I have a flagged patio. The flags are odd shapes and sizes and no two are at
the same level. Anywhere I put a four-legged table, it rocks. So I thought
I'd build a three-legged table, but I'd like it to be rectangular.
Here's the question: where do the legs go for maximum stability, assuming
they stick straight down underneath?
I think the simplest solution would be for a square top and I suspect that a
solution for a rectangle would be proportional to the square. There might be
two solutions, one with one leg in a corner and one with it half-way along
one edge.
The math is completely beyond me. Is there a genius amongst us?
Nemo
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On Jun 23, 12:07=A0pm, [email protected] (Doug Miller) wrote:
> In article <[email protected]>, "Bea Essor" <=
[email protected]> wrote:
>
> >I don't think you have a math problem. The way I see it, if you were to
> >build a square or rectangular table with three straight legs two of the
> >corners would be supported, and the other two would not. =A0If someone l=
eans
> >too heavily, or puts something =A0heavy on the table it may tip. =A0My s=
olution
> >would be to make a rectangular top. Place two straight legs on the narro=
w
> >end as you normally would. On the other end I would use a " V " shaped l=
eg
> >going from the corners to the center spot on the floor.
>
> That isn't going to make it any more stable -- it still has only one poin=
t of
> support at that end, and it's still in the same place.
Yes, but it fulfills the new picnic table seismic code requirement for
lateral bracing.
R
On Jun 29, 7:32=A0am, Upscale <[email protected]> wrote:
> On Mon, 28 Jun 2010 21:27:57 -0700 (PDT), Robatoy
>
> >> horizontal enough to stop things from sliding off it.
> >Now you want the fucking thing thing to be horizontal too?
>
> Yeah, well.... I get a little upset when my food slides away from me.
Then you will need 3 adjustable legs.
On Jun 29, 9:15=A0am, alexy <[email protected]> wrote:
> Upscale <[email protected]> wrote:
> >On Mon, 28 Jun 2010 22:58:50 -0400, alexy <[email protected]> wrote:
> >>>Go for 4 legs with adjustable feet. =A0(if the table just has to be
> >>>stable and not necessarily level, you just need 2 adjustable feet
>
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 ^^^^^^^^^^^^^^^^^^^^^
>
>
>
> >>Actually, only one.
>
> >That's not right. If the terrain that the table sits on is varied
> >enough, then two adjustable feet are needed to keep the table surface
> >horizontal enough to stop things from sliding off it.
>
> I was replying to the hypothetical that level is not needed. If level
> is needed (i.e., real world), it seems you would need three adjustable
> legs if you can't rotate the table. If you can rotate, and the surface
> is "continuous", two will do.
> --
> Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequen=
tly.
zactly
[email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two
> are at the same level. Anywhere I put a four-legged table, it rocks.
> So I thought I'd build a three-legged table, but I'd like it to be
> rectangular.
>
> Here's the question: where do the legs go for maximum stability,
> assuming they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect
> that a solution for a rectangle would be proportional to the square.
> There might be two solutions, one with one leg in a corner and one
> with it half-way along one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
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...
You can have 3 legs with 4 feet. Two legs on one end would be
attached in a permanent position, as normal. On the other end, one
leg with a fork, ie., two feet. This leg is able to be rotated in its
"socket" or attachment place.
Either 1) the feet (forks) should be of different lengths and the leg
be perfectly verticle or 2) the leg be slightly off verticle and the
feet equal lengths.
To stabilize the table on any uneven surface, rotate the forked leg
until both feet touch.
This also works if there's one rotating leg on each end, each with
forks (or feet), ie., 4 feet total. In sample 1 above, the longer
forks, of each leg, should be catacorner from each other.
The levelness of the tabletop won't be significantly off because of a
1/8" - 1/4" difference in fork/foot lengths.
Sonny
On Jun 28, 11:10=A0pm, Upscale <[email protected]> wrote:
> On Mon, 28 Jun 2010 22:58:50 -0400, alexy <[email protected]> wrote:
> >>Go for 4 legs with adjustable feet. =A0(if the table just has to be
> >>stable and not necessarily level, you just need 2 adjustable feet
> >Actually, only one.
>
> That's not right. If the terrain that the table sits on is varied
> enough, then two adjustable feet are needed to keep the table surface
> horizontal enough to stop things from sliding off it.
Just one will do. The three other legs, by themselves will form a
tripod and will find a place to stand, then all you do is lower the
fourth.
What you end up with in terms of level, well that's another matter
entirely.
On Sat, 26 Jun 2010 16:29:04 GMT, [email protected] (Doug Miller) wrote:
>In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>
>>Wrong. What matters is the *center* of the table (assuming a "normal" shaped
>>table) must not be outside the base. It doesn't matter how much of the edge
>>it outside, as long as the center of gravity is inside.
>
>Nonsense.
Nonsense yourself. Physics doesn't lie.
>Consider a table having a top six feet square, and four legs which form a
>one-foot square exactly centered under the top. The table is "stable" under
>your definition -- that is, it won't fall over in and of itself -- but it's
>obviously very susceptible to being tipped by even a modest weight. Probably a
>single coffee cup at the edge would be sufficient.
It is stable. However, the measure of stability, which I've stated *many*
times here, is the distance from the *CENTER* (of gravity) to the edges of the
base (defined as lines between the feet, whether these lines or the center are
in fact within the table, or not.
>Now consider a similar table, with the legs moved outward so that they form a
>*five*-foot square exactly centered under the top. The center of gravity has
>not moved, yet this second table is clearly far more resistant to being tipped
>over.
Do learn to read. The edges of the table have nothing to do with stability.
The stability is defined only by the center of gravity and the base. Moving
your legs changed the base. *Obviously* it's more stable. The *fact* is that
the stability is defined by the COG and the base.
>[...]
>>The edges don't matter at all. *ALL* of the mass acts as if it is located at
>>the center (of gravity).
>
>Sorry, but you're entirely mistaken, because you're considering the wrong
>problem.
I don't know what universe you're in. That's the way physics works in this.
>You have completely and entirely correctly described what is necessary to
>ensure that a table will not fall over _on its own_.
Nonsense.
>The problem under discussion, however, is how best to make a table that will
>provide the greatest resistance to tipping over when pressure is applied to
>the portion of the tabletop that overhangs the base. These are two entirely
>separate questions.
...and that is measured by the distance between the point on the "floor" under
the COG and the base line(s), *ONLY*.
>How much of the edge is outside the base is the *only* thing that matters.
Wrong. What matters is the distance form the COG to the base. Period!
>You're right that an object can't fall over if its center of gravity is over
>its base. But you're ignoring the simple and obvious fact that the farther its
>edges extend beyond the base, the easier it becomes to tip it far enough that
>the center of gravity is no longer over the base.
It's not a matter of falling over by itself at all. The force it requires tip
the table over is determined by the distance from the COG to the base edge as
the moment arm and the mass. The edge of the table top has *nothing* to do
with it.
On Jun 24, 7:48=A0pm, [email protected] (Robert Bonomi) wrote:
> In article <[email protected]>,
>
>
>
> alexy =A0<[email protected]> wrote:
> >[email protected] (Doug Miller) wrote:
>
> >>In article <[email protected]>, "Bea Essor"
> ><[email protected]> wrote:
>
> >>>I don't think you have a math problem. The way I see it, if you were t=
o
> >>>build a square or rectangular table with three straight legs two of th=
e
> >>>corners would be supported, and the other two would not. =A0If someone=
leans
> >>>too heavily, or puts something =A0heavy on the table it may tip. =A0My=
solution
> >>>would be to make a rectangular top. Place two straight legs on the nar=
row
> >>>end as you normally would. On the other end I would use a " V " shaped=
leg
> >>>going from the corners to the center spot on the floor.
>
> >>That isn't going to make it any more stable -- it still has only one po=
int of
> >>support at that end, and it's still in the same place.
>
> >Correct. Another "solution" posted here has a similar problem. If you
> >let two legs come together and attach at a single pivot point, they
> >might as well be one leg, as far as stability goes (assuming all the
> >mass is above the pivot point).
>
> NOT true. =A0Consider the stability of a trestle table. It has only -two-=
legs,
> each of which spreads into two widely separated feet at the ground.
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).
> On Jun 24, 7:48=A0pm, [email protected] (Robert Bonomi) wrote:
> > In article <[email protected]>,
> >
> >
> >
> > alexy =A0<[email protected]> wrote:
> > >[email protected] (Doug Miller) wrote:
> >
> > >>In article <[email protected]>, "Bea Essor"
> > ><[email protected]> wrote:
> >
> > >>>I don't think you have a math problem. The way I see it, if you were
t=
> o
> > >>>build a square or rectangular table with three straight legs two of
th=
> e
> > >>>corners would be supported, and the other two would not. =A0If
someone=
> leans
> > >>>too heavily, or puts something =A0heavy on the table it may tip.
=A0My=
> solution
> > >>>would be to make a rectangular top. Place two straight legs on the
nar=
> row
> > >>>end as you normally would. On the other end I would use a " V "
shaped=
> leg
> > >>>going from the corners to the center spot on the floor.
> >
> > >>That isn't going to make it any more stable -- it still has only one
po=
> int of
> > >>support at that end, and it's still in the same place.
> >
> > >Correct. Another "solution" posted here has a similar problem. If you
> > >let two legs come together and attach at a single pivot point, they
> > >might as well be one leg, as far as stability goes (assuming all the
> > >mass is above the pivot point).
> >
> > NOT true. =A0Consider the stability of a trestle table. It has only -two-
=
> legs,
> > each of which spreads into two widely separated feet at the ground.
>
> 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).
>
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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On 26 Jun 2010 00:41:06 GMT, [email protected] wrote:
>
>
>> On Jun 24, 7:48=A0pm, [email protected] (Robert Bonomi) wrote:
>> > In article <[email protected]>,
>> >
>> >
>> >
>> > alexy =A0<[email protected]> wrote:
>> > >[email protected] (Doug Miller) wrote:
>> >
>> > >>In article <[email protected]>, "Bea Essor"
>> > ><[email protected]> wrote:
>> >
>> > >>>I don't think you have a math problem. The way I see it, if you were
>t=
>> o
>> > >>>build a square or rectangular table with three straight legs two of
>th=
>> e
>> > >>>corners would be supported, and the other two would not. =A0If
>someone=
>> leans
>> > >>>too heavily, or puts something =A0heavy on the table it may tip.
>=A0My=
>> solution
>> > >>>would be to make a rectangular top. Place two straight legs on the
>nar=
>> row
>> > >>>end as you normally would. On the other end I would use a " V "
>shaped=
>> leg
>> > >>>going from the corners to the center spot on the floor.
>> >
>> > >>That isn't going to make it any more stable -- it still has only one
>po=
>> int of
>> > >>support at that end, and it's still in the same place.
