## PSN-L Email List Message

Subject: Ball pivot
From: "Randall Pratt" rpratt@.............
Date: Mon, 25 Nov 2002 00:08:08 -0600

```Chris,

In rolling contact the center of rotation of the ball will be the center =
of the ball and it will be in translation.  The instantanious center of =
rotation of the total boom will be the contact point. (wheel and axle)  =
If the compressive force in the boom is axial then any deflection from =
center will throw the force off axis. There will have to be contact =
friction sufficient to prevent the rotated boom from sliding on the =
plate since the boom is no longer perpendicular and this force will be =
tangent to the ball.  The friction force will be in the direction of =
pushing the boom toward center. =20
As to my earlier thought that the axis will be offset, I calculate that =
for a 24" boom and .125" motion the pivot will move .0003" left or right =
using a .125" ball.  With 12" between upper and lower pivot this would =
be less than 1% of the tilt angle you suggested and may not be a =
significant factor. =20
May I suggest an experiment for the proponents of the ball?  Operate =
with as little damping as possible and compare to a true sine wave =
equally damped.  If the ball pivot is somehow causing stability with a =
restoring force it should alter the peaks of the sine wave.  =20

Chris,

In rolling contact the center of =
rotation of the=20
ball will be the center of the ball and it will be in translation.  =
The=20
instantanious center of rotation of the total boom will be the contact=20
point. (wheel and axle)  If the compressive force in the boom =
is axial=20
then any deflection from center will throw the force off axis. There =
will have=20
to be contact friction sufficient to prevent the rotated boom from =
sliding on=20
the plate since the boom is no longer perpendicular and this force will =
be=20
tangent to the ball.  The friction force will be in the direction =
of=20
pushing the boom toward center.
As to my earlier thought that the axis =
will be=20
offset, I calculate that for a 24" boom and .125" motion the pivot will =
move=20
..0003" left or right using a .125" ball.  With 12" between upper =
and lower=20
pivot this would be less than 1% of the tilt angle you suggested and=20
may not be a significant factor.
May I suggest an experiment for the =
proponents of=20
the ball?  Operate with as little damping as possible and =
compare to a=20
true sine wave equally damped.  If the ball pivot is somehow =
causing=20
stability with a restoring force it should alter the peaks of the =
sine=20
wave.
```