why does a milking stool have three legs

I ll give it a go. Imagine we re standing in a room. I can put little dots anywhere I want and they ll float. I put one in one part of the room, then another dot somewhere else. Now say you have a strip of very stiff, very stretchy rubber. You can stick it to one point, and pull it over to the other dot, which you join the other end to. Now, you pull one end of your strip in the same direction as this line for as long as you want. This defines a line that we can carry on through the whole universe, if our thing is stretchy enough. Now say, we put a third point somewhere. You grab the side of the elastic strip, and pull it so the edge touches this third point. Now if you pull the side in the direction you were just pulling it, you ve defined a plane. Now add a 4th point.

If you don t put this point on the plane, you have to warp the sheet with a bump to make it touch. It s not even. The stability comes from knowing that if we have a 3 legged stool, the ends of the legs will make a plane. We imagine the ends of the legs as our points. If a surface is level, i. e another plane, we can just rotate the stool so our plane lies parallel to this one. for instance, we ll be able to turn or lift the stool around until it sits on this surface (these are called rigid body motions), and it won t rock when we push down on it. The 4th point is the end of the 4th leg. Now unless the surface has this bump in, there s no way to orient the stool so its legs are all touching the ground, and it ll rock. We d have to add a lump of newspaper or take a hammer to the ground.

For the uneven terrain, I think you use the argument about placing the points anywhere. This is much easier to visualise if you imagine smooth, sloped surfaces though.
For stability on uneven ground. Three-point suspension is the only inherently stable design. A lot of folding camping stools have three legs for the same reason. They are stable on an uneven surface. Three legs are used in a lot of other things too, even record player suspension sytems and of course the tripods that camera crews and others use. Four legs rock on an uneven surface. Some stools have two legs or even one, like a small shooting stick, and fold flat easily, relying on body adjustments to maintain balance. The three legs symbol of the Isle of Man is actually a three-dimensional object with each leg pointing in a different direction like a shoe-maker s last, but obviously has to be shown as two dimensions in print.

It s called a triskelion, and it s also used in Sicily and a few other places. Whichever way you throw it, it stands It does that because of the inherent stability of a three-point suspension. Here s a spindley three-dimensional one outside Ronaldsway airport in the south of the island. Most of us hate the thing. splindley modern art, not strong enough looking like the ones on the flag and the coins. Here is a shoemaker s last with a hammer and awl. It stands whichever way round it is, but the legs are at right angles so it isn t exactly like a triskelion.

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