>> >
>> > >Correct. Another "solution" posted here has a similar problem. If you
>> > >let two legs come together and attach at a single pivot point, they
>> > >might as well be one leg, as far as stability goes (assuming all the
>> > >mass is above the pivot point).
>> >
>> > NOT true. =A0Consider the stability of a trestle table. It has only -two-
>=
>> legs,
>> > each of which spreads into two widely separated feet at the ground.
>>
>> 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).
>>
>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!
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. ;-)
> On 26 Jun 2010 00:41:06 GMT, [email protected] wrote:
>
> >
> >
> >> On Jun 24, 7:48=A0pm, [email protected] (Robert Bonomi) wrote:
> >> > In article <[email protected]>,
> >> >
> >> >
> >> >
> >> > alexy =A0<[email protected]> wrote:
> >> > >[email protected] (Doug Miller) wrote:
> >> >
> >> > >>In article <[email protected]>, "Bea
> Essor"
> >> > ><[email protected]> wrote:
> >> >
> >> > >>>I don't think you have a math problem. The way I see it, if you were
> >t=
> >> o
> >> > >>>build a square or rectangular table with three straight legs two of
> >th=
> >> e
> >> > >>>corners would be supported, and the other two would not. =A0If
> >someone=
> >> leans
> >> > >>>too heavily, or puts something =A0heavy on the table it may tip.
> >=A0My=
> >> solution
> >> > >>>would be to make a rectangular top. Place two straight legs on the
> >nar=
> >> row
> >> > >>>end as you normally would. On the other end I would use a " V "
> >shaped=
> >> leg
> >> > >>>going from the corners to the center spot on the floor.
> >> >
> >> > >>That isn't going to make it any more stable -- it still has only one
> >po=
> >> int of
> >> > >>support at that end, and it's still in the same place.
> >> >
> >> > >Correct. Another "solution" posted here has a similar problem. If you
> >> > >let two legs come together and attach at a single pivot point, they
> >> > >might as well be one leg, as far as stability goes (assuming all the
> >> > >mass is above the pivot point).
> >> >
> >> > NOT true. =A0Consider the stability of a trestle table. It has only -
> two-
> >=
> >> legs,
> >> > each of which spreads into two widely separated feet at the ground.
> >>
> >> 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).
> >>
> >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!
>
> 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. ;-)
I think you've given an elegant definition of stability but I don't see how that fixes
the positions of the legs under the table. Haven't you just reworded the original
problem?
You're right, though - the solution for a rectangle is simply the projected solution for
a square. For a random shape 'trickier' doesn't begin to describe it. Try 'nightmarish'!
Incidentally, when you spread the three legs as far as possible, you end up with two in
adjacent corners and one half-way along the opposite side. That is _not_ the most stable
configuration. Another possibility is with two legs somewhere along adjacent sides and
one in the opposite corner. The greatest spread here would be with a leg in each of three
corners - not too stable either.
Tain't easy, is it!?
Nemo
-----------------------------------------------------------
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-----------------------------------------------------------
On 26 Jun 2010 22:25:55 GMT, [email protected] wrote:
>
>
>> On 26 Jun 2010 00:41:06 GMT, [email protected] wrote:
>>
>> >
>> >
>> >> On Jun 24, 7:48=A0pm, [email protected] (Robert Bonomi) wrote:
>> >> > In article <[email protected]>,
>> >> >
>> >> >
>> >> >
>> >> > alexy =A0<[email protected]> wrote:
>> >> > >[email protected] (Doug Miller) wrote:
>> >> >
>> >> > >>In article <[email protected]>, "Bea
>> Essor"
>> >> > ><[email protected]> wrote:
>> >> >
>> >> > >>>I don't think you have a math problem. The way I see it, if you were
>> >t=
>> >> o
>> >> > >>>build a square or rectangular table with three straight legs two of
>> >th=
>> >> e
>> >> > >>>corners would be supported, and the other two would not. =A0If
>> >someone=
>> >> leans
>> >> > >>>too heavily, or puts something =A0heavy on the table it may tip.
>> >=A0My=
>> >> solution
>> >> > >>>would be to make a rectangular top. Place two straight legs on the
>> >nar=
>> >> row
>> >> > >>>end as you normally would. On the other end I would use a " V "
>> >shaped=
>> >> leg
>> >> > >>>going from the corners to the center spot on the floor.
>> >> >
>> >> > >>That isn't going to make it any more stable -- it still has only one
>> >po=
>> >> int of
>> >> > >>support at that end, and it's still in the same place.
>> >> >
>> >> > >Correct. Another "solution" posted here has a similar problem. If you
>> >> > >let two legs come together and attach at a single pivot point, they
>> >> > >might as well be one leg, as far as stability goes (assuming all the
>> >> > >mass is above the pivot point).
>> >> >
>> >> > NOT true. =A0Consider the stability of a trestle table. It has only -
>> two-
>> >=
>> >> legs,
>> >> > each of which spreads into two widely separated feet at the ground.
>> >>
>> >> 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).
>> >>
>> >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!
>>
>> 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. ;-)
>
>I think you've given an elegant definition of stability but I don't see how that fixes
>the positions of the legs under the table. Haven't you just reworded the original
>problem?
>
>You're right, though - the solution for a rectangle is simply the projected solution for
>a square. For a random shape 'trickier' doesn't begin to describe it. Try 'nightmarish'!
Calculus.
>Incidentally, when you spread the three legs as far as possible, you end up with two in
>adjacent corners and one half-way along the opposite side. That is _not_ the most stable
>configuration. Another possibility is with two legs somewhere along adjacent sides and
>one in the opposite corner. The greatest spread here would be with a leg in each of three
>corners - not too stable either.
Largest distance between the CoG (center of the table) and the lines between
the legs.
>Tain't easy, is it!?
Yes, in this case it really is.
On 6/26/2010 6:25 PM, [email protected] wrote:
>> On 26 Jun 2010 00:41:06 GMT, [email protected] wrote:
>>
>>>
>>>
>>>> On Jun 24, 7:48=A0pm, [email protected] (Robert Bonomi) wrote:
>>>>> In article<[email protected]>,
>>>>>
>>>>>
>>>>>
>>>>> alexy =A0<[email protected]> wrote:
>>>>>> [email protected] (Doug Miller) wrote:
>>>>>
>>>>>>> In article<[email protected]>, "Bea
>> Essor"
>>>>>> <[email protected]> wrote:
>>>>>
>>>>>>>> I don't think you have a math problem. The way I see it, if you were
>>> t=
>>>> o
>>>>>>>> build a square or rectangular table with three straight legs two of
>>> th=
>>>> e
>>>>>>>> corners would be supported, and the other two would not. =A0If
>>> someone=
>>>> leans
>>>>>>>> too heavily, or puts something =A0heavy on the table it may tip.
>>> =A0My=
>>>> solution
>>>>>>>> would be to make a rectangular top. Place two straight legs on the
>>> nar=
>>>> row
>>>>>>>> end as you normally would. On the other end I would use a " V "
>>> shaped=
>>>> leg
>>>>>>>> going from the corners to the center spot on the floor.
>>>>>
>>>>>>> That isn't going to make it any more stable -- it still has only one
>>> po=
>>>> int of
>>>>>>> support at that end, and it's still in the same place.
>>>>>
>>>>>> Correct. Another "solution" posted here has a similar problem. If you
>>>>>> let two legs come together and attach at a single pivot point, they
>>>>>> might as well be one leg, as far as stability goes (assuming all the
>>>>>> mass is above the pivot point).
>>>>>
>>>>> NOT true. =A0Consider the stability of a trestle table. It has only -
>> two-
>>> =
>>>> legs,
>>>>> each of which spreads into two widely separated feet at the ground.
>>>>
>>>> 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).
>>>>
>>> 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!
>>
>> 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. ;-)
>
> I think you've given an elegant definition of stability but I don't see how that fixes
> the positions of the legs under the table. Haven't you just reworded the original
> problem?
>
> You're right, though - the solution for a rectangle is simply the projected solution for
> a square. For a random shape 'trickier' doesn't begin to describe it. Try 'nightmarish'!
>
> Incidentally, when you spread the three legs as far as possible, you end up with two in
> adjacent corners and one half-way along the opposite side. That is _not_ the most stable
> configuration. Another possibility is with two legs somewhere along adjacent sides and
> one in the opposite corner. The greatest spread here would be with a leg in each of three
> corners - not too stable either.
>
> Tain't easy, is it!?
Mathematically you'd want to find the position that minimizes the
tipping moment for all locations. Actually doing that would be more
work that I want to go into.
>
> Nemo
>
>
> -----------------------------------------------------------
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> .... http://www.sb-software.com/android
> -----------------------------------------------------------
<snip>
> >> 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. ;-)
> >
> > I think you've given an elegant definition of stability but I
don't see
> how that fixes
> > the positions of the legs under the table. Haven't you just
reworded the
> original
> > problem?
> >
> > You're right, though - the solution for a rectangle is simply
the
> projected solution for
> > a square. For a random shape 'trickier' doesn't begin to
describe it. Try
> 'nightmarish'!
> >
> > Incidentally, when you spread the three legs as far as
possible, you end
> up with two in
> > adjacent corners and one half-way along the opposite side. That
is _not_
> the most stable
> > configuration. Another possibility is with two legs somewhere
along
> adjacent sides and
> > one in the opposite corner. The greatest spread here would be
with a leg
> in each of three
> > corners - not too stable either.
> >
> > Tain't easy, is it!?
>
> Mathematically you'd want to find the position that minimizes the
> tipping moment for all locations. Actually doing that would be
more
> work that I want to go into.
J. Clarke, I think you're right. Mathematically, we want to find
the postions of the three legs that minimize the tipping moment.
So - any suggestions?
Nemo
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Posted using Android Newsgroup Downloader:
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In article <[email protected]>, [email protected] wrote:
><snip>
>
>J. Clarke, I think you're right. Mathematically, we want to find
>the postions of the three legs that minimize the tipping moment.
>
>So - any suggestions?
http://mathworld.wolfram.com/EquilateralTriangle.html
Scroll down to the two figures described by equations 18 through 21. The left
figure is the one you want. That's demonstrably optimal: any rotation or
translation of that triangle within the square necessarily moves the midpoint
of at least one side of the triangle farther away from the nearest corner of
the square and hence increases the tipping moment about that side.
> In article <[email protected]>,
> [email protected] wrote:
> ><snip>
> >
> >J. Clarke, I think you're right. Mathematically, we want to find
> >the postions of the three legs that minimize the tipping moment.
> >
> >So - any suggestions?
>
> http://mathworld.wolfram.com/EquilateralTriangle.html
>
> Scroll down to the two figures described by equations 18 through 21. The
> left
> figure is the one you want. That's demonstrably optimal: any rotation or
> translation of that triangle within the square necessarily moves the
> midpoint
> of at least one side of the triangle farther away from the nearest corner
of
> the square and hence increases the tipping moment about that side.
