## PSN-L Email List Message

Subject: Re: Is a Lehman geometry rolling pivot inherently unstable?
From: ChrisAtUpw@.......
Date: Sat, 5 Jul 2008 17:57:14 EDT

```In a message dated 2008/07/05, charles.r.patton@........ writes:

> Discussion:
> Assume:
> 1) That the Lehman is constructed in a typical =E2=80=9Cgarden gate=E2=80=
=9D fashion=20
> with a horizontal main beam with rolling pivot and a suspension wire to=20
> the pivot bearing.
> 2) At the point of the rolling pivot, the wire does not bend. I.e., the=20
> wire/pivot may be considered rigid in that area. This constraint will=20
> hold true if the wire rigidity is greater than the torque required to=20
> roll the pivot. Something I believe is a reasonable constraint/assumption.

Hi Charles,

Can you define the systems that you are considering more clearly,=20

I get a confused word picture in my mind.

There are two types of crossed flexure suspension. In one type two=20
flat strips / straight wires are clamped at right angles - the classic cross=
ed=20
foil suspension. As they flex, the suspension point moves to one side along=20=
an=20
In the other sort, you have figure of 8 foil / wire loops rolling on=20
cylinders and the flexure point moves in a circle around the fixed pivot.
Remember that the fixed clamp / vertical support rod is nearer to the=
=20
mass and the moving clamp / rod on the arm is on the far side of the support=
=20
rod.=20
However, in both systems as the mass moves to one side, the plane=20
containing the centre of mass, the top suspension and the bottom flexure mak=
es an=20
increasing angle to the vertical and hence, it is stable. =20
We need to consider deflections of less then 5 degrees.

I can imagine amateur constructors 'getting into trouble' with=20
inadequately designed levelling systems. I provide spherical ends to the lev=
elling=20
screws, either by fitting a SS dome nut or by gluing a SS bearing into the e=
nd=20
of the bolt (preferable). There is inevitably some side to side 'slop' in sc=
rew=20
threads. I provide a wavy spring washer and a locknut on the top side of the=
=20
frame to keep the levelling screws in fairly high tension at all times. The=20
levelling screw and the fixed thread should both be made of the same metal t=
o=20
mimise expansion effects. You definitely do need a smooth hard flat surface=20=
on=20
the ground for the spherical ends to rest on. I use 2" - 3" square x 1/8" th=
ick=20
SS plates.
=20
Regards,

Chris Chapman
=20
In a me=
ssage dated 2008/07/05, charles.r.patton@........ writes:

Discussion:
Assume:
1) That the Lehman is constructed in a typical =E2=80=9Cgarden gate=E2=80=
=9D fashion
with a horizontal main beam with rolling pivot and a suspension wire to
the pivot bearing.
2) At the point of the rolling pivot, the wire does not bend. I.e., the
wire/pivot may be considered rigid in that area. This constraint will
hold true if the wire rigidity is greater than the torque required to
roll the pivot. Something I believe is a reasonable constraint/assumption.

Hi Charles,

Can you define the systems that you are=

I get a confused word picture in my min=
d.

There are two types of crossed flexure=20=
suspension. In one type two flat strips / straight wires are clamped at righ=
t angles - the classic crossed foil suspension. As they flex, the suspension=
point moves to one side along an ellipse about the fixed member.
In the other sort, you have figure of 8=
foil / wire loops rolling on cylinders and the flexure point moves in a cir=
cle around the fixed pivot.
Remember that the fixed clamp / vertica=
l support rod is nearer to the mass and the moving clamp / rod on the arm is=
on the far side of the support rod.
However, in both systems as the mass mo=
ves to one side, the plane containing the centre of mass, the top suspension=
and the bottom flexure makes an increasing angle to the vertical and hence,=
it is stable.
We need to consider deflections of less=
then 5 degrees.

I can imagine amateur constructors 'get=
ting into trouble' with inadequately designed levelling systems. I provide s=
pherical ends to the levelling screws, either by fitting a SS dome nut or by=
gluing a SS bearing into the end of the bolt (preferable). There is inevita=
bly some side to side 'slop' in screw threads. I provide a wavy spring washe=
r and a locknut on the top side of the frame to keep the levelling screws in=
fairly high tension at all times. The levelling screw and the fixed thread=20=
should both be made of the same metal to mimise expansion effects. You defin=
itely do need a smooth hard flat surface on the ground for the spherical end=
s to rest on. I use 2" - 3" square x 1/8" thick SS plates.

Regards,

Chris Chapman

```