ChrisAtUpw@....... wrote:
> In a message dated 2008/10/22, charles.r.patton@........ writes:
> 
>> Randy Pratt asked:
>> > I see references to twist in the revision history so is
>> > this twist resulting from upper and lower pivot travel in opposite
>> > direction?  If so would not the support structure height play a role
>> as well
>> > as angle of the support wire to the boom?
> 
> 
> Hi Randy,
> 
>        It does. The axis tilts as the spheres roll sideways, or the 
> plane rolls on the sphere. If the mass is lower than the centre of the 
> rolling axis, this adds to the stability. If it is above this, it can 
> detract from the stability.

CRP - I argue that if the angle of the flat plates of the pivots are 
parallel to the real axis of swing (based on the center of locus points 
being found in our XLS pgms, then there is essentially no twist because 
then the pivot is "rotating" about the center of the locus with 
essentially no circular arc curvature error therefore there is no 
effective change of length of the suspension or boom and therefore the 
bob is describing a circular arc whose plane is set by the tilt of the 
vertical support and thereby the period of the pendulum.


> 
>> That revision was early in the discussion with Brett and Chris.  I had
>> taken a simplistic approach to the path based on the contact point.
>> Latter I agreed with Brett on the approach to finding the locus center
>> as is embodied in the current XLS calculations.  That If a locus center
>> point exists that makes the locus a circular arc, then the twist doesn’t
>> exist.  But even if twist exists, you choose your bob center-of-gravity
>> roughly half way in the Z axis between the upper and lower pivot points,
>> and its effect  should drop out of the considerations.  Either way, I
>> stopped considering it.
>>
>> > Why was the locus chosen as a point behind the plate rather than the
>> contact
>> > point? Reason - In a Lehman, translation of a rolling pivot will
>> result in unsymetric forces on the boom.  
> 
> 
>     Sorry but I don't understand what you are trying to say?
CRP-I didn't understand this question either.l
> 
>        The compression in the boom and the
>> tension
>> > in the support wire will move out of the vertical plane.  A horizontal
>> > friction force must be present to prevent slippage of the ball and this
>> > force is also a moment around the mass.  These forces would have to be
>> > analysed from the contact point. Larger angles and larger balls would
>> > increase this effect.
>> Please see my answer to Bob McClure on 10/16, posted to the PSN list.
>> The “center point” is chosen to give the “ best fit” to the calculated
>> locus.  It is not chosen for any other purpose than to answer
>> mathematically whether there is a close fit circular arc to the locus
>> that has been calculated.  If there is, then it can be said that the bob
>> with regards to the vertical beam travels a circular arc therefore a
>> pendulum fit can be realized.  You may be right about secondary effects
>> of the offset mass.
>> >
>> > An upper pivot does not travel a semicircle around the circumference in
>> > relation to a near horizontal swing. The semicircle is tilted by the 
>> support
>> > wire angle in relation to the near vertical swing axis.  Do you agree?
> 
> 
>        Yes, but it is the swing axis itself which rotates.
> 
>> No, because a ball always has circular cross section and tilt only
>> matters to the extent that it changes the length of CP.  
> 
> 
>     I don't agree.
> 
> So the
>> hypothetical center of the arc may not be where the physical contact
>> point is, but as you adjust the period of the swing, you will actually
>> be adjusting these centers in space to be almost in a vertical line,
>> with the upper just a bit forward to give the bob a pendulum arc that is
>> lowest in the center of the swing.
>> This was the whole point of doing all this analysis – trying to
>> understand just what the weight/bob was experiencing and what
>> arrangements of pivots had the best circular fit.  Additionally what
>> shows up is the ball on plate inferior to plate on ball with regard to
>> the side slipping you touch on.
>>
>> > Construction could change this I guess with rigid upper boom structure.
> 
> 
> 
>> But even if twist exists, you choose your bob center-of-gravity 
>> roughly half
>> way in the Z axis between the upper and lower pivot points, and its 
>> effect should drop out of the considerations.
> 
> 
>        It doesn't, since the swing axis is rotating about it's centre in 
> the near vertical plane. The gradient is still non linear.
CRP- as I argued above, the pivots are indeed swinging about a point 
This is a critical statement.  You will recall I initially argued in 
agreement with Randy – that the rotation of ball on plate or plate on 
ball caused the boom/suspension to move in opposite directions, leading 
to twist in addition to errors in length causing the bob to be raised or 
lowered in addition to the swing arc.  You (Chris and Brett) convinced 
me of the error of my ways, by introducing the concept of fitting a 
center to the locus and observing that one is available for all the 
pivots we’ve studied so far.  My contribution was gathering together 
exact locus calculations and encoding the error calculation of the 
center of locus fit.  So if the center of the locus is essentially a 
point at the low swing angles we’re dealing with (and typically it is 
within a few ppm, then twist is not possible.  (The LIGO suspension is a 
different case and does have twist, but it is also a different geometry.)
> 
>> --This point seems to be a large deviation from the traditional horizontal
>> boom with double support wires and or underslung mass to prevent 
>> rocking on
>> the axis. It may be the improvement point we need to consider and 
>> construct.
> 
> 
>        You still need to prevent the boom from rotating about it's long 
> axis. A V wire upper support is most desirable. The problem is that the 
> damping force is not usually precisely on the line joining the centre of 
> mass to the lower point of rotation. This is a common cause of unwanted 
> resonances, since such motions may be inadequately damped.
CRP-I agree.

> 
>        Regards,
> 
>        Chris Chapman
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