.. I don't understand your reasoning but that doesn't make it wrong.
I like the look of an equilateral triangle with one point at the mid-point of
one of the sides and the other two touching the adjacent sides (see Legs1.bmp
attached). I think this is close to the optimum placement of the legs, but
we're not there yet. If you move the side of the triangle that's parallel to
one of the sides of the square closer to the center I think you'll see that
stability increases, up to a point.
But I still can't prove it!!
BTW -- great web site! Thank you!
Nemo
-----------------------------------------------------------
Posted using Android Newsgroup Downloader:
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-----------------------------------------------------------
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end
In article <[email protected]>,
<[email protected]> wrote:
>
>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.
Nemo,
The 'theory' _is_ simple. <grin> figure out where the center of mass
is for whatever the table shape is, and position the _ground_ points of
the legs as far away as practical.
legs that slant outward from the table will provide better stability than
pure vertical ones.
The -best- three-legged placement you can do with a rectangular top is two
legs at opposite ends of one of the *short* sides, and the third leg in
the middle of the other short side. (comment, there is a _reason_ that
'ironing boards" -- for those who remember what _those_ are -- are built
that way.)
Here's the way it works: Draw the triangle that represents the leg
positions. No possible pressure _inside_ that triangle can cause the
table to tip, short of structural failure.
Tipping occurs when sufficient pressure is applied -outside- that triangle.
The shorter the moment arm that that pressure has to work on, where the
fulcrum is the nearest edge of the triangle, the more force it actually
takes to reach the tipping point.
For a rectangular top, there are two possible 'maximum size' triangles.
Two legs on a narrow end, and one in the middle of the other narrow end
and two legs on a wide side, with the third in the middle of the other side.
Both forms provide _exactly_ the same size 'stable area' (inside the triangle),
ie., half the total table surface.
*BUT* the distance from an 'unsupported' corner to the closest point _on_
the leg triangle is smaller when the 3rd leg is in the middle of the short
side. Which means that it is -harder- to tip by applying pressure there.
Also, and *very* counter-intuitively, angling the two short-side legs out
past the long side of the table does -more- to improve stability than does
extending the single leg past the short end. Of course, doing -both- is
better than doing just one (either one). <grin>
On Jun 23, 1:40=A0am, [email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two are=
at
> the same level. Anywhere I put a four-legged table, it rocks. So I though=
t
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect tha=
t a
> solution for a rectangle would be proportional to the square. There might=
be
> two solutions, one with one leg in a corner and one with it half-way alon=
g
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
Not so much math as physics. For an object to stand without falling
over, its center of gravity must be above its base. The further
inside the base the COG is the more stable it will be (you have to tip
it far enough to get the COG outside the base).
For your table, assume the mass is in the top (ignore legs). If it's
large compared to its thickness, ignore the thickness. The COG is
then pretty much the center of the top. The problem then is to place
the legs so this point is the furthest from the lines connecting the
legs (the "base"). In the case of a square, this is easy (pick two
corners and the middle of the opposing side). For a rectangle, I
think it becomes clear if the rectangle is exaggerated; two adjacent
corners on a long side and the opposite center.
On Jun 22, 11:40=A0pm, [email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two are=
at
> the same level. Anywhere I put a four-legged table, it rocks. So I though=
t
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect tha=
t a
> solution for a rectangle would be proportional to the square. There might=
be
> two solutions, one with one leg in a corner and one with it half-way alon=
g
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
> Nemo
>
> -----------------------------------------------------------
> Posted using Android Newsgroup Downloader:
> =A0 =A0 ....http://www.sb-software.com/android
> -----------------------------------------------------------
The simpliest solution is to make a small wedge of the wood of your
choice and slip it under the leg that appears to be the shortest when
the table is standing on the flagstore. It will make it solid. If the
table is moved a different leg will appear to be the shortest, so use
the wedge on that leg.
Al
On Wed, 23 Jun 2010 06:38:26 -0700 (PDT), RicodJour
<[email protected]> wrote:
>Substituting an inherently less stable form for a slightly wobbly
>table is a poor trade-off.
>All you need is to have one leg of the four adjustable.
An easier solution should the three leg choice be preferable is to
forgo the square/rectanble table and make it round.
On Mon, 28 Jun 2010 22:58:50 -0400, alexy <[email protected]> wrote:
>>Go for 4 legs with adjustable feet. (if the table just has to be
>>stable and not necessarily level, you just need 2 adjustable feet
>Actually, only one.
That's not right. If the terrain that the table sits on is varied
enough, then two adjustable feet are needed to keep the table surface
horizontal enough to stop things from sliding off it.
[email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two are at
> the same level. Anywhere I put a four-legged table, it rocks. So I thought
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect that a
> solution for a rectangle would be proportional to the square. There might be
> two solutions, one with one leg in a corner and one with it half-way along
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
Why wouldn't you vary the length of the legs?
--
Uno
[email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two are at
> the same level. Anywhere I put a four-legged table, it rocks. So I thought
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect that a
> solution for a rectangle would be proportional to the square. There might be
> two solutions, one with one leg in a corner and one with it half-way along
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
> Nemo
>
> -----------------------------------------------------------
> Posted using Android Newsgroup Downloader:
> .... http://www.sb-software.com/android
> -----------------------------------------------------------
Go for 4 legs with adjustable feet. (if the table just has to be
stable and not necessarily level, you just need 2 adjustable feet --
or one if you also get to turn the table)
Bob
On Jun 29, 12:21=A0am, "Josepi" <[email protected]> wrote:
> That's not right. If the terrain that the table sits on is varied
> enough, then two adjustable feet are needed to keep the table surface
> horizontal enough to stop things from sliding off it.
Now you want the fucking thing thing to be horizontal too?
Could I explain the post I would gladly do so.
I am a moron just as are you all so I am lost.
"Josepi" <[email protected]> wrote in message
news:fz%[email protected]...
We gotz some sucker bait floating here...LOL
"Swingman" <[email protected]> wrote in message
news:[email protected]...
Obviously one where practical overrules theoretical ... in theory trolls
can't live without bridges.
On 6/26/2010 11:42 PM, [email protected] wrote:
> I don't know what universe you're in.
"basilisk" <[email protected]> wrote in message
news:[email protected]...
>
> <[email protected]> wrote in message
> news:[email protected]...
>>I have a flagged patio. The flags are odd shapes and sizes and
>>no two are at
>> the same level. Anywhere I put a four-legged table, it rocks.
>> So I thought
>> I'd build a three-legged table, but I'd like it to be
>> rectangular.
>>
>> Here's the question: where do the legs go for maximum
>> stability, assuming
>> they stick straight down underneath?
>>
>> I think the simplest solution would be for a square top and I
>> suspect that a
>> solution for a rectangle would be proportional to the square.
>> There might be
>> two solutions, one with one leg in a corner and one with it
>> half-way along
>> one edge.
>>
>> The math is completely beyond me. Is there a genius amongst us?
>>
>> Nemo
>>
>> -----------------------------------------------------------
>> Posted using Android Newsgroup Downloader:
>> .... http://www.sb-software.com/android
>> -----------------------------------------------------------
>
> Make two triangular tables that can be arranged in the size
> rectangle
> you want. preserves balance and stability and gives you the
> shape you
> want.
>
> basilisk
>
The idea is good, but I suspect that the 6 resulting legs would
hinder the use of the table with chairs.
Nonny
--
On most days,
its just not worth
the effort of chewing
through the restraints..
In article <[email protected]>,
[email protected] <[email protected]> wrote:
>On Fri, 25 Jun 2010 21:33:10 -0500, [email protected] (Robert
>Bonomi) wrote:
>
>>In article <[email protected]>,
>>alexy <[email protected]> wrote:
>>>[email protected] (Robert Bonomi) wrote:
>>>
>>>>In article <[email protected]>,
>>>>alexy <[email protected]> wrote:
>>>>>[email protected] (Doug Miller) wrote:
>>>>>
>>>>>>In article <[email protected]>, "Bea Essor"
>>>>><[email protected]> wrote:
>>>>>>>
>>>>>>>I don't think you have a math problem. The way I see it, if you were to
>>>>>>>build a square or rectangular table with three straight legs two of the
>>>>>>>corners would be supported, and the other two would not. If
>someone leans
>>>>>>>too heavily, or puts something heavy on the table it may tip. My
>solution
>>>>>>>would be to make a rectangular top. Place two straight legs on the narrow
>>>>>>>end as you normally would. On the other end I would use a " V "
>shaped leg
>>>>>>>going from the corners to the center spot on the floor.
>>>>>>
>>>>>>That isn't going to make it any more stable -- it still has only one
>>>point of
>>>>>>support at that end, and it's still in the same place.
>>>>>
>>>>>Correct. Another "solution" posted here has a similar problem. If you
>>>>>let two legs come together and attach at a single pivot point, they
>>>>>might as well be one leg, as far as stability goes (assuming all the
>>>>>mass is above the pivot point).
>>>>
>>>>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.
>>>
>>>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.
>>
>>It doesn't matter. What counts is where the each foot is in relation to
>>the edge of the table.
>
>Actually, what matters is where each foot is in relation to the *center* of
>the table.
FALSE TO FACT.
Regardless of the shape of the top, *or* the number of legs, anything -inside-
the polygon described by the footprint of the legs is irrelevant to stability.
Any vertical pressure within that polygon cannot cause the table to tip, short
of induced structural failure, that is.
What matters is that which is _outside_ said polygon -- pressure 'out there'
_will_ provide a 'tipping force', with the fulcrum being the nearest segment
of the polygon. Best stability is attained by _minimizing_ the maximum
distance from the _edges_ of the top to the polygon of the legs.
Faked headers from the cyber bully gang.
"Josepi" <[email protected]> wrote in message
news:fz%[email protected]...
We gotz some sucker bait floating here...LOL
"Swingman" <[email protected]> wrote in message
news:[email protected]...
Obviously one where practical overrules theoretical ... in theory trolls
can't live without bridges.
On 6/26/2010 11:42 PM, [email protected] wrote:
> I don't know what universe you're in.
On Tue, 29 Jun 2010 09:23:12 -0400, alexy wrote:
> "Josepi" <[email protected]> wrote:
>
>>Sorry. Only one adjustable leg would be required for a three legged
>>table to keep it level anywhere.
>
> That requires a continuous (more accurately differentiable) surface.
> E.g.m consider a tripod with 2' spacing between feet, placed on a
> surface consisting of four 1.25' square blocks, with the taller ones 1",
> 2" and 3" above the lowest one. You can't fit two of the legs on the
> same block, so the two fixed legs will not be the same height--tilted
> table.
