A math challenge

[Nonny]

The idea is good, but I suspect that the 6 resulting legs would hinder the use of the table with chairs.

Nonny

[basilisk]

Why? The legs will all still be at the corners.

basilisk

[David Patnaude]

[e-mail] wrote in news:4c21ac68$0$28543$ [e-mail]:

Not nearly so glamorous, but why don't you just use some lege levelers.

[Larry W]

I suggest about 18 inches into the ground.

[Nemo]

I think the two triangles have to be the most ingenious response so far. You could save a couple of legs by building a regular rectangular table, cutting it diagonally to include three legs on one side of the cut, and hinging it along the cut. You wouldn't have a continuous surface but you wouldn't necessarily have that with the two triangular tables, either.

A mathematically precise solution would fit my personal idea of elegance, even if I was the only one to appreciate it. The adjustable-leg solutions, ranging from matchbooks to macpherson struts, are neat but not really elegant.

Legs in two adjacent corners and the third halfway along the opposite side are not the best solution. Better would be to bring the legs away from the corners and closer to the third leg - if I had a sketch pad, you'd see immediately why.

Oddly enough, you don't gain anything from making the table long and narrow. Draw lines between the legs and imagine them as the axes of rotation. Push down on the unsupported corners and you'll see that there's just as much mass counterbalancing the force with a rectangular table as with a square one.

The length of the legs do make a difference. I think the higher the table, the more it will resist tipping from a vertical force applied ouside the support triangle. However, I'd like my table to be at a standard height.

I agree that you can be too finicky with the design but if I go to the trouble of building this thing I'd like it to be an interesting solution to what has to be a very common problem.

I also like solving puzzles and, so far, this one has been beyond me. Nemo

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[HeyBub]

Go with three regular legs on each of three corners.

On the fourth corner, an adjustable leg - perhaps salvaged from a camera tripod.

Personally, I use folded napkins...

[Matt]

Make it a 4 leged table, with one of the legs with an adjustable / telescoping foot. For an example see

(I got mine for father's day)

However, the table may not end up level, but it will be stable.

Another solution would be standard threaded feet such as

were the stones not set level ? I can understand each stone being a unique shape - that is a feature of flagstones

[Larry Jaques]

On 23 Jun 2010 06:40:40 GMT, [e-mail] wrote the following:

Screw the math. Use adjustable (threaded) feet and tee-nuts.

nylon 1/4" are just peachy, wot?

Once you get the level set, put dots of fingernail polish where the legs go so your wife doesn't get upset when she moves the table and finds it uneven again. Demand that she heeds the finnernail polish.

-- Peace of mind is that mental condition in which you have accepted the worst. -- Lin Yutang

[RicodJour]

That word, elegant, I do not think it means what you think it means.

Getting unnecessarily complicated is not elegant, simple nor admirable.

Most people will thank you for that.

From your leg length description it sounds like you might have chosen the wrong moment arm as the important one.

Yes, and which has very common solutions. There's an old Chinese curse, "May you live in interesting times." You are proposing an interesting solution for your table. Making an adjustable leg that nobody can tell is an adjustable leg qualifies as elegant and interesting...to you, and that's the only one that will really be interested. No?

R

[Anonymous]

Ron, when your ass is as big as mine, bending over to adjust a table leg each time the table's moved is far from elegant!

I've sketched some approximate solutions and the three-legged table looks like it could be surprisingly stable. I was hoping that someone would rise to the mathematical challenge of optimizing the placement of the legs - more as an interesting puzzle than as a practical problem since there's a certain amount of leeway in the actual placement before stability is seriously affected. The answer would involve simultaneous equations - easy enough - and, probably, some fairly elementary calculus (an oxymoron if ever there was one!).

N

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[Robert Bonomi]

NOT true. Consider the stability of a trestle table. It has only -two- legs, each of which spreads into two widely separated feet at the ground.

[alexy]

But the two legs don't swivel at the top to allow them to conform to irregular surfaces. I.e., the contact points are always the same distance from the table above them, just as they would be if the contact points were at the end of separate legs.

[Upscale]

On Thu, 24 Jun 2010 19:48:24 -0500, [e-mail]

And the trestle table like the one I built, often has some type of cross member attachment joining those two legs into a solid structure.

[RicodJour]

{there seems to be an attribution missing...}

each time the table's moved is far

How often do you have to adjust a table leg? Certainly not every time you move it.

R

[keithw86]

Yes, it is true. A trestle table has four "legs". The base is defined by the points touching the floor. How they get there is immaterial, at least until the table moves (the base may change as it's tipped).

[Nemo]

Right. A rigid structure will transmit force in a straight line from the load point to the support point, assuming no other constraints. This would be true even if the line goes through empty space.

Bea, you're wrong, I'm afraid. I _do_ have a math problem. It's the one I issued in the math challenge, and I'm still looking for a purely mathematical solution. This means that solutions involving trailer jacks, anti-gravity devices, jet-packs, trained seals, skyhooks or even something as far-out as levelling off my patio are completely off-topic.

But I'm glad I'm not the only one who's having a problem with the answer!

Nemo

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[krw]

I guess I'm not seeing your problem. Spread the three legs as far as possible such that the COG, projected onto the floor, is furthest from the lines drawn between the feet. For a square the answer is obvious. A rectangle isn't much harder to see. For random shapes it gets trickier. ;-)

[Phil Kangas]

The flagged patio is a complication as is the rectangular table. If, for example, the patio was an undulating surface with no sudden changes of height a round table with four equal legs will have stability in two places in one revolution. Perhaps in the case of the flagstones if the table legs were spaced so that two ajacent legs would fit on the same stone then the other two legs will find one position that is stable so long as the other two are still on the same stone. Am I making sense? It would be easy to experiment with, just find chairs of different sizes and try it! But all this means a round table.....;>(( phil (_not_ a genius) kangas

[Robert Bonomi]

It doesn't matter. What counts is where the each foot is in relation to the edge of the table.

WORST CASE: the rotatable legs are perpendicular to the line of the two fixed legs. No worse than the three-legged design.

Best case: the rotatable legs are parallel to the line of the two fixed legs. Equivalent to a regular four-legged table.

Average case. stability is about 70.71% of the four-legged table.

[krw]

Actually, what matters is where each foot is in relation to the *center* of the table.