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. =20Chris,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.