I have the answer, not the one the OP wanted but an answer none the less.
Build a tripod with a center pipe mounted on a ball joint to fit the
table top to, the lower end of the pipe will have a 2 cubic foot
container filled with mercury(close as possible to floor) weighing about
1700 pounds,
table will be stable on any footing and top will be level
basilisk
--
A wink is as good as a nod to a blind horse
Make it a 4 leged table, with one of the legs with an adjustable /
telescoping foot.
For an example see
http://www.leevalley.com/en/garden/page.aspx?p=59776&cat=2,42194 (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
http://www.leevalley.com/en/hardware/page.aspx?p=40040&cat=3,40993,41283
Why were the stones not set level ? I can understand each stone being a
unique shape - that is a feature of flagstones
<[email protected]> wrote in message
news:[email protected]...
>I have a flagged patio. The flags are odd shapes and sizes and no two are
>at
> the same level. Anywhere I put a four-legged table, it rocks. So I thought
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect that
> a
> solution for a rectangle would be proportional to the square. There might
> be
> two solutions, one with one leg in a corner and one with it half-way along
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
> Nemo
>
> -----------------------------------------------------------
> Posted using Android Newsgroup Downloader:
> .... http://www.sb-software.com/android
> -----------------------------------------------------------
Sorry. Only one adjustable leg would be required for a three legged table to
keep it level anywhere.
This would not apply for a four legged table.
"Josepi" <[email protected]> wrote in message
news:[email protected]...
Only one would be required if you rotate it.
"Upscale" <[email protected]> wrote in message
news:[email protected]...
That's not right. If the terrain that the table sits on is varied
enough, then two adjustable feet are needed to keep the table surface
horizontal enough to stop things from sliding off it.
On Mon, 28 Jun 2010 22:58:50 -0400, alexy <[email protected]> wrote:
>>Go for 4 legs with adjustable feet. (if the table just has to be
>>stable and not necessarily level, you just need 2 adjustable feet
>Actually, only one.
Fuck Yes!
Keep it up and you will be horizontal. Fucked UP Google Tard TARD!
Robatoy <[email protected]> wrote in message
news:[email protected]
..
>On Jun 29, 12:21 am, "Josepi" <[email protected]> wrote:
>
>> That's not right. If the terrain that the table sits on is varied
>> enough, then two adjustable feet are needed to keep the table surface
>> horizontal enough to stop things from sliding off it.
>
>
>Now you want the fucking thing thing to be horizontal too?
We gotz some big bridges here...LOL
"Swingman" <[email protected]> wrote in message
news:[email protected]...
Obviously one where practical overrules theoretical ... in theory trolls
can't live without bridges.
On 6/26/2010 11:42 PM, [email protected] wrote:
> I don't know what universe you're in.
[email protected] wrote in
news:[email protected]:
> I have a flagged patio. The flags are odd shapes and sizes and no two
> are at the same level. Anywhere I put a four-legged table, it rocks.
> So I thought I'd build a three-legged table, but I'd like it to be
> rectangular.
>
> Here's the question: where do the legs go for maximum stability,
> assuming they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect
> that a solution for a rectangle would be proportional to the square.
> There might be two solutions, one with one leg in a corner and one
> with it half-way along one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
> Nemo
>
> -----------------------------------------------------------
> Posted using Android Newsgroup Downloader:
> .... http://www.sb-software.com/android
> -----------------------------------------------------------
Not nearly so glamorous, but why don't you just use some lege levelers.
"pete" <[email protected]> wrote in message
news:[email protected]...
> On 23 Jun 2010 06:40:40 GMT, [email protected] wrote:
>> I have a flagged patio. The flags are odd shapes and sizes and
>> no two are at
>> the same level. Anywhere I put a four-legged table, it rocks.
>> So I thought
>> I'd build a three-legged table, but I'd like it to be
>> rectangular.
>>
>> Here's the question: where do the legs go for maximum
>> stability, assuming
>> they stick straight down underneath?
>
> As a starting point, I'd suggest making the rectangle not too
> long (so the
> ratio of width to length isn't too great - maybe 2:1, max) and
> not too narrow.
> Then just place two of the legs at corners of the same long side
> with the
> third one in the middle of the opposite side.
> It'll be "good enough" if not mathematically, precisely optimal.
> However
> the advantage of this simple approach is that you'll get your
> table, rather
> than be frozen at the design stage trying to extract the last
> .001% of
> stability.
>
I agree with this. There's no rule or benefit from the triangle
formed by the three legs being equilateral.
Nonny
>> I think the simplest solution would be for a square top and I
>> suspect that a
>> solution for a rectangle would be proportional to the square.
>> There might be
>> two solutions, one with one leg in a corner and one with it
>> half-way along
>> one edge.
>>
>> The math is completely beyond me. Is there a genius amongst us?
>>
>> Nemo
>>
>> -----------------------------------------------------------
>> Posted using Android Newsgroup Downloader:
>> .... http://www.sb-software.com/android
>> -----------------------------------------------------------
--
On most days,
it's just not worth
the effort of chewing
through the restraints..
With reference to my post above, for you artistic folks:
The fork/foot lengths can be much greater difference when each fork's/
foot's angle, off the leg, differs also. Each fork's different angle,
off the leg, will dictate how long (*or there about) each fork/foot
will need to be.
*or there about: Since the leg rotates, you don't have to be exact
(1/8" to 1/4" variance in my first post), hence allowing for
adjusting, when rotated, any positioning on uneven surfaces.
The artistic look of your design can be had when the surface (floor)
is level, too, not just for uneven surfaces, LOL.
Sonny
On Fri, 25 Jun 2010 22:22:00 -0500, [email protected] (Robert
Bonomi) wrote:
>In article <[email protected]>,
>[email protected] <[email protected]> wrote:
>>On Fri, 25 Jun 2010 21:33:10 -0500, [email protected] (Robert
>>Bonomi) wrote:
>>
>>>In article <[email protected]>,
>>>alexy <[email protected]> wrote:
>>>>[email protected] (Robert Bonomi) wrote:
>>>>
>>>>>In article <[email protected]>,
>>>>>alexy <[email protected]> wrote:
>>>>>>[email protected] (Doug Miller) wrote:
>>>>>>
>>>>>>>In article <[email protected]>, "Bea Essor"
>>>>>><[email protected]> wrote:
>>>>>>>>
>>>>>>>>I don't think you have a math problem. The way I see it, if you were to
>>>>>>>>build a square or rectangular table with three straight legs two of the
>>>>>>>>corners would be supported, and the other two would not. If
>>someone leans
>>>>>>>>too heavily, or puts something heavy on the table it may tip. My
>>solution
>>>>>>>>would be to make a rectangular top. Place two straight legs on the narrow
>>>>>>>>end as you normally would. On the other end I would use a " V "
>>shaped leg
>>>>>>>>going from the corners to the center spot on the floor.
>>>>>>>
>>>>>>>That isn't going to make it any more stable -- it still has only one
>>>>point of
>>>>>>>support at that end, and it's still in the same place.
>>>>>>
>>>>>>Correct. Another "solution" posted here has a similar problem. If you
>>>>>>let two legs come together and attach at a single pivot point, they
>>>>>>might as well be one leg, as far as stability goes (assuming all the
>>>>>>mass is above the pivot point).
>>>>>
>>>>>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.
>>>>
>>>>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.
>>>
>>>It doesn't matter. What counts is where the each foot is in relation to
>>>the edge of the table.
>>
>>Actually, what matters is where each foot is in relation to the *center* of
>>the table.
>
>FALSE TO FACT.
Wrong.
>Regardless of the shape of the top, *or* the number of legs, anything -inside-
>the polygon described by the footprint of the legs is irrelevant to stability.
>Any vertical pressure within that polygon cannot cause the table to tip, short
>of induced structural failure, that is.
Right. But it's the CENTER OF GRAVITY that must be above the base, which for
a normalish table will be at the center of the table. Not that for a really
weird table the CoG doesn't even have to be on the surface. The entire table
can be outside the legs (think donut) and it can still be stable. The CoG
*must* be within the base for it to be stable.
>What matters is that which is _outside_ said polygon -- pressure 'out there'
Wrong. What matters is the *center* of the table (assuming a "normal" shaped
table) must not be outside the base. It doesn't matter how much of the edge
it outside, as long as the center of gravity is inside.
>_will_ provide a 'tipping force', with the fulcrum being the nearest segment
>of the polygon. Best stability is attained by _minimizing_ the maximum
>distance from the _edges_ of the top to the polygon of the legs.
The edges don't matter at all. *ALL* of the mass acts as if it is located at
the center (of gravity).
On 6/26/2010 11:42 PM, [email protected] wrote:
> I don't know what universe you're in.
Obviously one where practical overrules theoretical ... in theory trolls
can't live without bridges.
--
www.e-woodshop.net
Last update: 4/15/2010
KarlC@ (the obvious)
On Jun 23, 2:40=A0am, [email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two are=
at
> the same level. Anywhere I put a four-legged table, it rocks. So I though=
t
> I'd build a three-legged table, but I'd like it to be rectangular.
Substituting an inherently less stable form for a slightly wobbly
table is a poor trade-off.
All you need is to have one leg of the four adjustable.
R
On Jun 22, 11:40=A0pm, [email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two are=
at
> the same level. Anywhere I put a four-legged table, it rocks. So I though=
t
> I'd build a three-legged table, but I'd like it to be rectangular.
If the flags don't have sharp discontinuities where they meet (i.e. if
the surface is uneven but not abrupt) then you can rotate the
four-leg table into an orientation where all four legs are on the
ground.
Alternately, the table can be made to flex slightly
to take up the irregularity; this means your table top cannot
be glass or stone...
The 'adjustable leg' solution might be simplified with a
good McPherson strut.
We gotz some sucker bait floating here...LOL
"Swingman" <[email protected]> wrote in message
news:[email protected]...
Obviously one where practical overrules theoretical ... in theory trolls
can't live without bridges.
On 6/26/2010 11:42 PM, [email protected] wrote:
> I don't know what universe you're in.
In article <[email protected]>,
alexy <[email protected]> wrote:
>[email protected] (Robert Bonomi) wrote:
>
>>In article <[email protected]>,
>>alexy <[email protected]> wrote:
>>>[email protected] (Doug Miller) wrote:
>>>
>>>>In article <[email protected]>, "Bea Essor"
>>><[email protected]> wrote:
>>>>>
>>>>>I don't think you have a math problem. The way I see it, if you were to
>>>>>build a square or rectangular table with three straight legs two of the
>>>>>corners would be supported, and the other two would not. If someone leans
>>>>>too heavily, or puts something heavy on the table it may tip. My solution
>>>>>would be to make a rectangular top. Place two straight legs on the narrow
>>>>>end as you normally would. On the other end I would use a " V " shaped leg
>>>>>going from the corners to the center spot on the floor.
