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A puzzling issue: object with 8 degrees of freedom

A friend and I are having a bet. He states that there must be objects or mechanisms with 8 degrees of freedom (not counting translation} which have 3-fold symmetry (at least in some configurations). But we cannot find any.

He is thinking of objects like a deformable cubus with corners whose angles are not fixed. But such a cubus has

- three orientational degrees of freedom

- three internal angles which makes a total of only 6 degrees of freedom. A cubus has 3fold symmetry when seen along a diagonal, so that would fit; but 6 are not 8 degrees of freedom.

I brought up the idea of a tetrahedral skeleton, (like a methane molecule

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) . It has 8 degrees of freedom, it has 3fold symmetry in some configurations, but we do not see a way to build that in metal or rubber without having more or less than 8 degrees of freedom.

On the other hand, I am not able to prove that the puzzle is impossible to solve.

Is there another solution? Where can one look for such objects or related theorems? Are there books or sites on these issues?

Thanks in advance!

John

Reply to
john_m_stanton
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Hi John, The shape or makeup of an object does not change the freedom of it's motion. Freedom of motion has 6 directions, up- down, forward- backward,left-right. Those are the 6 "so called degrees" that I would call planes of motion instead.

6 maximum planes of motion only.
Reply to
Spaceman

In his first paragraph John specifically discounted=20 translational degrees of freedom. Another swing and a miss for James.

Reply to
Greg Neill

Poor Greg, does not understand I was simply stating that discounting translational degrees of freedom is simply wrong. But of course, you live in rubber ruler world where everything is wrong so you think all that crap is right even if it is wrong. :)

Reply to
Spaceman

Perhaps that's what you intended. If so it is a mystery how what you intended bears no resemblance to what you actually said. You're reply was a non-sequitur, since John is specifically not considering motion in his consideration of geometrical properties.

Reply to
Greg Neill

A pentagram has five sides. A vertex angle makes 5 a symmetry. Making one degree of freedom and one symmetry.

A line length or side length makes a five degree of freedom change, each side may be independent of the other. Allowing a legnth as a cause to ratio of side to side then making a ratio symmetry.

And a mirror of set of sides allows a ratio of areas. Draw a line between vertexes and mirror. Making the third degree symmetry. And two degrees of freedom for there are only two axis? NO there are three axis, making 9 degree of freedom.

SO use a square.

A square is a cubic and all cubic exhibit this majic property. Gold as a cubic crystal system allows a functional method of set to be developed. 3 symmetries and 8 degrees of freedom allows a functional set to be designed.

D(3) Length(4) Mirror ratio(2)

Wait the square has only 7 degree of freedom, sorry!

I went through several shapes and found this one.

*

__________

A triangloid with a certain number of sides. It haa No mirror property because the axis appears a side! SO the angle vertex makes a ratio of side length to side length For all equal sides, two vertexs exist. One degree for each.

Allowing the dies to equal the rest of the degrees of freedom.

And the third mirror symmetry exists only as a NON-degree of freedom effect.

Reply to
Douglas Eagleson

Greg, when one talks about degrees of freedom They have jumped on the motion bus. I am sorry you can't grasp such a simple fact.

Reply to
Spaceman

I forgot to mention. A base line or axis drawn through the base to mirror CAN NOT because the Volume of the mirror appears nonexistent. You can not mirror a volume with a line in other words, except as given. A top vertex line only appears to have the property of symmetric formal applied volume, but it appears ZERO.

If the base was square

_________ | | | | | | | | _________________________ axis

An axis trough the base side can not make a volume mirrior as with the top vertex because the DEGREE of Freedom of the top vertex was a third symmetrical form. It depends as a symmetry on base and side legnth, while the base verticies depende only on square side length.

Reply to
Douglas Eagleson

If translational motion is specifically being=20 discounted for the given problem then it is simply not germaine to the problem. Case closed.

Reply to
Greg Neill

Specifically discounting translational motion only makes the problem, not a problem of degrees of freedom at all. If you have 0 translational motion, you are not moving in any degree of freedom at all. Poor Greg, You skipped over all that classical stuff to jump into your "warped" mathematical joke world. LOL

Reply to
Spaceman

The reason there's only 6 degrees of freedom in in idiot translational physics though, is because they only live in the moron universe of "entropy says".

Rather than in the non-zero intellgence world of lasers, digital, robo++, satellites, and cruise missiles.

Reply to
zzbunker

Nope, The only nonsense is motion without a translational motion from one point to another like you wish you believe can occur.

All translational motion still Greg. one point or more "translating" to another point or more. You sure are lost without a clue about motion anymore huh?

Reply to
Spaceman

Poor guy, You also must have lost the simple fact that all motion is translational motion and all such motion only has

6 planes to move in. You poor things, all warped beyond repair. LOL
Reply to
Spaceman

So we add "translational motion" to the list of terms that you don't understand. Fine. Keep up the good work.

Reply to
Greg Neill

LOL Too bad that list you are making actually shows your own faults and misunderstandings.

Do you really think a rotation or a flexing has no translational motion? You poor poor thing.. LOL

Reply to
Spaceman

An object with movable appendages, such as the human body, has multiple degrees of freedom.

Dave

Reply to
Dave

=20

See? You don't understand what translational motion of an object is. Why don't you look it up?

Reply to
Greg Neill

I know all about it Greg. It is you that is clueless that any motion is still a translational motion. I think it is amazing how ignorant you are to such a fact. I will ask you again, Do you really think rotational motion has no translational motion?

Reply to
Spaceman

You certainly don't show it.

Wrong.

A rotational motion of an object is not translational motion.

Reply to
Greg Neill

So you say that not even a single point of the object that is rotating will translate to another position. Poor thing. You are lost as usual. LOL

Reply to
Spaceman

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