Brf wrote:Hi Votan, a couple of comments:
#1 #2 and #4 – we might be saying the same thing. When I use a clock face reference, I am referencing the a/s assembly’s center of mass position, not the actual pole position. As an example, with a two unloaded poles 90 degrees opposed attached to a single axis of rotation, the center of mass is 45 degree from each pole (right in the middle). I this instance, maximum torque is achieved when the center of mass is at it farthest from the axis of rotation. That would position the two poles 45 and 135 degrees to achieve the center of mass at 90 degrees.
#3 The distance used to determine the torque is the distance from the pivot to the force acting on the center of mass but measured perpendicular to the direction of the force. With Fg constant acting on the center of mass and the distance increases linear, as defined by the arc, I am not us how torque cannot be anything but linear.
I’ am afraid that we should go to calculus once more, something that could bother those who watch the topic. The non linearity of the a/s mechanism torque occurs from the calculations and relevant charts and sketches of my previous posts.
In any case, with respect to your comments, I agree that with the two unloaded poles 90° opposed, the center of mass (C of G) is 45° from each pole (right in the middle).
As well, I agree that the each time a/s torque is T=FgxD, where D is the each time distance (the lever arm) from the hub’s pivot to the force Fg, always measured perpendicular to the direction of the Fg (which is vertical).
According to what you mention, in a random position of the a/s mechanism where lower pole has an angle φ from vertical (where 0°<φ<90°), then the a/s mechanism’s C of G should be in an angle φ+45° (see sketch attached below).
- A-s torque of bare poles.jpg (38.62 KiB) Viewed 1801 times
If R the (constant and known) radius from hub’s pivot to a/s C of G, then distance D=Rxsin(45°+φ), so the a/s mechanism’s torque should always be:
T=FgxD=FgxRxsin(45°+φ)
That means (Fg and R been constant and known) that a/s mechanisms torque T is not at all linear changing, as depended from sin(45°+φ). For example, with bare poles and for the lower pole in 3 discrete positions of 06:00’, 07:30’ and 09:00 o’clock we should have:
For φ=0° (06:00’), T=FgxRx0,71, For φ=45° (07:30’), T=FgxRx1,0, For φ=90° (09:00’), Τ=FgxRx0,71, i.e. not at all linear increasing, but a curve, exactly just as an extreme case from the calculations in my previous posts and charts. Indeed, in the above extreme example, from φ=45° and up, a/s torque starts degreasing (turning point).
Of course, adding load to the lower pole, the turning point of the a/s non linear curve goes higher from φ=45°. For example (looking at the charts of my previous posts) with 4 rubber donuts in the lower pole turning point is above 60°, adding 1 brass washer it goes above 75°. This is a conclusion in full agreement with what Golear noticed by ear in his setup, namely degreasing a/s torque in the inner grooves.
Truncating the higher pole, with 4 rubber donuts turning point goes above 75°, adding 1 brass washer, it goes up to 90° namely all the way increasing but not linear.
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