Hi Charles and Others,  I have a small shop and love to build new things, 
some work, some don't, but I always learn in doing.
I can not picture your idea, could you send me a sketch?   I have made a 
couple of the Folded Pendulums sensors and found the concept very promising.
If I can I would like to try your idea in the shop.

Ted


----- Original Message ----- 
From: "Charles Patton" 
To: 
Sent: Sunday, February 17, 2008 10:08 PM
Subject: Re: pivots vs bearing structures


> Randall,
> I understand the folded pendulums you mention, but I want to touch on 
> several related subjects.  Back of the napkin pendulum length for 10 secs 
> is about 1000 inches.  A one inch swing would be a ½ milli-inch rise. 
> This gives me a bit of feel/insight on possible error mechanisms. It 
> strikes me that one general problem with flexures is that they are not a 
> pivot in the sense of having a known axis like a bearing does.  I haven’t 
> totally worked out the ramifications, but I’m sure this is the reason many 
> amateurs have problems taking Lehman style instruments to long periods. 
> Even if they’re not using flexures, pivot points are a round point that 
> also may or may not have a constant point of rotation, depending whether 
> it is rotating in a pocket or rolling on the surface of its pivot support, 
> so the length may well be getting shorter as it rotates and a shorter 
> length on the beam equates to the weight dropping, not rising as is 
> necessary for stability and so the distance to un-stability is around ½ a 
> milli-inch.
>
> So the way I perceive it, a big problem is having a system where the axis 
> of rotation remains constant, quite accurately.  Unfortunately the only 
> solutions I keep coming back to are bearing style things.  So then the 
> question becomes, “Can a bearing be made that has low loss?”  But a 
> concurrent question is do I really need a very low amount of loss?  I know 
> recent discussions have experimented with crossed pivots of extremely low 
> loss.  Why?  The immediate next step will be to add a damper to get to 
> something close to critical damping.   My understanding is that the only 
> reason to have low loss is to be able to use lots of feedback to lengthen 
> the period.  But if the period can be achieved directly, and it includes 
> some damping, so what?  In my mind, the important item is 
> hysteresis/stiction.   As bearings and bearing surfaces can easily be 
> ground to a ten-thousandth or even better, 10 or 20 second period 
> structures should be in reach.
>
> Back to possible structures.  The structure I originally presented is 
> probably not possible geometrically.  But one that is obviously possible 
> is as follows.  Imagine a hollow cylinder (like a pipe) that has been 
> centerless ground to be round.  Now take a high density rod like lead or 
> tungsten and center it down the axis of the cylinder with fine adjustment 
> screws so you can offset the center of gravity by a fraction of a 
> thousandth.  (The hollow cylinder construction is to reduce the rotational 
> moment of inertia.)  Now place this cylinder on a surface plate (again a 
> commonly available object that can be obtained flat to fractions of a 
> ten-thousandth.) that is level better than a ten-thousandth per inch.  Use 
> very fine steel (a few thousandths) wire as Rollamite bands.  The cylinder 
> should roll to center the mass down. So lets assume a three inch dia. 
> pipe.  That’s roughly 10 inches circumference, or 2.5 inches to 90 
> degrees, and raising the mass by the amount of the off-center that could 
> be easily set to 1 mill.  Easily greater than 10 seconds rotation period? 
> Once you have that structure in mind, chop off ¾ of the cylinder not in 
> contact with the surface plate.  As long as the center of mass is below 
> the center of rotation this has become an upside down pendulum that is 
> stable on the surface place and the rotational inertia has been reduced to 
> a minimum.  The position sensor is placed to monitor the mass at the ‘top’ 
> of this pendulum.
> Just some more idle musings.
> Regards,
> Charles R. Patton
>
>
> Randall Peters wrote:
>> Charles,
>>     In effect, what you have described, is to take advantage of the same 
>> property that is used by the folded pendulum, which
>> comprises both a `regular' pendulum and also an 'inverted pendulum. 
>> Separated from each other and connected by a rigid
>> horizontal boom, their relative influence ('restoring' from the one, and 
>> 'destoring' from the other) is determined by how close
>> the inertial mass is placed to one or the other.
>>     Because the folded pendulum can be made to have a very long period, 
>> upper valuve being limited by mesoanelastic complexity,
>> it appears clear then, that the feedback drive of the primary pendulum by 
>> an inverted secondary one is capable (for ideal
>> meaterials) of very long period indeed, and therefore very great 
>> sensitivity.  Moreover, since the adverse effects of material
>> problems can be essentially eliminated by means of the feedback, I see 
>> this as a really attractive idea to try and demonstrate!
>> Are there any takers?  (meaning folks like Brett who know how to make 
>> control systems work right).
>>     Randall
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