## PSN-L Email List Message

Subject: Re: Other thoughts on an inverted pendulum
From: ChrisAtUpw@.......
Date: Mon, 27 Jan 2003 01:06:56 EST

```At 07:40 AM 1/26/2003, you wrote:
> John, some other thoughts......I am attaching a drawing......I hope you
> receive it. I will describe it to you anyway.......
>  I am thinking of possibly extending the brass rod down into the spring
> while it still protrudes from the top. I would also attach a very small
> level at the bottom of the brass rod to insure leveling and possibly
> increase damping. Instead of placing four wooden dowels (as shown in the
> drawing) around the spring to possibly prevent the magnet/weight from
> getting to the point where it falls/hangs over the spring I would replace
> them with a transparent (to view the level) glass/plastic circular column
> that reached the elevation of the magnet. Please remember one thing....I
> don't know what I'm talking about.....Ed.

In a message dated 26/01/03, johnjan@........ writes:
> Hi Ed,
>
> The way to think about the inverted pendulum is that we are balancing two
> forces.
> Gravity wants to tip the pendulum over, and the greater the angle the
> greater this
> force is.  The spring at the base wants to keep the pendulum upright, and
> the
> greater the angle the greater the force of the spring is in this direction.
>
> If I have the math correct, then the problem I had with instability may have
> been due to my setup.  My inverted pendulum was made from mounting a
> thin metal rod vertically and putting a mass at the top.  The entire rod
> bent.
> When I tried to achieve a long period, the rod would bend to one side and
> stay there!
>
> The CSM student design has a solid rod with a spring at the base.
> http://jjlahr.com/science/psn/epics/reports/sens/index.html
> I think for that design.....
>
> Damping is another thing that will need to be worked out......
>
> My suggestion would be to first work on getting as long a period as
> possible and then work on the damping.
> Cheers,
> John
>
Hi John, Ed,

I have some serious reservations about the above design. Firstly, with
a brass rod and a magnet weight supported by a coil spring, there is nothing
to prevent the spring / rod system 'twanging' or oscillating, laterally or
vertically. There is no damping at all for such motion. As a general rule in
seismometer construction, if parasitic oscillations can occur and are not
damped, they will give problems.
Secondly, since an equal voltage will be induced in the single coil
for equal motion in any lateral direction, the output signal for a quake will
be 'frequency doubled'. The output sensitivity will also be very low, since
although the field through the coil is high, the total field over the coil is
almost constant for small motions. I suspect that the largest signal would be
due to vertical motions of the well sprung magnet!
This can be corrected if you use four small coils in place of the
single one, with the same vertical axis, but connected in opposing pairs. The
motion will be resolved into two signals. An increase in the flux through one
coil of a pair will be added to a decrease in flux through the other coil.
Since the coil centres are now offset to maybe about half the maximum field,
the change in flux with any lateral movement will be high. Vertical motion
will give opposing voltages in a coil pair which ~cancel out.
I would suggest that you try using a light ~1/8" Al rod (knitting
needle?) with the magnet bob on one end and a single spring wire glued /
swaged into an axial hole bored in the other end. If you have a two bar clamp
on the baseplate, you can vary the length of spring wire used. This should be
fairly rigid for vertical movements. The rod can be threaded through a disk
of 1/4" Al plate with a 1/4" hole in the centre, to provide damping. This
seems to give adequate damping with >1/8" separation. You centre the rod in
the hole and move the plate vertically closer to the magnet to increase the
damping. This hole would also control the maximum allowed lateral movement.
The overall stability could be finely adjusted by mounting a second
axial magnet above the bob magnet and positioning it vertically. This could
either increase or decrease the centralising force, depending on whether the
two magnets attract or repel. You will need to adjust the final damping after
setting the period.
However, I would expect the period to be limited by variations in the
spring constant and the magnetic fields with temperature. If you used a
stiffer spring and repelling fields, you might be able to partially
compensate the decrease in stiffness of the spring with the decrease in the
magnetic fields. Precision levelling / balancing the device will be critical.
