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Wonder at the intricate movement of the exactly balanced scales. Marvel as each ball rolls onto or off a scale, causing the arm to assume a new point of equilibrium, to point the hand to the next hour or five minutes.
These are scales that turn 360 degrees. On one side is a fixed weight. On the
other is a dish that is filled and then emptied, a ball at a time, to move the hand clockwise to the next number. The balls enter or leave through 12 openings in the clock face.
A ratchet keeps the scales moving in the right direction when the arm is vertical. The only mechanical parts are for transporting the balls from exit to entrance openings and for timing the movement of each ball to or from the dish. Click on the illustration for clarification.
illustration
http://www.geocitie...ie/timebalance.html
[FarmerJohn, Oct 04 2004, last modified Oct 21 2004]
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Father Time does it again... |
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But I'm missing something. How does the scale keep from bottoming out when one side is heavier than the other? Do the balls roll on and then roll off at the right moment or something? |
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Each additional ball, delivered every hour or 5 minutes, causes the scales to tilt a little more. With small weight changes it doesn't bottom out until loaded with six balls. |
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Then, when the arm is vertical, each removed ball causes it to tilt a little less. In the picture the ball above the "5" is soon entering the dish and will cause it to move to the ball to the left of the "5" and to move the hand to 2 o'clock. |
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[FarmerJohn], I bet you have the_coolest_ever_sandbox! |
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I don't see how you get 360 degrees of movement out of a balance arm. I thought that the centre of mass of the empty arm had to be lower than the pivot for the thing to find a balance point. Can you explain? |
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(thinks about it...) You could add a weight to the centre of the swing arm that moves above or below axis depending on which half of the face the hand is pointing. In your illustration the weight would move from left to right on the minute hand to allow it to advance. Does this make sense? |
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Farmer, I take it that there's a coil spring in action then, in order to balance the forces. It doesn't matter how small the force differential is between the sides, it will always bottom out at 9:00 unless counteracted by an opposing force. Or are we talking about a more complex mechanism than a simple dial? |
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st3f: The balance arm with hanging scales has a center of mass lower than the pivot. The back overhang of the hour/minute hand would be weighted to make its effect neutral. The scales hang behind the balance arm, between it and the clock face
to avoid colliding with the balance arm and to receive and deliver balls. |
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When the balance arm is vertical as is the case with the minutes illustration, the ratchet holds it a little past the vertical. When the first ball (under the 60) rolls onto the dish, the arm tilts clockwise so that the hand is then pointing at the 50. |
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RayfordSteele: This is not much different than a flattened, wire coat hanger with something heavy on one end. I'm talking of a simple dial with precise weights. |
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Upon adding a ball, the center of mass shifts to favor one side. Because the entire mechanism rotates around a fixed axis, that side is favored in weight until the center of mass is again below the pivot point. I submit that that won't happen until the clock bottoms out, because there's nothing to reduce the favor that the heavy side has, unless something else changes. |
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Wait... you might be right, at least when the hand is in the left half of the clock. Since the weights are not at a fixed distance to the pivot center when on the tray, a balance point could be possible. My bad... |
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The next difficulty, though, lies between 12:00 and 1:00, and I'm not talking about the directionality rachet. The time comes to add a ball. The scale hand tips towards 1:00. Now, since the counterweight is past the 9:00 position, it moves closer to the pivot point, raising it and reducing its effective lever-arm. The right side gets heavier from the ball addition, (while also reducing its lever-arm as well). |
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//The balance arm with hanging scales has a center of mass lower than the pivot// |
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I think I need to clarify. When I said that you needed to add a weight I meant a 'fixed weight' so that if you nudge the arm out of balance it will tend to shift back (there is an energy minimum at balance). A flat bar pivoted around its mid-point does not provide this, whether you hang weights at the end or not. What will happen is that, as soon as you put a weight on one side that is larger than the weight on the other, the bar will swing to vertical. |
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Think of your design as being like a propellor -- it is 'happy' at any orientation and feels no urge to hang at any angle over any other. Attach a weight to one blade and (if you let it swing freely) if will turn to vertical with the weighted blade at the bottom. |
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What you need is something more like a coathanger which, when hung by the hook, will balance. Push one side down and the weight will transfer across the centre axis, pushing back. The coathanger will balance at different angles depending on the weight you attach to each side. |
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The off-centre weight I was suggesting would be the equivalent of combining a pendulum with a horizontal propellor. The propellor would be the arm while the pendulum provides the balance. The ability to shift the weight across the axis would allow the arm to operate both ways up. |
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This clock would be pretty and would work, provided that you made some alterations to allow the arms to balance. |
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St3f, you're missing the fact that because the weights are hanging, they're effectively not a fixed distance to the pivot; that might throw a twist into the off-balance propeller scenario. Essentially the shape of the propeller 'morphs' as it moves, and the center of balance changes. This is why you can get a slide balance scale to balance at a range of multiple points, dependent upon the weight added. But there still may be a bug with it, requiring the large counterweight to move in one axis, like a balance scale, instead of rotationally. |
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Because of that dependent variable, this could possibly work, if you get past the other difficulty I raised. |
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I always hated dynamics... |
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Sorry guys, I guess this 3 way debate is getting a bit dull for all. Three quick things, then I'm out. |
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1) Don't worry about dynamics. Thnk about one position and what happens when you shift slightly from it. Think statics. |
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2) Ray - The weights are suspended from fixed points on the arm. Its those distances that count, not the exact positioning of the weights. |
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3) Thing about energy minima. To balance you need to create an energy minimum. I've suggested one way of doing this. There are other ways, but without an energy minimum there can be no balance. |
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St3f, yeah, thinking about this on the way home, you're right. The hanging of the weights doesn't matter, since it's off of a fixed position on the hand lever. I was thinking that in different rotational positions, that the effective force action point would change. My bad. A force is a force, of course, of course... |
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Perhaps what's needed are sliding weights. I dunno, my brain hurts. |
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Boiling it down to bare engineering, the question becomes this: is there a way to reposition the center of gravity in such a way so that upon imminent movement, it is always 30 degrees to the right of lowest energy? |
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Yes, I think I have it. It's not as exciting as first post, though. Instead of 12 balls placed around the clock, what you need is only one ball position, placed at 5:00, with a continuous ball-feed system, and essentially 12 'baskets' for that ball to sit in, like a ferris wheel. Keep its diameter small so as not to overwhelm the entire face. The ball enters the closest basket to the 5:00 position at 1:59:59.999, rotates the otherwise balanced clock hand (now sitting at 1:00), to the 2:00 position, and the ball exits at the exit in the 6:00 position. |
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Okay guys, now I've thoroughly tested this, which I should have done before, and you're right of course. The weights' pivot points must always be slightly lower than the arm's pivot point to avoid bottoming out. Another way to achieve this would be to have larger hole(s) in the arm than one or all three pivot shafts. |
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RS: That's a neat variation and a whole different design than a scales idea. |
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I hated statics, too. Oddly, I loved mechanics of materials. (stress analysis) Maybe it was the prof. |
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You could also do this: have entrances / exits at the 6 'downstroke' positions. That way you'd only need two baskets, with one always being empty, and one only containing a ball when moving to the next position, but also otherwise empty. Oddly enough, now that I notice it, I've come 'full circle' to my original anno. |
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