User:RealGrouchy/FalkirkGearing

=Thanks!=

Thanks, RealGrouchy! This is a beautifully detailed and complete explanation. I am going to make a link from the Falkirk Wheel page to here, in case there are any other users who might benefit. I don't suppose it's the right way to do it, but I expect some senior Wikipedian who knows the ropes will come and tidy the whole thing up! --King Hildebrand 12:52, 19 January 2007 (UTC)
 * I was just wandering around, and came here from Falkirk Wheel. I heartily second Hildebrand's sentiment.  This page makes the whole thing so clear that even i understand it first time through.  Lindsay 22:45, 21 January 2007 (UTC)
 * Thanks, everyone! I appreciate the love! Adding arrows to the diagrams would probably help illustrate, if anyone has time/energy/etc. for that. -- RealGrouchy 04:30, 22 January 2007 (UTC)

Thanks, this is an excellent explanation. I do have 2 questions though: how is the arm driven to rotate if the central gear is fixed in place? would it have been worked if the caissons were just suspended freely from an arm? Wouldn't thay have stayed level due to their weight? I imagine they have been prone to swinging a bit perhaps though? —The preceding unsigned comment was added by 89.101.97.195 (talk • contribs).
 * (1) All you'd need is a motor to rotate the entire mechanism; it doesn't have to involve the gears (e.g. a motor on the non-geared side?).
 * (2) If they were suspended, they likely would remain level in most circumstances; however, there would still be some influence from wind/swinging/etc. The gears ensure that they are level at all times. --RealGrouchy 06:25, 18 February 2007 (UTC)

=How the Falkirk Wheel levelling system works=

This page is meant to explain, from first principles, how the gearing on the Falkirk Wheel keeps the caissons level. The reason behind creating it is twofold: to help User:King Hildebrand understand it, and to kill some time. I put it in my userpage area for lack of a better place to put it (maybe wikibooks?). I used Lego because it was the easiest, and I wanted an excuse to dig out my old lego.

Feel free to move it or take ownership of it (especially if a better explanation or if (a) better illustration(s) come(s) along), or label/crop the images, etc. --RealGrouchy 03:26, 19 January 2007 (UTC)

Gears (same size)
Here are three gears. They're all the same size. When you look at the cross-like holes on them, the outside ones are "horizontal" and the middle one is "vertical".



Gear Directions
I've rotate the leftmost one. Because they're gears, of course all three of them turn. I turn the left one clockwise a bit, and the middle one turns counter-clockwise a bit, and the right one turns clockwise a bit. Because they're all the same size, they all move the same amount. The middle one goes in one direction, and the outer ones go in the other direction. Since both the direction and the distance is the same on the outer ones, they both end up in the same position as each other.



Gears (different sizes)
Now here are four gears, this time of different sizes. Let's call them (from left to right), G1, G2, G3, and G4.



If I turn G1 clockwise, they will all turn. G1 and G3 will turn clockwise, while G2 and G4 will turn counter-clockwise. If we added more gears into this line, all odd-numbered gears will turn clockwise, and all even-numbered gears will turn counter-clockwise--no matter what their size. However, the amount they travel will depend on their size.

Gear Ratios
G1 has 40 teeth, G2 has 24 teeth, and G3 and G4 each have 8 teeth. The gear ratio between the them is designated with colons like this: 40:24:8:8. However, each of these numbers can be divided by 8 to get a whole number (8 is the greatest common factor of 40, 24 and 8). Therefore, the gear ratio of these four gears, in simplest terms, is 5:3:1:1.

What this means is that for every time G1 goes full circle, G2 will go around 1 2/3 times (5 divided by 3 is 5/3 or 1 2/3). For every time G2 goes full circle, G3 will go around 3 times (3 divided by 1). G3 and G4 will always make the same number of rotations as each other, although they will do so in opposite directions.

If we turn G1 around a full circle, how many rotations will G3 make? It will be 5/3 multiplied by 3/1. 5/3 * 3/1 = 5/3 * 3 = 5÷3*3 = 5÷1 = 5

G3 will make five rotations. Note that we actually didn't need to put G2 into the mix. We could have simply divided the ratio number for G1 (5) by the ratio number for G5 (1). Five divided by one is five.

Gear Ratio "unconversions"
Below I have added another large gear to the end. It will be called G5, although it's the same size of G1 (40 teeth).



G1 and G5 are both odd-numbered gears, so we know that they will always rotate in the same direction as each other. But G1 is next to a medium-size gear, and G5 is next to a small gear. Will they turn at the same speed, or at a different speed?

To calculate this, we'd have to take each step along the way: G1/G2 * G2/G3 * G3/G4 * G4/G5 = 5/3 *  3/1  *  1/1  *  1/5

But remember: we determined above that we only have to take the ratio numbers from the two gears that we are interested in! So the above simplifies to: G1:G5 = 5:5 = 5÷5 = 1

Therefore when G1 makes one full rotation, so will G5. They will both turn at the same speed, and since they are both odd-numbered gears, they will turn in the same direction.

The Falkirk Wheel
Here is a mockup of how the gears work on the Falkirk Wheel.



There is a big gear in the middle, and there are two black things (representing the caissons) connected to gears of similar size. The "caissons" are connected to the gears in two places, so they don't simply hang.

Between the three large gears are two small gears. These are important so that the big gears are all "odd-numbered" gears (in reference to the gear numbering used above). And, as we learned above, the large gears will turn in the same direction, and at the same speed.

You can see the Falkirk Wheel's actual gears on this image of the Wheel.

The Falkirk "Fix"
But we don't want the caissons to turn, now do we? Well, not in relation to the ground.

However, the arm (the red horizontal piece in the above photo) rotates. We want the wheels to rotate in relation to that arm. The solution? To fix it!

That is, to fix the middle gear so it does not rotate at all. This piece on the back is connected to the middle gear, and there's a little brown thing keeping it from turning. Therefore, the middle gear does not turn in relation to the back piece (which is theoretically fixed to the ground).



As the arm rotates, the gears rotate in relation to the arm. However, because the middle gear is always oriented the same way, the other two big gears are also oriented the same way. And that way is horizontal, so that the caissons are always level.

The proof!
Build it with your own lego if you still don't quite grasp it.

Although I don't have any software that can make an animated gif (Corel Photo-Paint might be able to, but it's a PITA to use/understand), I have made 12 frames that can be used to make one (see gallery below).

If you use Windows XP, you can download the 12 photos into their own folder, and use the "photo preview" thing to scroll through them quickly and see a quasi-animation. Needless to say, the "caissons" are always level.