>>>>
>>>>That isn't going to make it any more stable -- it still has only one
>point of
>>>>support at that end, and it's still in the same place.
>>>
>>>Correct. Another "solution" posted here has a similar problem. If you
>>>let two legs come together and attach at a single pivot point, they
>>>might as well be one leg, as far as stability goes (assuming all the
>>>mass is above the pivot point).
>>
>>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.
>
>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.
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.
"Nonny" <[email protected]> wrote in message
news:[email protected]...
>
> "basilisk" <[email protected]> wrote in message
> news:[email protected]...
>>
>> <[email protected]> wrote in message
>> news:[email protected]...
>>>I have a flagged patio. The flags are odd shapes and sizes and no two are
>>>at
>>> the same level. Anywhere I put a four-legged table, it rocks. So I
>>> thought
>>> I'd build a three-legged table, but I'd like it to be rectangular.
>>>
>>> Here's the question: where do the legs go for maximum stability,
>>> assuming
>>> they stick straight down underneath?
>>>
>>> I think the simplest solution would be for a square top and I suspect
>>> that a
>>> solution for a rectangle would be proportional to the square. There
>>> might be
>>> two solutions, one with one leg in a corner and one with it half-way
>>> along
>>> one edge.
>>>
>>> The math is completely beyond me. Is there a genius amongst us?
>>>
>>> Nemo
>>>
>>> -----------------------------------------------------------
>>> Posted using Android Newsgroup Downloader:
>>> .... http://www.sb-software.com/android
>>> -----------------------------------------------------------
>>
>> Make two triangular tables that can be arranged in the size rectangle
>> you want. preserves balance and stability and gives you the shape you
>> want.
>>
>> basilisk
>>
>
> The idea is good, but I suspect that the 6 resulting legs would hinder the
> use of the table with chairs.
>
> Nonny
>
Why? The legs will all still be at the corners.
basilisk
> "Nonny" <[email protected]> wrote in message
> news:[email protected]...
> >
> > "basilisk" <[email protected]> wrote in message
> > news:[email protected]...
> >>
> >> <[email protected]> wrote in message
> >> news:[email protected]...
> >>>I have a flagged patio. The flags are odd shapes and sizes and no two
are
> >>>at
> >>> the same level. Anywhere I put a four-legged table, it rocks. So I
> >>> thought
> >>> I'd build a three-legged table, but I'd like it to be rectangular.
> >>>
> >>> Here's the question: where do the legs go for maximum stability,
> >>> assuming
> >>> they stick straight down underneath?
> >>>
> >>> I think the simplest solution would be for a square top and I suspect
> >>> that a
> >>> solution for a rectangle would be proportional to the square. There
> >>> might be
> >>> two solutions, one with one leg in a corner and one with it half-way
> >>> along
> >>> one edge.
> >>>
> >>> The math is completely beyond me. Is there a genius amongst us?
> >>>
> >>> Nemo
> >>>
> >>> -----------------------------------------------------------
> >>> Posted using Android Newsgroup Downloader:
> >>> .... http://www.sb-software.com/android
> >>> -----------------------------------------------------------
> >>
> >> Make two triangular tables that can be arranged in the size rectangle
> >> you want. preserves balance and stability and gives you the shape you
> >> want.
> >>
> >> basilisk
> >>
> >
> > The idea is good, but I suspect that the 6 resulting legs would hinder
the
> > use of the table with chairs.
> >
> > Nonny
> >
> Why? The legs will all still be at the corners.
>
> basilisk
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
-----------------------------------------------------------
Posted using Android Newsgroup Downloader:
.... http://www.sb-software.com/android
-----------------------------------------------------------
On Jun 23, 5:50=A0pm, [email protected] wrote:
>
> 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, cutt=
ing
> it diagonally to include three legs on one side of the cut, and hinging i=
t
> 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.
That word, elegant, I do not think it means what you think it means.
Getting unnecessarily complicated is not elegant, simple nor
admirable.
> Legs in two adjacent corners and the third halfway along the opposite sid=
e
> are not the best solution. Better would be to bring the legs away from th=
e
> 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 narr=
ow.
> Draw lines between the legs and imagine them as the axes of rotation. Pus=
h
> 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.
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.
> 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.
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
> On Jun 23, 5:50=A0pm, [email protected] wrote:
> >
> > 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, cutt=
> ing
> > it diagonally to include three legs on one side of the cut, and hinging i=
> t
> > 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.
>
> That word, elegant, I do not think it means what you think it means.
>
> Getting unnecessarily complicated is not elegant, simple nor
> admirable.
>
> > Legs in two adjacent corners and the third halfway along the opposite sid=
> e
> > are not the best solution. Better would be to bring the legs away from th=
> e
> > 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 narr=
> ow.
> > Draw lines between the legs and imagine them as the axes of rotation. Pus=
> h
> > 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.
>
> 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.
>
> > 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.
>
> 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
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
-----------------------------------------------------------
Posted using Android Newsgroup Downloader:
.... http://www.sb-software.com/android
-----------------------------------------------------------
On Jun 24, 8:09=A0pm, [email protected] wrote:
> > On Jun 23, 5:50=3DA0pm, [email protected] wrote:
{there seems to be an attribution missing...}
>
>
> > Yes, and which has very common solutions. =A0There's an old Chinese
> > curse, "May you live in interesting times." =A0You are proposing an
> > interesting solution for your table. =A0Making 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. =A0No?
>
>
> 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!
How often do you have to adjust a table leg? Certainly not every time
you move it.
R
On Fri, 25 Jun 2010 21:33:10 -0500, [email protected] (Robert
Bonomi) wrote:
>In article <[email protected]>,
>alexy <[email protected]> wrote:
>>[email protected] (Robert Bonomi) wrote:
>>
>>>In article <[email protected]>,
>>>alexy <[email protected]> wrote:
>>>>[email protected] (Doug Miller) wrote:
>>>>
>>>>>In article <[email protected]>, "Bea Essor"
>>>><[email protected]> wrote:
>>>>>>
>>>>>>I don't think you have a math problem. The way I see it, if you were to
>>>>>>build a square or rectangular table with three straight legs two of the
>>>>>>corners would be supported, and the other two would not. If someone leans
>>>>>>too heavily, or puts something heavy on the table it may tip. My solution
>>>>>>would be to make a rectangular top. Place two straight legs on the narrow
>>>>>>end as you normally would. On the other end I would use a " V " shaped leg
>>>>>>going from the corners to the center spot on the floor.
>>>>>
>>>>>That isn't going to make it any more stable -- it still has only one
>>point of
>>>>>support at that end, and it's still in the same place.
>>>>
>>>>Correct. Another "solution" posted here has a similar problem. If you
>>>>let two legs come together and attach at a single pivot point, they
>>>>might as well be one leg, as far as stability goes (assuming all the
>>>>mass is above the pivot point).
>>>
>>>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.
>>
>>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.
>
>It doesn't matter. What counts is where the each foot is in relation to
>the edge of the table.
Actually, what matters is where each foot is in relation to the *center* 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.
>
In article <[email protected]>, "Bea Essor" <[email protected]> wrote:
>
>I don't think you have a math problem. The way I see it, if you were to
>build a square or rectangular table with three straight legs two of the
>corners would be supported, and the other two would not. If someone leans
>too heavily, or puts something heavy on the table it may tip. My solution
>would be to make a rectangular top. Place two straight legs on the narrow
>end as you normally would. On the other end I would use a " V " shaped leg
>going from the corners to the center spot on the floor.
That isn't going to make it any more stable -- it still has only one point of
support at that end, and it's still in the same place.
[email protected] (Doug Miller) wrote:
>In article <[email protected]>, "Bea Essor" <[email protected]> wrote:
>>
>>I don't think you have a math problem. The way I see it, if you were to
>>build a square or rectangular table with three straight legs two of the
>>corners would be supported, and the other two would not. If someone leans
>>too heavily, or puts something heavy on the table it may tip. My solution
>>would be to make a rectangular top. Place two straight legs on the narrow
>>end as you normally would. On the other end I would use a " V " shaped leg
>>going from the corners to the center spot on the floor.
>
>That isn't going to make it any more stable -- it still has only one point of
>support at that end, and it's still in the same place.
Correct. Another "solution" posted here has a similar problem. If you
let two legs come together and attach at a single pivot point, they
might as well be one leg, as far as stability goes (assuming all the
mass is above the pivot point).
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
"[email protected]" <[email protected]> wrote:
>On Jun 23, 1:40 am, [email protected] wrote:
>> I have a flagged patio. The flags are odd shapes and sizes and no two are at
>> the same level. Anywhere I put a four-legged table, it rocks. So I thought
>> I'd build a three-legged table, but I'd like it to be rectangular.
>>
>> Here's the question: where do the legs go for maximum stability, assuming
>> they stick straight down underneath?
>>
>> I think the simplest solution would be for a square top and I suspect that a
>> solution for a rectangle would be proportional to the square. There might be
>> two solutions, one with one leg in a corner and one with it half-way along
>> one edge.
>>
>> The math is completely beyond me. Is there a genius amongst us?
>>
>Not so much math as physics. For an object to stand without falling
>over, its center of gravity must be above its base. The further
>inside the base the COG is the more stable it will be (you have to tip
>it far enough to get the COG outside the base).
>
>For your table, assume the mass is in the top (ignore legs). If it's
>large compared to its thickness, ignore the thickness. The COG is
>then pretty much the center of the top. The problem then is to place
>the legs so this point is the furthest from the lines connecting the
>legs (the "base"). In the case of a square, this is easy (pick two
>corners and the middle of the opposing side). For a rectangle, I
>think it becomes clear if the rectangle is exaggerated; two adjacent
>corners on a long side and the opposite center.
Good explanation. Thanks. I particularly like the lines between
support points, which are obviously (well, obvious once you suggested
them!) directly above the axes of rotation if the table were to tip.
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
alexy wrote:
...
> Good explanation. Thanks. I particularly like the lines between
> support points, which are obviously (well, obvious once you suggested
> them!) directly above the axes of rotation if the table were to tip.
The problem w/ square/rectangular top on three lets still is, of course,
that the lever arm for applying a tipping force is longer from the
corners at the one-legged end. Minimize the normal (perpendicular)
distance form the corners to the lines between the support points; the
greatest of those is the highest moment arm and the point most prone to
tip. The circular top has no "longest" length in any preferred
direction; the maximum is the same in each of symmetric views.
Just ottomh w/o actually doing the geometry, seems to me the disparity
is greatest for the square and gradually decreases as the L/W ratio
increases for the rectangle. I'd look at the size required/wanted for
the purpose and even if don't want round, potentially look at cutting a
45 or similar off a long corner if it were overall, square. Of course,
a mockup from just ply and simple legs would make it much simpler to get
an actual feel for just how unsteady any given size would feel.
