A puzzling issue: object with 8 degrees of freedom

Many answers! Of course a rigid body has only six degrees of freedom. That is why we are thinking about deformable objects or mechanisms.

Are there any canonical lists of such mechanisms? We are looking for one with threefold symmetry and

John

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/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

.....

You are embarrassing yourself spaceman, I am sorry to report. Wouldn't you feel more comfortable on a non-engineering group?

BrianW

| > 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

| > 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 | | Many answers! Of course a rigid body has only six | degrees of freedom. That is why we are thinking about | deformable objects or mechanisms. | | Are there any canonical lists of such mechanisms? | We are looking for one with threefold symmetry and | 8 degrees of freedom in total. | | John

An object deformed is not symmetric about one of its three axes of symmetry unless the deformation is also symmetric; but that merely returns the 6-DOF of the rigid body. You can't have your cake with a bite out of it.

You are not truly finding 2 extra degrees of freedom You are counting a degree more than once. If you really think that creates multiple degrees of freedom Then a porcupines needles must really blow your mind for degrees of freedom. and boy oh boy Don't even try to think about a forest full of trees and millions (and billions) of branches and leaves etc. :)

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. :)

Hmm? There is an engineer here that states there are more than 6 degrees of freedom? Where? I would like to see how he makes up degrees as new degrees even though they already exist.

Will this one suit your purpose?

On the axis of trifold symmetry, a long finger (1) with a central ball joint permitting the one half (1a) to rotate in the axis of symmetry only,

At the end of this member, three fingers (2,3,4) attached to it, with pin joints, so they can each rotate in just one plane.

At the tip of each of these three members (2,3,4) , a finger joined to each with a pin joint also permitting just one axis of rotation, (labeled 2a,3a,4a). This appears to provide the trifold symmetry you want, in that the mechanism can rotate on the axis of finger (1) and in the colinear axis of finger (1a). Each of three fingers can sweep an angle about the axis of finger (1a) and each of three finger tips (2a,3a,4a) can also sweep an angle with respect to the finger to which they connect.

This is only one of numerous way to provide this specification, it seems.

Brian W

So as I stated, re-using the degrees already known is how you would play with the term "more than six degrees of freedom". Sadly, You are only using the same 6 degrees of freedom of motions more than once. You have a multiple angles of motion in the same 6 degrees occuring in different places only. Don't ever try and engineer the hair on a shaggy dog. :)

| >John | >

| >

| | Will this one suit your purpose? | | On the axis of trifold symmetry, a long finger (1) with a central | ball joint permitting the one half (1a) to rotate in the axis of | symmetry only, | | At the end of this member, three fingers (2,3,4) attached to it, with | pin joints, so they can each rotate in just one plane. | | At the tip of each of these three members (2,3,4) , a finger joined to | each with a pin joint also permitting just one axis of rotation, | (labeled 2a,3a,4a). | This appears to provide the trifold symmetry you want, in that the | mechanism can rotate on the axis of finger (1) and in the | colinear axis of finger (1a). | Each of three fingers can sweep an angle about the axis of finger (1a) | and each of three finger tips (2a,3a,4a) can also sweep an angle | with respect to the finger to which they connect. | | This is only one of numerous way to provide this specification, it | seems. | | Brian W

HAHAHA!

You may find it useful to google for the combination "kinematic geometry" and "robotics".

Ken Pledger.

john_m snipped-for-privacy@yahoo.co.uk wrote:

"Brian Whatcott" wrote

"Androcles" wrote

hanson wrote: ... ahahahaha... Yeah, to you their exchange may sound funny... ahahahahaha... but John and Brian are simply having a standard "machine shop operator" talk. That is their line and their language. Why they posted that into sci.physics & sci math that is the funny part.... ahaha... Both of them are probably laughing louder then you do... ahahaha... Thanks for the laughs, guys... ahahahahanson

| > | >

| "Brian Whatcott" wrote | > | Will this one suit your purpose? | > | On the axis of trifold symmetry, a long finger (1) with a central | > | ball joint permitting the one half (1a) to rotate in the axis of | > | symmetry only, | > | At the end of this member, three fingers (2,3,4) attached to it, with | > | pin joints, so they can each rotate in just one plane. | > | | > | At the tip of each of these three members (2,3,4) , a finger joined to | > | each with a pin joint also permitting just one axis of rotation, | > | (labeled 2a,3a,4a). | > | This appears to provide the trifold symmetry you want, in that the | > | mechanism can rotate on the axis of finger (1) and in the | > | colinear axis of finger (1a). | > | Each of three fingers can sweep an angle about the axis of finger (1a) | > | and each of three finger tips (2a,3a,4a) can also sweep an angle | > | with respect to the finger to which they connect. | > | This is only one of numerous way to provide this specification, it | > | seems. | > | Brian W | >

| "Androcles" wrote | > HAHAHA! | >

| hanson wrote: | ... ahahahaha... Yeah, to you their exchange may sound | funny... ahahahahaha... but John and Brian are simply | having a standard "machine shop operator" talk. That | is their line and their language. Why they posted that | into sci.physics & sci math that is the funny part.... ahaha... | Both of them are probably laughing louder then you do... | ahahaha... Thanks for the laughs, guys... ahahahahanson |

Brian W is definitely having a laugh, John Stanton may have his head up his arse.

Brian, thank you for the proposal. (It almost looks as if it had 4fold symmetry - or am I wrong?)

You also mention "numerous ways" to do this. Can you give a few more?

In any case, thank you very much!

John