Yet another update: this time I am re-writing this so that it is hopefully more clearer. Where I said "bend" previously, I should have said "pivot" instead. Poor word choice on my part. This writing supercedes all the previous annotations I've made.

I was sitting at a wobbly table at a sandwich
restaurant (Jimmy John's) yesterday. I've seen these generic two legged tables at many of the restaurants and bars I've been to on campus. Views of the unmodified, problematic table (with labels):

View from the side
.. _________X_________..
...............|...............
...............|...............
...............|...............
...............|...............
...............|...............
...............|...............
.....A______G______B.....

In this generic table, the feet touch the floor at spots A, B, C, and D. Bars AB and CD are just above the floor.

Consider imaginary lines AD and BC. If these diagonals intersect, then the table must be stable because the diagonals form a plane containing A, B, C, and D. On the other hand, if line BC is closer to the floor, then both A and D cannot be touching the floor at the same time so they touch the floor alternatingly, thus causing the wobblyness.

In my modified version of the table, The leg XG can pivot at X, while everywhere else remains sturdy including the other leg. The pivot at X allows the leg to rotate only on the plane containing A, B, and X, such that the rotational axis for the leg coincides with line XY. In the example, line BC is closer to the floor, so one would turn XG counter-clockwise (in the side view diagram), bringing foot A closer to the floor and B further away from the floor. Line AD and BC can then intersect, restoring stability. Leg XG pivots at X as opposed to G, so that an upright, non-wobbly position would be the most gravitationally stable position.

Benefits:
Non-wobblyness is the main benefit. The original unmodified version of the table is nice because it has only two legs and doesn't clutter up human leg space as much as a four legged table would. It also has four points of contact with the ground, making it harder to tip the table over than a three-legged table.

very close. more like this.http://www.novainte...eria-NOVAREC_sm.jpg the two vertical legs aren't attached with a horizontal bar because one would need to be able to swing. [rhatta, Oct 17 2004]

An unstable tablehttp://sodaplay.com...l=waxthumb+tableaux gone terribly, terribly awry [thumbwax, Oct 17 2004]

Well, this is a challenge to describe in just text. I'll cheat a little with crappy ascii art once again. This time I'll use phoenix's terminology of leg and feet.

I was sitting at a wobbly table at a sandwich restaurant (Jimmy John's) today. I've seen these generic two legged tables at many of the restaurants and bars I've been to on campus. Here's a view of the unmodified, problematic table seen from underneath (with labels):
____________
|___________|
|_A___X___B_|
|___________|
|___________|
|___________|
|___________|
|___________|
|_C___Y___D_|
|___________|

In this generic table, the feet touch the floor at spots A, B, C, and D. A and B are connected by a bar horizontal to the floor. The bar is just above the floor. From the middle of that bar, a vertical leg reaches the tabletop at X. Same deal for C, D, and Y.

Consider imaginary lines AD and BC. If these diagonals intersect, then the table must be stable because the diagonals form a plane containing A, B, C, and D. On the other hand, if line BC is closer to the floor, then both A and D cannot be touching the floor at the same time so they touch the floor alternatingly, thus causing the wobblyness.

In my modified version of the table, The leg for C and D will be able to pivot at Y so that C, D can rotate to the left or to the right. In other words, the rotational axis for the leg coincides with line XY. In the example, line AD is further away from the ground, so one would turn the leg for C and D to the left (in the diagram), bringing foot D closer to the floor. Then line AD can be lowered to intersect with line BC, restoring stability.

[rhatta], I'm fairly sure that if imaginary lines AD and BC
do not already intersect, then at least one of the feet of
the table's legs is bent.

If this is the case, your problem won't be solved by
rotating the leg at point Y unless you are fortunate
enough to find a high spot in the floor within the arc of
imaginary line YD.

Going along with the previous case that I was talking about, the leg YG would be turned clockwise so that foot C is closer to edge E while D is further away from edge F. sin(|DYF|) would increase, while sin(|EYC|) would decrease. Leg YG bends at Y as opposed to G, so that an upright, non-wobbly position would be the most gravitationally stable position.

[rhatta], as of your last annotation, it seemed you had
replaced
the function of bending with that of pivoting in your
explanation. My comment was based on leg CYD being
adjustable only by pivoting as in'rotating' at point Y.

If 'upright' YG is bendable, what's to stop it from flexing
further when somone leans their elbows on the table?

What material do you have in mind for creating this
'bendable' quality? Are you thinking of using a component
like a flex spring at the join where Y connects to the
table or perhaps something more along the lines of a leaf
spring that comprises the whole of the upright from points
Y to G?

I admit, I'm a little lost also on visualizing how this table
works.

*[tw], I LOVE sodaplay... I just wish I was better at using
it.

Just click on "how to play" - the secret is in the muscles. Alternatively, to get a grasp on how easy it is to create one:
simply connect two dots
then click on the line created - **while you are clicking on the line, ^^look to the left frame.^^**
(As you'll note on the left, the line with a dot on it between the 2 graph fields is a slider, and it reacts to the click.)
Take the slider and move it into the top wave field.
You just created a muscle.
Knock yourself out.

Is it your contention that because the pivot point is farther from the floor that the proposed design is more stable than a fixed single leg would be in place of the pivoting leg with 2 feet? Still seems like if someone leans hard on a corner of the end with the pivoting leg that the table would tip as it might with 3 legs. Intuitively, without drawing force vector diagrams and actually thinking about this, it does seem like it could possibly be less prone to tipping than the 3 legged version though.

My mind still wants to say that it's less stable than a table with 4 fixed feet.

Some folding tables have enough flex along the longitude (twisting the table top slightly) that 4 legs will sit flat on a slightly uneven surface. I think that might be the general effect that is desired here.

"Wouldn't a three-legged table always be more, inherently, stable than any other configuration?" Yes, stable in terms of not wobbling. But, unless the table is triangular, there is enough of an overhang (round table) that pushing downward on the outer edge can cause the table to tip.

What if there were three 10lb ballasts attached to the
underside of a round table having three legs, with one
ballast centered between each pair of legs?