## PSN-L Email List Message

Subject: Ball Pivots
From: "Randall Pratt" rpratt@.............
Date: Mon, 25 Nov 2002 23:30:02 -0600

John,

Thanks for the nice explanation and drawing.  You are correct about the =
lengthening effect.
http://jjlahr.com/science/psn/pivots

To further the discussion, would not the center of rotation move from =
the contact point at no displacement to a point behind the plane and in =
the direction of travel as the boom is displaced rather than be =
considered a lengthening of the boom on the boom side?  The radius to =
any point from the center of rotation must be perpendicular to the =
velocity of the point.  Thus the center of the pivot ball to the contact =
point will define one line and a line perpendicular to the now flatter =
motion of the mass on the end define a second line.  When the system is =
rotated to the horizontal, the movement of the center away from the mass =
to a point behind the support will also tilt the axis of rotation =
between the pivots to a more stable direction. =20

As you say, the upper pivot would best be designed to accomodate axis =
change.  In the arrangements I have seen in PSN, the upper ball is on =
the opposite side of a support so as to be in compression.  Therefore =
the rolling would now move the center of rotation in the upper pivot =
toward the mass with an end result of the new axis tilting the boom down =
to a shorter period.  A ball style support will require a good bit more =
engineering than just using a conveniently sized ball.  Do the =
proponents have anything to offer regarding design?

Randy

John,

Thanks for the nice explanation and = drawing. =20 You are correct about the lengthening effect.
http://jjlahr.com/science/p= sn/pivots

To further the discussion, would not the center of rotation move = from the=20 contact point at no displacement to a point behind the plane and in the=20 direction of travel as the boom is displaced rather than be considered a = lengthening of the boom on the boom side?  The radius to any point = from the=20 center of rotation must be perpendicular to the velocity of the=20 point.  Thus the center of the pivot ball to the contact point will = define=20 one line and a line perpendicular to the now flatter motion of the mass = on the=20 end define a second line.  When the system is rotated to the = horizontal,=20 the movement of the center away from the mass to a point behind the = support will=20 also tilt the axis of rotation between the pivots to a more stable=20 direction.

As you say, the upper pivot would best be designed = to=20 accomodate axis change.  In the arrangements I have seen in = PSN, the=20 upper ball is on the opposite side of a support so as to be in=20 compression.  Therefore the rolling would now move the center of=20 rotation in the upper pivot toward the mass with an end result of = the new=20 axis tilting the boom down to a shorter period.  A ball style = support will=20 require a good bit more engineering than just using a conveniently sized = ball.  Do the proponents have anything to offer regarding = design?

Randy

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