--
In article <[email protected]>,
<[email protected]> wrote:
<...snipped...>
>Here's the question: where do the legs go for maximum stability, assuming
>they stick straight down underneath?
<...snipped...>
I suggest about 18 inches into the ground.
--
There are no stupid questions, but there are lots of stupid answers.
Larry Wasserman - Baltimore Maryland - lwasserm(a)sdf. lonestar. org
<[email protected]> wrote in message
news:[email protected]...
>I have a flagged patio. The flags are odd shapes and sizes and no two are
>at
> the same level. Anywhere I put a four-legged table, it rocks. So I thought
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect that
> a
> solution for a rectangle would be proportional to the square. There might
> be
> two solutions, one with one leg in a corner and one with it half-way along
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
> Nemo
>
> -----------------------------------------------------------
> Posted using Android Newsgroup Downloader:
> .... http://www.sb-software.com/android
> -----------------------------------------------------------
Make two triangular tables that can be arranged in the size rectangle
you want. preserves balance and stability and gives you the shape you
want.
basilisk
[email protected] (Robert Bonomi) wrote:
>In article <[email protected]>,
>alexy <[email protected]> wrote:
>>[email protected] (Doug Miller) wrote:
>>
>>>In article <[email protected]>, "Bea Essor"
>><[email protected]> wrote:
>>>>
>>>>I don't think you have a math problem. The way I see it, if you were to
>>>>build a square or rectangular table with three straight legs two of the
>>>>corners would be supported, and the other two would not. If someone leans
>>>>too heavily, or puts something heavy on the table it may tip. My solution
>>>>would be to make a rectangular top. Place two straight legs on the narrow
>>>>end as you normally would. On the other end I would use a " V " shaped leg
>>>>going from the corners to the center spot on the floor.
>>>
>>>That isn't going to make it any more stable -- it still has only one point of
>>>support at that end, and it's still in the same place.
>>
>>Correct. Another "solution" posted here has a similar problem. If you
>>let two legs come together and attach at a single pivot point, they
>>might as well be one leg, as far as stability goes (assuming all the
>>mass is above the pivot point).
>
>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.
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.
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
On Jun 28, 8:59=A0pm, "Phil Kangas" <[email protected]> wrote:
> "HeyBub" <> wrote in message
> > [email protected] wrote:
>
> >>> Right, that's what I said -- according to you, my two
> >>> hypothetical
> >>> tables A
> >>> and B must be equally stable, because they each have the
> >>> same
> >>> lateral distance
> >>> from the COG to the edge of the base.
>
> >> Wrong. =A0I never said any such thing. =A0My point was only
> >> that the
> >> stability of a table is relative only to its base and
> >> COG.
>
> > You're correct as far as your definition of the problem.
> > But there's the ancillary problem of a single fly
> > alighting on the nether edge of a table whose legs are WAY
> > inside the perimeter.
>
> > Come to think on it, I've never seen a dining room table
> > held up by a single 1" pole attached at its center of
> > gravity.
>
> And the COG is changing as items are placed on or removed
> from the
> table in normal service. That's the concern, eih? phil
Bingo.
[email protected] wrote:
>>
>> Right, that's what I said -- according to you, my two hypothetical
>> tables A
>> and B must be equally stable, because they each have the same
>> lateral distance
>> from the COG to the edge of the base.
>
> Wrong. I never said any such thing. My point was only that the
> stability of a table is relative only to its base and COG.
You're correct as far as your definition of the problem. But there's the
ancillary problem of a single fly alighting on the nether edge of a table
whose legs are WAY inside the perimeter.
Come to think on it, I've never seen a dining room table held up by a single
1" pole attached at its center of gravity.
On Sun, 27 Jun 2010 19:05:37 GMT, [email protected] (Doug Miller) wrote:
>In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>>On Sun, 27 Jun 2010 12:41:23 GMT, [email protected] (Doug Miller) wrote:
>>
>>>In article <[email protected]>,
>> "[email protected]" <[email protected]> wrote:
>>>>On Sat, 26 Jun 2010 16:29:04 GMT, [email protected] (Doug Miller) wrote:
>>>>
>>>>>How much of the edge is outside the base is the *only* thing that matters.
>>>>
>>>>Wrong. What matters is the distance form the COG to the base. Period!
>>>
>>>Consider these two tables.
>>>
>>>Table A is a square, 32 inches on a side, with four legs forming a square base
>>>30 inches on a side. Obviously the tabletop overhangs the base by 1 inch all
>>>the way around.
>>>
>>>Table B is also a square, 32 *feet* on a side, with four legs forming a square
>>>base 30 *inches* on a side, and hence the tabletop overhangs the base on each
>>>side by fourteen feet and change.
>>
>>The OP's question was how to optimize the legs for a (given) table.
>
>That's correct. And I'm attempting to help you see why your approach to
>solving his problem is not correct, because your understanding of the problem
>is also not correct.
>>
>>>Same base. COG is in the same place. The distance from the COG to the edge of
>>>the base is the same.
>>>
>>>According to you, the only thing that matters is the distance from the COG to
>>>the base -- which is the same in both cases -- and hence the tables are
>>>equally stable. Table B is no easier to tip over than Table A on your planet.
>>
>>No, according to me, the stability of a *given table* is quantified by
>>measuring the lateral distance from the COG to edge of the base.
>
>Right, that's what I said -- according to you, my two hypothetical tables A
>and B must be equally stable, because they each have the same lateral distance
>from the COG to the edge of the base.
Wrong. I never said any such thing. My point was only that the stability of
a table is relative only to its base and COG.
In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>On Sun, 27 Jun 2010 19:05:37 GMT, [email protected] (Doug Miller) wrote:
>
>>In article <[email protected]>,
> "[email protected]" <[email protected]> wrote:
>>>On Sun, 27 Jun 2010 12:41:23 GMT, [email protected] (Doug Miller) wrote:
>>>
>>>>In article <[email protected]>,
>>> "[email protected]" <[email protected]> wrote:
>>>>>On Sat, 26 Jun 2010 16:29:04 GMT, [email protected] (Doug Miller) wrote:
>>>>>
>>>>>>How much of the edge is outside the base is the *only* thing that matters.
>
>>>>>
>>>>>Wrong. What matters is the distance form the COG to the base. Period!
>>>>
>>>>Consider these two tables.
>>>>
>>>>Table A is a square, 32 inches on a side, with four legs forming a square
> base
>>>>30 inches on a side. Obviously the tabletop overhangs the base by 1 inch all
>
>>>>the way around.
>>>>
>>>>Table B is also a square, 32 *feet* on a side, with four legs forming a
> square
>>>>base 30 *inches* on a side, and hence the tabletop overhangs the base on
> each
>>>>side by fourteen feet and change.
>>>
>>>The OP's question was how to optimize the legs for a (given) table.
>>
>>That's correct. And I'm attempting to help you see why your approach to
>>solving his problem is not correct, because your understanding of the problem
>>is also not correct.
>>>
>>>>Same base. COG is in the same place. The distance from the COG to the edge
> of
>>>>the base is the same.
>>>>
>>>>According to you, the only thing that matters is the distance from the COG
> to
>>>>the base -- which is the same in both cases -- and hence the tables are
>>>>equally stable. Table B is no easier to tip over than Table A on your
> planet.
>>>
>>>No, according to me, the stability of a *given table* is quantified by
>>>measuring the lateral distance from the COG to edge of the base.
>>
>>Right, that's what I said -- according to you, my two hypothetical tables A
>>and B must be equally stable, because they each have the same lateral distance
>>from the COG to the edge of the base.
>
>Wrong. I never said any such thing. My point was only that the stability of
>a table is relative only to its base and COG.
Of course you did. You said it before, and you said it again just now: "the
stability of a table is relative only to its base and COG". Hence two tables
having identical bases, with their centers of gravity in the same place, must
be (according to you) equally stable -- regardless of any other factors such
as the size of the tabletop.
"HeyBub" <> wrote in message
> [email protected] wrote:
>>>
>>> Right, that's what I said -- according to you, my two
>>> hypothetical
>>> tables A
>>> and B must be equally stable, because they each have the
>>> same
>>> lateral distance
>>> from the COG to the edge of the base.
>>
>> Wrong. I never said any such thing. My point was only
>> that the
>> stability of a table is relative only to its base and
>> COG.
>
> You're correct as far as your definition of the problem.
> But there's the ancillary problem of a single fly
> alighting on the nether edge of a table whose legs are WAY
> inside the perimeter.
>
> Come to think on it, I've never seen a dining room table
> held up by a single 1" pole attached at its center of
> gravity.
>
>
And the COG is changing as items are placed on or removed
from the
table in normal service. That's the concern, eih? phil
<Nemo....> wrote in message
>I have a flagged patio. The flags are odd shapes and sizes
>and no two are at
> the same level. Anywhere I put a four-legged table, it
> rocks. So I thought
> I'd build a three-legged table, but I'd like it to be
> rectangular.
>
> Here's the question: where do the legs go for maximum
> stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top
> and I suspect that a
> solution for a rectangle would be proportional to the
> square. There might be
> two solutions, one with one leg in a corner and one with
> it half-way along
> one edge.
>
> The math is completely beyond me. Is there a genius
> amongst us?
>
> Nemo
>
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
In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>Wrong. What matters is the *center* of the table (assuming a "normal" shaped
>table) must not be outside the base. It doesn't matter how much of the edge
>it outside, as long as the center of gravity is inside.
Nonsense.
Consider a table having a top six feet square, and four legs which form a
one-foot square exactly centered under the top. The table is "stable" under
your definition -- that is, it won't fall over in and of itself -- but it's
obviously very susceptible to being tipped by even a modest weight. Probably a
single coffee cup at the edge would be sufficient.
Now consider a similar table, with the legs moved outward so that they form a
*five*-foot square exactly centered under the top. The center of gravity has
not moved, yet this second table is clearly far more resistant to being tipped
over.
[...]
>The edges don't matter at all. *ALL* of the mass acts as if it is located at
>the center (of gravity).
Sorry, but you're entirely mistaken, because you're considering the wrong
problem.
You have completely and entirely correctly described what is necessary to
ensure that a table will not fall over _on its own_.
The problem under discussion, however, is how best to make a table that will
provide the greatest resistance to tipping over when pressure is applied to
the portion of the tabletop that overhangs the base. These are two entirely
separate questions.
How much of the edge is outside the base is the *only* thing that matters.
You're right that an object can't fall over if its center of gravity is over
its base. But you're ignoring the simple and obvious fact that the farther its
edges extend beyond the base, the easier it becomes to tip it far enough that
the center of gravity is no longer over the base.
[email protected] wrote:
...
> The edges don't matter at all. *ALL* of the mass acts as if it is located at
> the center (of gravity).
