To: amul49{at}eth.net, atm{at}shore.net
From: mdholm{at}telerama.com
Reply-To: mdholm{at}telerama.com


In a sense, all mirror cells are 3-point cells.  3 points are both the
minimum and maximum for precise support.  Any more and it becomes
impossible for all of them to be in contact at once without something
flexing.  Any less, and the mirror is not stable.  We wish to minimize and
control mirror flexure, so more than three points, which leads to
uncontrolled flexure, is out.

So how do we make 4, 5, 6, 9, etc. point cells?  We do it by turning them
all into 3 point cells.

Let's examine a 6 point cell of the most common type.  There are 6 support
points arranged in a ring under the mirror.  But as we said, 6 is too many.
They have to be reduced to three.  So, we use three bars.  Each bar
supports two of the 6 mirror support points.  NOw each bar is conected in
its middle to the back structure of the cell.  The connections allow the
bars to pivot a little, like the playground device we call a teeter-totter
or see-saw.  There are three bars, thus three pivots, thus we have the
magical three points required by geometry, but the mirror is supported by
six points.  The important thing is that the bars are free to pivot.  The
pivoting motion only needs to be small, enough to allow the two support
points on each bar to adjust to the back of the mirror.  Because the bars
can pivot, they adjust automatically when the mirror is placed on top of
them, evenly distributing the load.

The cell is built in layers.  The bottom layer connects to the rest of the
telescope, holds the bar pivots, and has some mechanism for alignment
adjustment.  The middle layer is the bars with the mirror support points. 
The top layer is the mirror.  (Although I write mirror support points, it
is common to actually make the "points" out of small circular
resiliant pads.)

If we use triangles instead of bars, with each triangle having a mirror
support near each of its corners and a pivot in the middle of each
triangle, then we have a 9 point cell instead of a six point.

For more than 9 points, another layer has to be added into the design.  The
most points that can be had with two layers between the cell back and the
mirror is 3 x 9 = 27.  For really large mirrors, another layer can be added
to go to a maximum of 3 x 27 = 81.  Various combinations of bars and
triangles lead to a variety of different numbers of mirror support points.



Mark Holm
mdholm{at}telerama.com

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