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In lugnet.build.mecha, Eric Sophie writes:
>
> My Mecha is kick arse! It has lot's of movement. It rocks! It has 12 POA
> giving the Mecha 24 DOF! Whoooo hooooo!
Pedant's corner:
This reminds me of an argument I've had several times, and to be honest have
yet to come to a definitive answer. The maximum number of degrees of freedom
an object can have in three dimensional space is six; translation in the X,
Y, and Z planes and rotation about in the X, Y, and Z axes. Giving a device
more points of articulation does not necessarily increase the degrees of
freedom, although it can increase the envelope or ability of the device to,
for example, work round corners.
There can be other oddities, where an object can move in more than one plane
and/or rotation and have less degrees of freedom than the movement initially
implies; think of a ball bearing rolling down a spiral race. This has
translation in all three planes but only one parameter is needed to specify
any possible location in those three planes, i.e. the distance of the ball
from the start of the race. If the ball rolls in a predictable way then the
same parameter can be used to derive the rotation of the ball at an
arbitrary position as well.
Think of an excavator boom with a joint at one end attaching it to the
chassis and a rotating bucket on the other. To me this has 2 DOF; the
translation of the boom (which will follow an arc) and the rotation of the
bucket. Ok, so translating the boom will also rotate the bucket, but this is
not an independent parameter so it is still only contributes 1 DOF. If you
split the boom and add another similar joint to give the standard excavator
boom, the boom can now cover an area rather than an arc, so you now have 3
DOF. If you now split the boom again and another joint, similar to many long
reach demolition excavators, however, the boom still only covers an area so
you still have only 3 DOF. No matter how many joints of this type you add,
you still have only 3 DOF.
Is there a case to be made here for a description based on internal state of
a machine vs. external state? It is possible to conceive of a machine where
many internal states can correspond to one external or viewed one, for
example. Presumably the answers are out there rather than the mere
conjecture I put forward here.
Of course, if your mecha inhabits a higher dimension, and therefore
genuinely uses the extra DOFs available, I take it all back :-)
Jennifer
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Message has 4 Replies:
 | | Re: articulation points?
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| (...) Oh? Hmmm...do tell. (...) Right! I see. In my own way I work around certain "movements" or joints by making two separete joints cover the same envelope or Area or Control. I mean in that, for example. The Arms of my Super Mech-Bot don't have (...) (22 years ago, 20-Nov-02, to lugnet.build.mecha, lugnet.technic, lugnet.robotics)
| | | RE: articulation points?
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| (...) However, a device is made up of several objects. Each component, if treated separately, has six degrees of freedom. Thus each component of, for example, the human arm (reduced to an upper arm, lower arm, and hand) has 6 DOF, for a total of 18. (...) (22 years ago, 20-Nov-02, to lugnet.build.mecha, lugnet.technic, lugnet.robotics)
| | | Re: articulation points?
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| Everything I've ever seen mentioning DOF refers to absolute reference points (a focus, if you will, or origin) that the range is controlled by. In terms of articuation, each DOF corresponds to a joint, which is a fixed focus point that the range (...) (22 years ago, 20-Nov-02, to lugnet.robotics)
| | | Re: articulation points?
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| All this talk of articulation points reminds me of an actual splined robot. Basically, it was a series of convex circles through which ran a series of wires, with a space in the middle for a spray hose or pressure cleaning equipment to pass through. (...) (22 years ago, 23-Nov-02, to lugnet.build.mecha, lugnet.technic, lugnet.robotics)
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Message is in Reply To:
| | Re: articulation points?
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| Hello, I would define a POA as a point when mobility occurs whereas the rotattion is counted once. That is to say if a Shoulder joint spins forwards and back it counts as one POA and should not be counted as two. Example: In this picture of the (...) (22 years ago, 19-Nov-02, to lugnet.build.mecha)
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