Only if the table surface is unloaded outside the supporting line(s).
It is, as at least two others have already said, also dependent on the
lever arm from the edge to the line of the legs--if that is very long,
it doesn't take much force irrespective of where the legs are wrt the
actual COG...
Simple 1D drawing of table on end or side view (nonproportional font)...
Elbows
| | |
\ / COG \/
_____A__________B__
| |
| |
| |
---------------------- Floor/ground...
Clearly the amount of force to tip is much less at the "elbows on table"
position owing to the larger distance between that applied force point
and the resistance at leg A attach point as opposed to a butt resting on
the edge closest to leg B.
As noted upthread, the most tipping stability assuming the legs are far
enough apart to avoid the weight of the table alone being a significant
factor is to minimize the maximum normal distance along the lines of
support. That keeps the largest lever arm at the smallest it can be for
any given size of table top.
--
> [email protected] wrote:
> ...
>
> > The edges don't matter at all. *ALL* of the mass acts as if it is
located
> at
> > the center (of gravity).
>
> Only if the table surface is unloaded outside the supporting line(s).
>
> It is, as at least two others have already said, also dependent on the
> lever arm from the edge to the line of the legs--if that is very long,
> it doesn't take much force irrespective of where the legs are wrt the
> actual COG...
>
> Simple 1D drawing of table on end or side view (nonproportional font)...
>
> Elbows
> | | |
> \ / COG \/
> _____A__________B__
> | |
> | |
> | |
> ---------------------- Floor/ground...
>
> Clearly the amount of force to tip is much less at the "elbows on table"
> position owing to the larger distance between that applied force point
> and the resistance at leg A attach point as opposed to a butt resting on
> the edge closest to leg B.
>
> As noted upthread, the most tipping stability assuming the legs are far
> enough apart to avoid the weight of the table alone being a significant
> factor is to minimize the maximum normal distance along the lines of
> support. That keeps the largest lever arm at the smallest it can be for
> any given size of table top.
>
> --
Let me throw in another factor here. Since this is a real table, the top and
legs will have weight. You really have to factor in the mass of the table on
either side of the tipping line. This means that just finding the shortest
fulcrum doesn't necessarily give the greatest stability. A 1' fulcrum where
the tipping line is parallel to an edge will require a lesser tipping force
than if the line cut across a diagonal.
To make the answer as general as possible, I've been considering a square
slab supported on three points. That way, the weight or length of the legs
don't complicate matters. (But I _still_ haven't found an answer!)
Nemo
-----------------------------------------------------------
Posted using Android Newsgroup Downloader:
.... http://www.sb-software.com/android
-----------------------------------------------------------
[email protected] (Robert Bonomi) wrote:
>In article <[email protected]>,
>alexy <[email protected]> wrote:
>>[email protected] (Robert Bonomi) wrote:
>>
>>>In article <[email protected]>,
>>>alexy <[email protected]> wrote:
>>>>[email protected] (Doug Miller) wrote:
>>>>
>>>>>In article <[email protected]>, "Bea Essor"
>>>><[email protected]> wrote:
>>>>>>
>>>>>>I don't think you have a math problem. The way I see it, if you were to
>>>>>>build a square or rectangular table with three straight legs two of the
>>>>>>corners would be supported, and the other two would not. If someone leans
>>>>>>too heavily, or puts something heavy on the table it may tip. My solution
>>>>>>would be to make a rectangular top. Place two straight legs on the narrow
>>>>>>end as you normally would. On the other end I would use a " V " shaped leg
>>>>>>going from the corners to the center spot on the floor.
>>>>>
>>>>>That isn't going to make it any more stable -- it still has only one
>>point of
>>>>>support at that end, and it's still in the same place.
>>>>
>>>>Correct. Another "solution" posted here has a similar problem. If you
>>>>let two legs come together and attach at a single pivot point, they
>>>>might as well be one leg, as far as stability goes (assuming all the
>>>>mass is above the pivot point).
>>>
>>>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.
>>
>>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.
>
>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.
I disagree. A little thought experiment here. A table 10' square.
Along one edge are traditional fixed legs, 4' apart. on the opposite
edge is one trestle leg, free to pivot where it meets the table, but
spreading to feet 20' apart. The table will be VERY easy to tip with
pressure 5' away from the trestle leg, as it will just rotate around
the attachment point. Attach that leg rigidly, and it will be VERY
stable.
>
>Average case. stability is about 70.71% of the four-legged table.
>
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>On Sat, 26 Jun 2010 16:29:04 GMT, [email protected] (Doug Miller) wrote:
>
>>How much of the edge is outside the base is the *only* thing that matters.
>
>Wrong. What matters is the distance form the COG to the base. Period!
Consider these two tables.
Table A is a square, 32 inches on a side, with four legs forming a square base
30 inches on a side. Obviously the tabletop overhangs the base by 1 inch all
the way around.
Table B is also a square, 32 *feet* on a side, with four legs forming a square
base 30 *inches* on a side, and hence the tabletop overhangs the base on each
side by fourteen feet and change.
Same base. COG is in the same place. The distance from the COG to the edge of
the base is the same.
According to you, the only thing that matters is the distance from the COG to
the base -- which is the same in both cases -- and hence the tables are
equally stable. Table B is no easier to tip over than Table A on your planet.
In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>On Sun, 27 Jun 2010 12:41:23 GMT, [email protected] (Doug Miller) wrote:
>
>>In article <[email protected]>,
> "[email protected]" <[email protected]> wrote:
>>>On Sat, 26 Jun 2010 16:29:04 GMT, [email protected] (Doug Miller) wrote:
>>>
>>>>How much of the edge is outside the base is the *only* thing that matters.
>>>
>>>Wrong. What matters is the distance form the COG to the base. Period!
>>
>>Consider these two tables.
>>
>>Table A is a square, 32 inches on a side, with four legs forming a square base
>>30 inches on a side. Obviously the tabletop overhangs the base by 1 inch all
>>the way around.
>>
>>Table B is also a square, 32 *feet* on a side, with four legs forming a square
>>base 30 *inches* on a side, and hence the tabletop overhangs the base on each
>>side by fourteen feet and change.
>
>The OP's question was how to optimize the legs for a (given) table.
That's correct. And I'm attempting to help you see why your approach to
solving his problem is not correct, because your understanding of the problem
is also not correct.
>
>>Same base. COG is in the same place. The distance from the COG to the edge of
>>the base is the same.
>>
>>According to you, the only thing that matters is the distance from the COG to
>>the base -- which is the same in both cases -- and hence the tables are
>>equally stable. Table B is no easier to tip over than Table A on your planet.
>
>No, according to me, the stability of a *given table* is quantified by
>measuring the lateral distance from the COG to edge of the base.
Right, that's what I said -- according to you, my two hypothetical tables A
and B must be equally stable, because they each have the same lateral distance
from the COG to the edge of the base.
In article <[email protected]>, [email protected] (Doug Miller) wrote:
>In article <[email protected]>,
> "[email protected]" <[email protected]> wrote:
>>On Sun, 27 Jun 2010 12:41:23 GMT, [email protected] (Doug Miller) wrote:
>>
>>>In article <[email protected]>,
>> "[email protected]" <[email protected]> wrote:
>>>>On Sat, 26 Jun 2010 16:29:04 GMT, [email protected] (Doug Miller) wrote:
>>>>
>>>>>How much of the edge is outside the base is the *only* thing that matters.
>>>>
>>>>Wrong. What matters is the distance form the COG to the base. Period!
>>>
>>>Consider these two tables.
>>>
>>>Table A is a square, 32 inches on a side, with four legs forming a square
> base
>>>30 inches on a side. Obviously the tabletop overhangs the base by 1 inch all
>>>the way around.
>>>
>>>Table B is also a square, 32 *feet* on a side, with four legs forming a
> square
>>>base 30 *inches* on a side, and hence the tabletop overhangs the base on each
>
>>>side by fourteen feet and change.
>>
>>The OP's question was how to optimize the legs for a (given) table.
>
>That's correct. And I'm attempting to help you see why your approach to
>solving his problem is not correct, because your understanding of the problem
>is also not correct.
>>
>>>Same base. COG is in the same place. The distance from the COG to the edge of
>
>>>the base is the same.
>>>
>>>According to you, the only thing that matters is the distance from the COG to
>
>>>the base -- which is the same in both cases -- and hence the tables are
>>>equally stable. Table B is no easier to tip over than Table A on your planet.
>>
>>No, according to me, the stability of a *given table* is quantified by
>>measuring the lateral distance from the COG to edge of the base.
>
>Right, that's what I said -- according to you, my two hypothetical tables A
>and B must be equally stable, because they each have the same lateral distance
>from the COG to the edge of the base.
And let's add Table C, just like Table A -- but the legs are forty feet long.
And Table D, just like Table A, but the legs are only an inch long.
All four tables have the same lateral distance from the COG to the edge of the
base. That's your phrase, Keith. And according to you, that distance is all
that matters. Thus, according to you, all four are equally stable.
In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>You don't think a mass at the end of a lever is going to change the COG?
Setting an object on the edge of a tabletop doesn't change the center of
gravity of the *table*, no.
zxcvbob <[email protected]> wrote:
>Go for 4 legs with adjustable feet. (if the table just has to be
>stable and not necessarily level, you just need 2 adjustable feet
Actually, only one.
>--
>or one if you also get to turn the table)
Actually, only one whether or not you get to turn the table.
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
Upscale <[email protected]> wrote:
>On Mon, 28 Jun 2010 22:58:50 -0400, alexy <[email protected]> wrote:
>>>Go for 4 legs with adjustable feet. (if the table just has to be
>>>stable and not necessarily level, you just need 2 adjustable feet
^^^^^^^^^^^^^^^^^^^^^
>
>>Actually, only one.
>
>That's not right. If the terrain that the table sits on is varied
>enough, then two adjustable feet are needed to keep the table surface
>horizontal enough to stop things from sliding off it.
I was replying to the hypothetical that level is not needed. If level
is needed (i.e., real world), it seems you would need three adjustable
legs if you can't rotate the table. If you can rotate, and the surface
is "continuous", two will do.
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
"Josepi" <[email protected]> wrote:
>Sorry. Only one adjustable leg would be required for a three legged table to
>keep it level anywhere.
That requires a continuous (more accurately differentiable) surface.
E.g.m consider a tripod with 2' spacing between feet, placed on a
surface consisting of four 1.25' square blocks, with the taller ones
1", 2" and 3" above the lowest one. You can't fit two of the legs on
the same block, so the two fixed legs will not be the same
height--tilted table.
