Tom,

Sean-Thomas Morrissey, has a lot more experience with force-balance devices 
and can probably add a lot to what I could say, but I'll be happy to offer 
a few comments.

At 10:47 AM 6/20/2000 -0400, you wrote:
>Question
>
>I am considering building a force balance seismometer. I have some
>questions>
>
>(1) The recommended position sensor is a capacitive bridge, the details are
>on the Uni-Stuttgart geophysics page. Has anyone on the list done this? If
>so what problems, or more importantly, what solutions, ;) , evolved.

I haven't used one, yet, but that's the way I'm leaning.  Sean-Thomas 
prefers the Variable Reluctance Differential Transducer,  VRDT.  Although 
the ultimate performance of the capacitance bridge is probably better, I 
think your chances of getting a VRDT design working well are likely to be 
much greater.  For more info.on the capacitive bridge, try to find 
"Capacitive Sensors" by Larry K. Baxter IEEE press 1997.  He thoroughly 
covers the real-world issues and circuit designs and he gives a good idea 
of what's involved in making capacitive sensors work up to their potential.

>(2) How important is linearity of the spring? My daughter asked me why we
>didn't float a beam using opposing magnets. That is a F = k(r^3) force to
>distance relationship and the perfect seismometer spring would have F =
>k(r). For vanishingly small displacements do the problems go away?

Linearity isn't likely to be a fundamental problem in a force-balance 
device, since, as you mentioned, the displacements will be relatively 
small.  By far the larger problem is variation in the restoring force with 
temperature and time.  Most permanent magnets are not very temperature 
stable.  Even a steel spring isn't all that great, and you would need to 
keep the rates of temperature change well below the longest period you 
wanted to observe in order to avoid seeing large amounts of 
temperature-change noise.

>(3) I seem to remember someone has a source of material for zero  force
>hinges.  Is it still available and who has it?

Try McMaster-Carr at http://www.mcmaster.com/ Then search on "shim 
stock"  I'm not sure, but I don't think they have any order minimum.  The 
thickness and material would depend on how much force the hinge would have 
to resist.  In general, the thinner, the better.

I had been playing with trying to see just how far you can go in making a 
hinge with minimal (zero) restoring force 
at:  http://members.home.net/nordgren/ on the downloads page.  In that 
design, the one area I'm still not completely comfortable with is just how 
good it would be at resisting sideways rotation of the beam.  As a 
practical matter, any well-designed crossed-flexure hinge would probably 
work just fine.

Regards,
Brett

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