>      If not please ask questions. I am trying to paraphrase
>      so ordinary mortals (non-engineers) can understand it :)
>
>
>      The University of Queensland School of Engineering. Quote:
>
>      "Mechanical failure is generally interpreted in terms of change,
>      some physical or chemical process having produced failure.
>      However the improper location and guidance of components
>      also constitutes an important mode of failure often ignored
>      in mechanical engineering practice."
>
>      Any object is said to have six degrees of freedom or movement.
>      Rotation about the X, Y, and Z axises.
>      Translation (movement) in the X, Y, Z directions.
>
>      In order to hold any object from moving in any way requires only
>      three connections. If a fourth, or more, connections are added
>      additional loads and stresses are introduced that cannot be determined
>      by simple means. A three legged stool is a classic example.
>      It is trivial to calculate the loads in the three legs and
>      the forces these loads apply to the floor. A four legged chair
>      on the other hand is a much more complicated situation and it
>      usually requires a finite element analysis computer program
>      to resolve the individual loads and stresses. The fourth leg
>      is therefore redundant and in fact considered undesirable.
>
>      Paul Lamar ...No rotor no motor.
>
>      A three legged round stool is more stable supporting a downward
>      force only when that force is applied on the area included in the
>      area defined by a triangle connecting the legs (since the legs are
>      not attached to the floor).
>      In this case, four legs have greater stability.  I have crashed &
>      burned more than once on of those stools when trying to sit on the
>      edge.  Also recall why the three wheel RTV's were replace by quads.
>
>      Fortunately for us, the three point mount IS constrained, hence a
>      better design.
>
>      Joel
>      Wondering why I get involved on subjects out of my Expertise.
>
> Thanks Joel. Good thinking. Agreed.
>
> You are absolutely right but for our purposes and audience IMHO it
> is too much detailed.  Do you think I need to go down that
> slippery slope and draw a 3 legged stool where the force is applied
> on the area included in the area defined by a triangle connecting
> the legs ?
>
> The constrained word is good but for the average person I think
> the connected word is better.
>
> -------------------------------------------------------
>
> Ok here is another way of putting it. This is from Bruhn,
> "Analysis and Design of Flight Vehicle Structures."
>
> "A2. 5 Statically Determinate and Statically Indeterminate Structures.
>
> A statically determinate structure is one in which all external reactions
> and internal stresses for a given load system can be found by use of the
> equations of static equilibrium, and a statically indeterminate structure
> is one in which all reactions and internal stresses cannot be found by
> using only the equations of equilibrium."
>
> A 3 legged stool connected to the floor is statically determinate.
>
> "If the structure has more external reactions or internal members than
> is necessary for stability of the structure under a given load system
> it is statically indeterminate."
>
> A four legged stool connected to the floor.
>
> "The additional equations that are needed to solve a statically
> indeterminate structure are obtained by considering the distortion of
> the structure."
>
> In other words FEA which they did not have when this book was written
> in 1965.
>
>
> Paul Lamar ...No rotor no motor.


Most desk chairs used to be sold with 3 or 4 wheels,
but now they have five or six wheels.

If I'm on a three legged stool and lean forward onto two
of the legs the force on the third leg goes to zero.

If I'm on a four legged stool and lean forward onto two
legs then the force on the back two legs goes to zero.
As the force on the back two legs goes to zero it looks
more and more like a three legged stool.

Therefore my six wheeled desk chair is really just six
three legged stools.

-Jeff Martin

I've read it about 6 times now and I think I understand it.

Use your stool analogy all the way through.

Start with a relatively short stool with weight and rubber feet on
a rough concrete surface.
Talk about turning the stool around. Talk about pushing the
stool left, right, forward and back. Talk about tipping the stool
over.

Point out that the stool won't turn around, rotation around the vertical
axis, because the friction provided by the rubber feet on the
rough concrete are well conditioned to restrain that movement.
Because, they are well conditioned we can say they have good
closure. (Do I have this right?)

Compare some kind of low friction feet. A stool on ice maybe.

If you add a fourth leg and the stool does not flex then one leg
will always be off the floor and therefore provides no additional
friction or support.

If you have a flexible stool then the added friction and stability
of the fourth leg is offset by the flexing.

I hope this gives you some ideas. I don't have time to write
my own version.

-Jeff Martin



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