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
In article <[email protected]>,
alexy <[email protected]> wrote:
>[email protected] (Doug Miller) wrote:
>
>>In article <[email protected]>, "Bea Essor"
><[email protected]> wrote:
>>>
>>>I don't think you have a math problem. The way I see it, if you were to
>>>build a square or rectangular table with three straight legs two of the
>>>corners would be supported, and the other two would not. If someone leans
>>>too heavily, or puts something heavy on the table it may tip. My solution
>>>would be to make a rectangular top. Place two straight legs on the narrow
>>>end as you normally would. On the other end I would use a " V " shaped leg
>>>going from the corners to the center spot on the floor.
>>
>>That isn't going to make it any more stable -- it still has only one point of
>>support at that end, and it's still in the same place.
>
>Correct. Another "solution" posted here has a similar problem. If you
>let two legs come together and attach at a single pivot point, they
>might as well be one leg, as far as stability goes (assuming all the
>mass is above the pivot point).
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.
On Wed, 23 Jun 2010 09:23:26 -0700 (PDT), RicodJour
<[email protected]> wrote:
>Yes, but it fulfills the new picnic table seismic code requirement for
>lateral bracing.
Must be a California brand picnic table that's going to be used on a
volatile fault line.
On Sun, 27 Jun 2010 12:41:23 GMT, [email protected] (Doug Miller) wrote:
>In article <[email protected]>, "[email protected]" <[email protected]> wrote:
>>On Sat, 26 Jun 2010 16:29:04 GMT, [email protected] (Doug Miller) wrote:
>>
>>>How much of the edge is outside the base is the *only* thing that matters.
>>
>>Wrong. What matters is the distance form the COG to the base. Period!
>
>Consider these two tables.
>
>Table A is a square, 32 inches on a side, with four legs forming a square base
>30 inches on a side. Obviously the tabletop overhangs the base by 1 inch all
>the way around.
>
>Table B is also a square, 32 *feet* on a side, with four legs forming a square
>base 30 *inches* on a side, and hence the tabletop overhangs the base on each
>side by fourteen feet and change.
The OP's question was how to optimize the legs for a (given) table.
>Same base. COG is in the same place. The distance from the COG to the edge of
>the base is the same.
>
>According to you, the only thing that matters is the distance from the COG to
>the base -- which is the same in both cases -- and hence the tables are
>equally stable. Table B is no easier to tip over than Table A on your planet.
No, according to me, the stability of a *given table* is quantified by
measuring the lateral distance from the COG to edge of the base.
dpb wrote:
> [email protected] wrote:
> ...
>
>> The edges don't matter at all. *ALL* of the mass acts as if it is
>> located at the center (of gravity).
>
> Only if the table surface is unloaded outside the supporting line(s).
>
> It is, as at least two others have already said, also dependent on the
> lever arm from the edge to the line of the legs--if that is very long,
> it doesn't take much force irrespective of where the legs are wrt the
> actual COG...
>
> Simple 1D drawing of table on end or side view (nonproportional
> font)...
> Elbows
> | | |
> \ / COG \/
> _____A__________B__
> | |
> | |
> | |
> ---------------------- Floor/ground...
>
> Clearly the amount of force to tip is much less at the "elbows on
> table" position owing to the larger distance between that applied
> force point and the resistance at leg A attach point as opposed to a
> butt resting on the edge closest to leg B.
>
> As noted upthread, the most tipping stability assuming the legs are
> far enough apart to avoid the weight of the table alone being a
> significant factor is to minimize the maximum normal distance along
> the lines of support. That keeps the largest lever arm at the
> smallest it can be for any given size of table top.
Elbows on the table = soup in the lap.
At least that's what my granny taught me.
<[email protected]> wrote in message
news:[email protected]...
>I have a flagged patio. The flags are odd shapes and sizes and no two are
>at
> the same level. Anywhere I put a four-legged table, it rocks. So I thought
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
>
> I think the simplest solution would be for a square top and I suspect that
> a
> solution for a rectangle would be proportional to the square. There might
> be
> two solutions, one with one leg in a corner and one with it half-way along
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
> Nemo
>
> -----------------------------------------------------------
> Posted using Android Newsgroup Downloader:
> .... http://www.sb-software.com/android
> -----------------------------------------------------------
>
I don't think you have a math problem. The way I see it, if you were to
build a square or rectangular table with three straight legs two of the
corners would be supported, and the other two would not. If someone leans
too heavily, or puts something heavy on the table it may tip. My solution
would be to make a rectangular top. Place two straight legs on the narrow
end as you normally would. On the other end I would use a " V " shaped leg
going from the corners to the center spot on the floor.
Bea
On 23 Jun 2010 06:40:40 GMT, [email protected] wrote the following:
>I have a flagged patio. The flags are odd shapes and sizes and no two are at
>the same level. Anywhere I put a four-legged table, it rocks. So I thought
>I'd build a three-legged table, but I'd like it to be rectangular.
Screw the math. Use adjustable (threaded) feet and tee-nuts.
http://fwd4.me/UDX 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.
<bseg>
--
Peace of mind is that mental condition in which you have accepted the worst.
-- Lin Yutang
"Upscale" <[email protected]> wrote in message
news:[email protected]...
> On Wed, 23 Jun 2010 06:38:26 -0700 (PDT), RicodJour
> <[email protected]> wrote:
>
>>Substituting an inherently less stable form for a slightly wobbly
>>table is a poor trade-off.
>>All you need is to have one leg of the four adjustable.
>
> An easier solution should the three leg choice be preferable is to
> forgo the square/rectanble table and make it round.
Maybe a matchbook or a rolled up napkin under one leg.
It works at some of the better restaurants I have been in.
Seriously, this group is great, there is no question that can't be asked and
get realistic and practical answers.
Larry C
On Sat, 26 Jun 2010 12:08:48 -0500, dpb <[email protected]> wrote:
>[email protected] wrote:
>...
>
>> The edges don't matter at all. *ALL* of the mass acts as if it is located at
>> the center (of gravity).
>
>Only if the table surface is unloaded outside the supporting line(s).
Then it becomes "part of" the table top. If you want to get pissy, you don't
mention the coefficient of friction between your load and the top (it may fall
of before the table tips).
Obviously I'm simplifying this a lot, for instance ignoring that the table top
is three dimensional and ignoring the mass of the legs. These assumptions
were made above.
>It is, as at least two others have already said, also dependent on the
>lever arm from the edge to the line of the legs--if that is very long,
>it doesn't take much force irrespective of where the legs are wrt the
>actual COG...
You don't think a mass at the end of a lever is going to change the COG?
>Simple 1D drawing of table on end or side view (nonproportional font)...
>
> Elbows
> | | |
> \ / COG \/
> _____A__________B__
> | |
> | |
> | |
>---------------------- Floor/ground...
^ ^
A' C'
>Clearly the amount of force to tip is much less at the "elbows on table"
>position owing to the larger distance between that applied force point
>and the resistance at leg A attach point as opposed to a butt resting on
>the edge closest to leg B.
The distance between my A' and C' defines how much resistance to "Elbows"
there is. Yes, A' to E' is a lever arm and that must be countered by the
table's mass * A'-C'.
>As noted upthread, the most tipping stability assuming the legs are far
>enough apart to avoid the weight of the table alone being a significant
>factor is to minimize the maximum normal distance along the lines of
>support. That keeps the largest lever arm at the smallest it can be for
>any given size of table top.
Huh?
True enough.
My scenario only works for a planar surface tipped at any angle. The three
legged chair can always be turned so two are horizontal to each other and
the adjustable compensate for the slope.
"alexy" <[email protected]> wrote in message
news:[email protected]...
That requires a continuous (more accurately differentiable) surface.
E.g.m consider a tripod with 2' spacing between feet, placed on a
surface consisting of four 1.25' square blocks, with the taller ones
1", 2" and 3" above the lowest one. You can't fit two of the legs on
the same block, so the two fixed legs will not be the same
height--tilted table.
"Josepi" <[email protected]> wrote:
>Sorry. Only one adjustable leg would be required for a three legged table
>to
>keep it level anywhere.
On Thu, 24 Jun 2010 19:48:24 -0500, [email protected]
>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.
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.
On 23 Jun 2010 06:40:40 GMT, [email protected] wrote:
> I have a flagged patio. The flags are odd shapes and sizes and no two are at
> the same level. Anywhere I put a four-legged table, it rocks. So I thought
> I'd build a three-legged table, but I'd like it to be rectangular.
>
> Here's the question: where do the legs go for maximum stability, assuming
> they stick straight down underneath?
As a starting point, I'd suggest making the rectangle not too long (so the
ratio of width to length isn't too great - maybe 2:1, max) and not too narrow.
Then just place two of the legs at corners of the same long side with the
third one in the middle of the opposite side.
It'll be "good enough" if not mathematically, precisely optimal. However
the advantage of this simple approach is that you'll get your table, rather
than be frozen at the design stage trying to extract the last .001% of
stability.
> I think the simplest solution would be for a square top and I suspect that a
> solution for a rectangle would be proportional to the square. There might be
> two solutions, one with one leg in a corner and one with it half-way along
> one edge.
>
> The math is completely beyond me. Is there a genius amongst us?
>
> Nemo
>
> -----------------------------------------------------------
> Posted using Android Newsgroup Downloader:
> .... http://www.sb-software.com/android
> -----------------------------------------------------------
Sorry again. My sleep patterns are all over the shop I
just cannot get the group out of my head!
WHY DO YOU NOT LOVE ME!
ME ME ME ME ME ME ME ME!!!!
What you need is a single leg table with a gyro mounted.
This way even on a moving bus the table will balance!
Now I just happen to have such a table kept safe in
my butt. Collapsible and folds in no more space than
a medium sized gerbil there is one for everyone!
Share anyone?
"Josepi" <[email protected]> wrote in message
news:RweWn.5532$3%[email protected]...
Sorry. Only one adjustable leg would be required for a three legged table to
keep it level anywhere.
This would not apply for a four legged table.
"Josepi" <[email protected]> wrote in message
news:[email protected]...
Only one would be required if you rotate it.
"Upscale" <[email protected]> wrote in message
news:[email protected]...
That's not right. If the terrain that the table sits on is varied
enough, then two adjustable feet are needed to keep the table surface
horizontal enough to stop things from sliding off it.
On Mon, 28 Jun 2010 22:58:50 -0400, alexy <[email protected]> wrote:
>>Go for 4 legs with adjustable feet. (if the table just has to be
>>stable and not necessarily level, you just need 2 adjustable feet
>Actually, only one.
Only one would be required if you rotate it.
"Upscale" <[email protected]> wrote in message
news:[email protected]...
That's not right. If the terrain that the table sits on is varied
enough, then two adjustable feet are needed to keep the table surface
horizontal enough to stop things from sliding off it.
On Mon, 28 Jun 2010 22:58:50 -0400, alexy <[email protected]> wrote:
>>Go for 4 legs with adjustable feet. (if the table just has to be
>>stable and not necessarily level, you just need 2 adjustable feet
>Actually, only one.