Subject:
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Re: articulation points?
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Newsgroups:
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lugnet.robotics
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Date:
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Wed, 20 Nov 2002 06:15:46 GMT
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Original-From:
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Rob Limbaugh <rlimbaugh@greenfieldgroup.=spamcake=com>
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Viewed:
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1242 times
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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 corresponds to that can be mathematically reference for
any point within that DOF's range of valid values. Anything beyond those
values for that joint (regardless of it's orientation in 3D space) is
unacceptable.
> 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.
"Degree of freedom" directly implies a range, or limit. Therefore, I would
think that any coordinate system you have only 1DOF because either an object
exists within that coordinate system or it does not. How an existing object
can move (a part of) itself to any particular location or orientation is a
result of the state(s) of all the DOF's.
One could also probably argue that "time" itself is a DOF because without
it, your range limit is fixed so that dof1=current position=dof2 because
there is no way for the value in the DOF range to change. (I'm sure quantum
physics or theories on relativity can be used to argue that, but in the
meantime, try moving your hand from your mouse to your face without time
passing between those two position ranges.)
> 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.
I think the ball would be the "joint", of sorts. It still has 3DOF, even
though the race could be constructed to ensure that only 1DOF is used. As
far as the ball is concerned, it behaves the same as if in a straight line.
Everything else is displacement caused by the limit imposed by a radius or
the rate of change between levels of a spiral for every certain unit of
distance traveled. In order to determine the position based soley on the
value of that single DOF used, the race would have to be equal to the length
of the circumference of the ball.
> 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.
For each joint, you add at least 1DOF, so long as another joint doesn't
restrict the movement of another joint. If there is no motion possible in a
joint, then you have zero-DOF in that joint (at that moment, anyway). The
bucket position in space, in your example, only has the 1DOF, but it can be
placed anywhere in 3D space that the additional joints allow range of motion
in.
> 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.
If you mean, "Can a machine/robot hold a hand in a specific location and
orientation in more than one way?", then the answer is yes.
I have an old book called "In The Beginning" (edited by Carl T. Helmers,
1983, ISBN 0-8104-6325-3). It was spawned from Robotics Age magazine
articles. Pages 48 through 80 deal with robot manipulation and control. In
there, they show how to translate orientation of a manipulator (hand,
bucket, whatever) from one position to another. The coordinate of the
manipulator is in terms of 3D coordinates, the orientation it has at that
point is space is used to determine the proper position of all the DOF's in
the system. Or, you can use all the values of each DOF in the system to
calculate the 3D coordinate and manipulator orientation about that point.
Of course, this is how I have always understood things to be and I'm sure my
line of thinking is wrong in a couple aspects...
- Rob
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Message has 1 Reply:
 | | Re: articulation points?
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| You present interesting aspects of the term, could it be that the term has many meanings and really if we understood it correctly we would do justice to the proper meaning. Context is everything, yet you raise ideas and examples that indeed (...) (22 years ago, 20-Nov-02, to lugnet.robotics)
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Message is in Reply To:
| | Re: articulation points?
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| (...) 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 (...) (22 years ago, 20-Nov-02, to lugnet.build.mecha, lugnet.technic, lugnet.robotics)
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