charge,
  resistivity, optical reflectivity, and diameter come to mind.

-- 
<kragen@pobox.com>       Kragen Sitaker     <http://www.pobox.com/~kragen/>
Perilous to all of us are the devices of an art deeper than we ourselves
possess.
                -- Gandalf the Grey [J.R.R. Tolkien, "Lord of the Rings"]