You won't need a spirit level - the rod will do that for you. HAVE FUN!

Regards,

Chris Chapman
At 07:40 AM 1/26/2003, you wrote:
John, some other thoughts......I am attaching a drawing......I hope you receive it. I will describe it to you anyway.......
I am thinking of possibly extending the brass rod down into the spring while it still protrudes from the top. I would also attach a very small level at the bottom of the brass rod to insure leveling and possibly increase damping. Instead of placing four wooden dowels (as shown in the drawing) around the spring to possibly prevent the magnet/weight from getting to the point where it falls/hangs over the spring I would replace them with a transparent (to view the level) glass/plastic circular column that reached the elevation of the magnet. Please remember one thing....I don't know what I'm talking about.....Ed.

In a message dated 26/01/03, johnjan@........ writes:
Hi Ed,

The way to think about the inverted pendulum is that we are balancing two forces.
Gravity wants to tip the pendulum over, and the greater the angle the greater this
force is.  The spring at the base wants to keep the pendulum upright, and the
greater the angle the greater the force of the spring is in this direction.

If I have the math correct, then the problem I had with instability may have
been due to my setup.  My inverted pendulum was made from mounting a
thin metal rod vertically and putting a mass at the top.  The entire rod bent.
When I tried to achieve a long period, the rod would bend to one side and
stay there!

The CSM student design has a solid rod with a spring at the base.
http://jjlahr.com/science/psn/epics/reports/sens/index.html
I think for that design.....

Damping is another thing that will need to be worked out......

My suggestion would be to first work on getting as long a period as possible and then work on the damping.
Cheers,
John

Hi John, Ed,

I have some serious reservations about the above design. Firstly, with a brass rod and a magnet weight supported by a coil spring, there is nothing to prevent the spring / rod system 'twanging' or oscillating, laterally or vertically. There is no damping at all for such motion. As a general rule in seismometer construction, if parasitic oscillations can occur and are not damped, they will give problems.
Secondly, since an equal voltage will be induced in the single coil for equal motion in any lateral direction, the output signal for a quake will be 'frequency doubled'. The output sensitivity will also be very low, since although the field through the coil is high, the total field over the coil is almost constant for small motions. I suspect that the largest signal would be due to vertical motions of the well sprung magnet!
This can be corrected if you use four small coils in place of the single one, with the same vertical axis, but connected in opposing pairs. The motion will be resolved into two signals. An increase in the flux through one coil of a pair will be added to a decrease in flux through the other coil. Since the coil centres are now offset to maybe about half the maximum field, the change in flux with any lateral movement will be high. Vertical motion will give opposing voltages in a coil pair which ~cancel out.
I would suggest that you try using a light ~1/8" Al rod (knitting needle?) with the magnet bob on one end and a single spring wire glued / swaged into an axial hole bored in the other end. If you have a two bar clamp on the baseplate, you can vary the length of spring wire used. This should be fairly rigid for vertical movements. The rod can be threaded through a disk of 1/4" Al plate with a 1/4" hole in the centre, to provide damping. This seems to give adequate damping with >1/8" separation. You centre the rod in the hole and move the plate vertically closer to the magnet to increase the damping. This hole would also control the maximum allowed lateral movement.
The overall stability could be finely adjusted by mounting a second axial magnet above the bob magnet and positioning it vertically. This could either increase or decrease the centralising force, depending on whether the two magnets attract or repel. You will need to adjust the final damping after setting the period.
However, I would expect the period to be limited by variations in the spring constant and the magnetic fields with temperature. If you used a stiffer spring and repelling fields, you might be able to partially compensate the decrease in stiffness of the spring with the decrease in the magnetic fields. Precision levelling / balancing the device will be critical. You won't need a spirit level - the rod will do that for you. HAVE FUN!

Regards,

Chris Chapman
```