A puzzling issue: object with 8 degrees of freedom

wrote:


I understand perfectly well. If you are moving to the East with speed 10 (in some units) your velocity is v = 10; but if you are going West at speed 10 your velocity is v = -10. If you 5 units to the right of the origin your coordinate is x = 5, but if you are 5 units to the left it is c = -5. That is how physicists use these concepts; mathematicians do so as well.

Nonsense.
Well, some bodies have fewer than 6 degrees of freedom, while others have more than 6. They can have as many as 8 degrees, but if counting the three "position" coordinates (which the OP did not want to do).

No, it is well-documented dynamics. For example, when studying the specific heats of dilute gasses by statistical thermodynamics, we need to worry about these thing; and if we count correctly, we get perfect agreement with experiment. That matters, because physics is an experimental science, after all.

No, it is not just fun mathematics; it is known to anybody who has taken undergraduate statistical mechanics or undergraduate classical mechanics. People who go to the library and read appropriate textbooks know about these things.
R.G. Vickson

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Ray Vickson wrote:

You say you understand the above and then you prove you actually do not by stating that. Sorry.

Some bodies have less than 6 only when something is in the way. There are no extra degrees of freedom just because of a shape or position of an object.

So you can't do basic math anymore using 3 dimensions and 6 degrees of freedom?

Classical mechanics has no such bullshit at all. physical objects also have no such bullshit about extra degrees of freedom at all. You are only fooling yourself with "multiple dimension bullshit if you are finding more than 6 degrees of freedom.
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James M Driscoll Jr
Creator of the Clock Malfunction Theory
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wrote: | > > 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 moleculehttp://en.wikipedia.org/wiki/Methane ) . | > > 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! | > | > 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. | | No: under the conventions that mathematicians and physicists use (and | those *are* the relevant ones, after all, in this "math" newsgroup) | you have described only three degrees of freedom, not six. These three | degrees are East-West, up-down and in-out. This just says that there | are three lines along which the motion can be projected, or three | coordinates needed to describe velocity. For a generally-shaped so- | called rigid body there can be two more degrees of freedom, associated | with rotational angles and the like (i.e., the object's orientation). | For non-rigid bodies there can be additional degrees of freedom, | associated with vibrational modes, internal angles, etc. You need to | be careful to count these correctly in order to obtain correct figures | for specific heats in polyatomic gasses when doing statistical | thermodynamics. | | Anyway, the OP is, presumably, dealing with only orientation and | internal-structure degrees of freedom. I'm still not sure about the | exact answer to the OP's question. | | R.G. Vickson
6-DOF x, y, z, pitch, roll, yaw.
6-DOF platforms:
http://www.inmotionsimulation.com/images/6-dof-2.jpg
http://www.inmotionsimulation.com/images/6-dof-1.jpg
http://www.ckas.com.au/CKAS%20V4%206DOF%20Motion%20Platform.jpg
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On Aug 1, 10:03 pm, john_m snipped-for-privacy@yahoo.co.uk wrote:

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.
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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.
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Douglas Eagleson wrote:

[snip crap]
Uncle Al counts 10 external sides. Idiot.
<
http://img74.imageshack.us/img74/5304/pentagram9hm.gif <
http://i.peperonity.com/c/9936AE/991727/ssc3/home/073/wicca.wisdom/the_pentagram.jpg_320_320_0_9223372036854775000_0_1_0.jpg
<
http://adoptanamerican.com/version/imgs/pentagram.jpg
<h
http://i175.photobucket.com/albums/w145/The_Advenger/pentagram_bm.jpg
http://www.electricwitch.com/pentagram2.gif
--
Uncle Al
http://www.mazepath.com/uncleal/
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The pentagram was a postulated shape, I then tried a square, then a triangloziod. THe last was OK.
*
__________
The formal name escapes me now.
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On Aug 2, 12:03 am, john_m snipped-for-privacy@yahoo.co.uk wrote:

An object with movable appendages, such as the human body, has multiple degrees of freedom.
Dave
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On Fri, 1 Aug 2008 22:03:19 -0700 (PDT), john_m snipped-for-privacy@yahoo.co.uk wrote:

///
Better not take the other end of the bet.
A rotational degree of freedom occurs in one object capable of rotating with respect to another.
An object with several rotatable links can provide several degrees of rotary freedom for each successive link with respect to the base attachment.
An object like the Manx three-legged object, can rotate three ways at each ankle with respect to its limb.
Brian W
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On Aug 1, 10:03 pm, john_m snipped-for-privacy@yahoo.co.uk wrote:

