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Jennifer Clark writes:
> 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.
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. However, the parts are attached to
each other in a certain way which restricts their movement. Each
constraint reduces the DOF by 1. When you add them all up, you get 11
constraints, reducing the DOF of the arm to 7. Instead of counting the
constraints, it's easier to count the DOF at each joint.
o Shoulder: spherical joint, 3 DOF (rotation about x0,y0,z0)
o Elbow: hinge joint, 1 DOF (rotation about z1)
o Wrist: spherical joint, 3 DOF (rotation about x2,y2,z2)
...for a total of 7 degrees of freedom.
I guess you would count each joint as a point of articulation (POA)?
In robotics, we generally treat a spherical joint as three different
joints whose axes all happen to intersect at the same point. Then there
is only one DOF per joint, making it easier to count :)
> 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.
With each joint, you add a degree of freedom...you just make the
manipulator (boom, whatever), more redundant with each added joint. The
more redundancy you have, the more different ways you can reach the same
position. The DOF you describe in your example is the Range Space of
the manipulator. The multiple different ways to get there is the Null
Space. DOF = Null Space + Range Space. But we'll leave that for
robotics class.
So in short:
POA : number of joints
DOF : 1 for each telescope
: 1 for each hinge or turntable
: 3 for each ball joint
Maybe that clears things up a bit for everyone :)
--Bram
Bram Lambrecht
bram@cwru.edu
www.bldesign.org
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Message has 3 Replies:
 | | Re: articulation points?
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| Not to be a goof, but, OMG! Bram is Crazy Smart! I gotta go a take some more vitamins and drink Carrot Juice! Ahhh! I see the concept much the same, I figure if we refer to a POA in a Mecha model as the counting scheme, we won't get alot of run away (...) (22 years ago, 20-Nov-02, to lugnet.build.mecha, lugnet.technic, lugnet.robotics)
| | | Re: articulation points?
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| (...) Very interesting thread. A bit OT (and picky ;) mabye, but about the human arm: If you examine your arm closley you'll find that the rotation of the hand actualy comes from the elbow witch rotates the under arm. The wrist only actes as a dual (...) (22 years ago, 20-Nov-02, to lugnet.build.mecha, lugnet.technic, lugnet.robotics)
| | | Re: articulation points?
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| (...) >be honest have yet to come to a definitive answer. The (...) Opinion seems to be divided on the meaning of this term. In my field (computer graphics), I'd say that each joint in the mechanism had between zero and six degrees of freedom, but (...) (22 years ago, 21-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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