Ted,
The whole thing is an upside down pendulum.  Think about a rocking 
chair.  It has the same properties as this cylinder.  The center of mass 
of the body sitting in the chair is below the center of the circle 
formed by the rockers on the floor.  So the top of the rocker and the 
person rock back-and-forth on the floor.  Now imagine that the floor is 
jerked by some force such as an earthquake.  The mass of the body in the 
chair stays in place but the rockers stay in contact with the floor but 
they assume a “rocked” position.  Now the chair will rock back and forth 
over the new position.  So by analogy, due to inertia this rolling 
pendulum will tend to stay in position while the plate is moved, but due 
to the contact with the plate the cylinder will be rotated. The result 
will be that the weight will want to roll back to restore the weight to 
its lowest point so the cylinder will rock until it dissipates the 
potential energy transferred to it by the plate displacement.  This is 
exactly what happens to a normal pendulum.  The bob stays in place while 
the support pivot moves in synchronization with the floor, so if the bob 
position relative to the floor is measured, it yields the displacement 
due to the seismic event.  In exactly the same way the rolling 
cylinder’s position will be displaced relative to the floor/surface 
plate in proportion to the seismic event.  (It’s interesting to note 
that you can have a free 2X gain simply by monitoring the position of 
the top of the cylinder rather than the axis of it.)  What complicates 
this rolling pendulum is that it will also have significant rotational 
inertia.  So it lowers the resonant frequency a bit from what might be 
expected by the weight unbalance distance plugged into a simple pendulum 
equation based on T=2*Pi*Sqrt(l/g).  (Recognize that this equation only 
works on small angles and assumes all weight is concentrated at the bob 
point.  Furthermore, in some ways it obscures the relation of the swing 
angle vs. the height change of the bob weight by talking about the 
length of the pendulum.  The length is only important in that as it 
increases, it reduces the amount the weight is lifted vs the distance 
the pendulum swings.  The cylinder pendulum brings to the fore that the 
weight is lifting by very small amounts as the pendulum swings.)  You 
don’t even need sine/cosines to do the simple math for this one.  
Imagine a 1000” pendulum.  Now swing it 1”.  What’s the lift?  Since the 
numbers are so big, just take the square root of the sum of the squares 
(the old Pythagorean theorem) and subtract the pendulum length. 
(Sqrt ( 1000^2 + 1^2)) – 1000 = 0.0005”
(The purists out there may hate me as this isn’t set up geometrically 
correct, but it’s simple and quick and close enough that I can’t measure 
the difference without a laser interferometer.)
 
So to tweak the cylinder pendulum into a 10 second period you’ll need to 
be able to tweak the center of mass to something like 0.007 inch off 
center (not likely with my micrometer!)  But the rocking period comes to 
the rescue.  Just keep tweaking until the period is about right.  Go too 
far and the cylinder will want to topple, i.e., rotate 180 degrees and 
come to a rest.
In practical terms it will have some of the same problems all long 
period pendulums do—notably the sensitivity to tilt inherent in long 
period pendulums.  As Randall points out, friction is critical.  An 
important consequence of the weight height changing very little for long 
periods is that the restoring force – that force trying to return the 
pendulum bob or cylinder back to its resting point is being reduced to 
very small numbers.  And that change in resting point is the very item 
being measured for indication of a seismic event.  The one thing that 
this should have over standard pendulums is it’s ability to handle big 
seismic displacements, perhaps plus/minus two inches or so for a three 
inch cylinder.  Potentially another advantage would be better 
temperature stability due to the geometric symmetry not present in a 
Lehman for instance.  The simple test will be to build it, give it a 
gentle shove and see if it can approach a 10 or 20 second period of 
rocking back and forth.  Another point I want to mention is that I’m 
sure the “Rollamite” wires are critical for another reason.  At a 
microscopic level, the surfaces of the plate and cylinder, even if 
mirror polished, will have hills and valleys that will want to “lock” 
the cylinder to a position due to the low restoring force mentioned 
above.  The wires will have only point contacts that I feel will help 
ameliorate the problem, so although Chris mentions thin foils, I lean in 
the direction of thinking fine wire is better.
 
Hope this helps,
Charles Patton

tchannel1@............ wrote:
> Charles,  Yes the .jpg helps...  Please can you now explain how a 
> pendulum is attached, or to which part it is attached?
> Ted
> ----- Original Message ----- From: "Charles R. Patton" 
> 
> To: 
> Sent: Monday, February 18, 2008 10:22 AM
> Subject: Re: pivots vs bearing structures
>
>
>> Hi Ted,
>> See:
>> www.myeclectic.info/RollingPendulum.jpg
>> It's about 350 KB so you can download it at your leisure.
>> The "Rollamite" like wires primarily keep the orientation of the 
>> cylinder under control.  They are also likely to make the cylinder 
>> less likely to hang or stick due to dust and lint ( the relatively 
>> high pressure of the wires will cut through many of the contaminants. 
>> I recommend non-magnetic parts, lead, brass, aluminum so that the 
>> changing magnetic field of the earth is not a factor.  (It might not 
>> be anyway, but I believe in trying to head off some variables from 
>> the start.)
>>
>> Hope this makes the idea a bit clearer.
>> Regards,
>> Charles Patton
>>
>> tchannel1@............ wrote:
>>> 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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