feedback and automated fabrication
kragen at pobox.com
kragen at pobox.com
Thu Oct 27 03:37:01 EDT 2005
You could build a pretty simple hexapod with just six cables to move a
hanging flutterwumper in six degrees of freedom, and you could probably
control the lengths of the cables with great precision; but by itself
that doesn't give you much accuracy in the finished product.
Closed-loop control, though, could give you the accuracy you need. If
you can measure the position of the flutterwumper to great precision,
you can correct the position until it works; similarly, to correct for
cutting-head loading errors, cutting-head wear, etc., if you can
measure the depth of cuts in the material, you can correct for
whatever inaccuracies arise.
Ultrasound seems like a plausible approach at first, but for
manufacturing metal parts, you need shape accuracy (thus measurement
accuracy) on the order of 25 microns. At sea level, that's 75
nanoseconds of timing accuracy on the sound, which means you need a
13.3 MHz sound. Air cannot carry sounds close to that frequency.
Radio seems like a plausible approach at first too, but 25 microns is
85 * 10^-15 seconds --- 85 attoseconds. There are no circuits
contemplated that can measure the round-trip time of radio pulses that
So light interferometry, of one form or another, is the only feedback
mechanism I can think of that might work. Laser phase shifts can
measure the distance of movement of an object; a circularly polarized
laser can tell which direction, too. Using this principle you can
measure the shape of a macroscopic continuous surface. I still don't
quite know how to measure its position to within a few microns, but
maybe I don't need to.
Suppose you wanted to measure nearby vibrations with LEDs and
a multi-megapixel camera. The LEDs and the camera are mounted some
distance apart facing one another; the camera measures the direction to
each LED within a small fraction of a pixel. So perhaps you could use
cheaper cameras for CNC feedback.
"Cheap" (around US$100-$300) consumer CCD cameras, such as the Minolta
DImage G500, commonly have 100-degree fields of view and roughly
2000x2500 square pixels, with 2500 pixels across the 100 degrees
--- so about 1/25 of a degree per pixel, or about 700 microradians.
That means that a pixel subtends 25 microns at a range of about 3.6cm,
and a hundredth of a pixel subtends 25 microns at a range of about 3.6m.
Optical zoom extends this range; 3x optical zoom I believe reduces the
linear field of view by a factor of 3, to about 33 degrees in this case,
so would increase the range to about 10cm at one pixel per 25 microns.
You could mount the camera either on the movable platform, with reference
LEDs on a fixed point (or possibly just referencing from the workpiece,
if the workpiece is not the fixed point), or on a fixed point looking
at LEDs on the movable platform. In either case, two cameras looking
in different directions should give dramatically better results, since
the precision of measured depth will be much worse than the transverse
(Maybe purely mechanical feedback would work too, like monitoring
stepper motor voltage/current waveforms.)
The standard hexapod design makes the six legs out of precision ballscrews
which change length; Hexel has a clever design called the "Rotobot"
where the legs don't change length; instead, the points where they are
attached to a fixed object can be moved independently all the way around
Rather than using ballscrews, it seems that a compression spring (for
example, a piece of bamboo or PVC pipe bent into a semicircle) with a
braided nylon rope would be cheaper and might suffice for many purposes.
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