Just to clarify the meaning of a degree of freedom in my thinking.
"An independent geometric variable."
Angle as a side length appear to be the issue and the basic variable where angle appears dependent was all that need be discussed.
_______ | | |
here is a right angle and it is clearly independent of side length. A constructed geometric as a whole then allows side to cause angle.
IN mechanical interpretation a machine can be described as a geometric function. MY right angle machine above has three apparent degrees of freedom. Two sides and the angle. As soon as a machine is a triangle it has three again, but the angles are side length determined and the meaning as machine itself in abstract appear to be a school idea I am trying to understand.
A function of machine applies to any design wheather a robot like device or not. A location of machine parts as function allows a complexity design such as a robot to be discussed, but exact question was apparently unclear to me.
A thoughtful man would allow all machine whether a simple constant structure to be a fuunctionally defined structure.
A robot type of machine appears the issue. A three fold symmetry mean it has three axises and so all machines with threee axis are functionally equivalent.
An inverted triangleoizoid;) was used at the National Insitute of Standards and Technology, NIST as a robot arm/platform. Cables varying the side lengths functionally could cause the tip of the volume to be motionable in an exact functional fashion. It translates left and right and up and down and spins in the center in a circle if required.
So all that was required was to allow an actual usage to be stated. I thought it was a crystallike common question and not a mechanical engineeering question. Analogy to crystal was a possible reason for the NIST discovery as a class of robot though.
If there is a question concerning the usage of crystal design in robots I would entertain them because there are few machines able to be used in crystal analogy!
Here is a small novel machine design based on a crystal geometric.
A cubic structure has like maybe ten degree of freedom. And to functionally control side length to cause the function meant the solution would be indeterminate! A rather airfcraft like control function would have to be defined for a cubic to be used as a robot and a test loop in control code would have to prevent nonsolution motion.
Making the nIST inverted triangleosoid a truely novel discovery.
Maechanical design is very interesting and the basic question here is to either talk of the method of machine analogy or not.
Thanks Doug
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Douglas Eagleson wrote:

Hi Doug, The cubic structure still does not have more than 6 degrees of freedom, What you are doing is allowing for the degrees to have a multiple of positions or multiple motions within the normal 6 degrees. That is not "extra degrees" that is still just an extra motion in the normal 6 degrees of freedom.
Any point of the object can have no more than 6 different directions (up, down, left, right, forward, backward) of motion in the 3 planes of 3D space they reside it. Motions that combine lets say up and left, are not an extra degree of freedom. They are a combination of 2 or more of the normal degrees of freedom.
--
James M Driscoll Jr
Creator of the Clock Malfunction Theory
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a truss member has two degree of freedom, namely compress and extension which is the axial force at both ends. a frame member has six degree of freedom, namely translation in the x, y axis plus a rotation at each ends. that means 3 degree of freedom at each end. a cubic would would have three degree of freedom on each faces which is 6 times 3 which is 18 degree of freedom. a material is not measure by it's atomic structure but rather the material property of isotropical or anisotropical which is measure by the modulus of elasticity and the possion ratio.....done
wrote:

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freddy osbourne wrote:

Again, The rotation at each end you speak of is still just freedom of motion in the same 6 degrees known. and each end also has a compression factor to allow 6 degrees to still exist at each end. You are merely mixing already known degrees of freedom into "extra" degrees that are not actually there. You are adding already known degrees of freedom as "extra" degrees.
A cube, has 6 degrees of freedom only, Any single point on the cube or inside the cube also only has 6 degrees of freedom. You can combine any of the degrees for different motion in such free 3D space. But it still only moves with 6 degrees of freedom.
Just because it has ends does not give it "extra" degrees by adding the same degrees. Each end can move in the same 6 degrees the other end can move in. There is no "addition of degrees occuring".
--
James M Driscoll Jr
Creator of the Clock Malfunction Theory
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Dear freddy osbourne:

A truss member has at least three degrees of freedom: 1) change in length (+/-) 2) bending off the central axis (up/down, left/right, etc., Euler column) 3) torsion around the central axis
David A. Smith
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N:dlzc D:aol T:com (dlzc) wrote:

Using only 2 degrees of the 6 known.

Using 4 degrees of the 6 known.

Again Using same 4 degrees of (2) of the 6 known. (up down left right motion of points with a variable of motion for each point)
Still only 6 degrees of actual freedom total.
--
James M Driscoll Jr
Creator of the Clock Malfunction Theory
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Dear Spaceman:

No, that is a single degree of freedom.

Only two.

No, this is three degrees of freedom.
David A. Smith
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N:dlzc D:aol T:com (dlzc) wrote:

No, two directions of motion is 2 degrees of freedom in a single plane of motion.

No, again 4 degrees but now in two planes. I think you are confusing planes with degrees. Each plane has 2 directions of freedom. (2 degrees)

Nope. It is the same as above. It has 2 directions for for any point in one plane and 2 more directions in the other again, 4 degrees of freedom.
--
James M Driscoll Jr
Creator of the Clock Malfunction Theory
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On Sun, 3 Aug 2008 12:46:17 -0700, "N:dlzc D:aol T:com \(dlzc\)"
///

/and so on/

Dave, I see a problem for you; debating with the folks who have strayed onto an engineering group that actually uses the concept of DoF: it's the one called "rassling with pigs...."
You WILL get muddy! :-)
Better to leave them to campout on sci.physics, sci.maths.....
Brian W
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Brian Whatcott wrote:

Actually physics does not actually use more than 6 degrees of freedom It is only the math heads that play with such sillyness instead of realizing they are just re-using the same known degrees of freedom already. So it would be best to play with such porcupine needled degrees of freedom that increase with the amount of objects and rubberyness in the math group alone. :)
--
James M Driscoll Jr
Creator of the Clock Malfunction Theory
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correction, a frame member has six degree of freedom at each end which is 12 degree of freedom total. i was thinking about 2d instead of 3d solution. a cubic would have six degree of freedom at each faces making it 6 times 6 equals to 36 degree of freedom. i think yahoo answer is more fun because i can correct each answer before it is consolidated within a reasonable time...

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