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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. I think there were something like 50-75 stacked
on one another - one pretty good use of it was shown as a painting robot.
Not strong, mind you, but I think it would have had something close to N-1
DoF. [N being the number of splines on it. ;-)]
I saw it featured in "The Robot Book" by Richard Pawson (I'm not sure of his
name, must look it up in the library sometime.) amongst other things, how to
build robots with either LEGO (I'm talking *early* LEGO, using 4.5V motors
and both types of gear-reduction boxes that were then available, along with
a considerable amount of gear reduction trains.) or Fischertechnik. I'm
pretty sure if he is still around today, he'd be pleased at how far LEGO has
come. I reckon it would rival Fischertechnik nowadays, although
Fischertechnik has always had the touch sensors and light beams, and
possibly also the rotation sensors, for ages, compared to how long it took
for LEGO to design and develop theirs.
There was also nothing like the Mindstorms or Fischertechnik control units
available today, back then, the author recommended using a card or an
external parallel device that could run up to six motors and four sensors -
or various combinations thereof - attached to the serial port of a Commodore
Vic 20 or similar precursor to the modern-era computers! :-)
Also, DoF isn't the limiting factor in most models, the space (or, as it is
sometimes referred to, the working envelope) that the additional DoF gives
the model is a much more important factor - with your excavator example an
excavator with only 2 DoF can scoop up and move earth around, and even rake
it in a short distance. But add in the extra DoF that making the elbow
joint bendable instead of rigid gives it, and it can make a huge difference
to the effectiveness of the excavator.
Providing their hydraulic leverages are correctly positioned, supported, and
mechanically designed, an excavator can quite literally reshape the world we
live in, many times over!
--
Cheers ...
Geoffrey Hyde
(Remove spamblock to reply.)
"Jennifer Clark" <jen@vulture.dmem.strath.ac.uk> wrote in message
news:H5uqt4.GF4@lugnet.com...
> 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 1 Reply:
 | | Re: articulation points?
|
| A few years back i was showing my platform arm )now defunct) to a friend of mine in engineering,and while talking about degrees of freedom and he said something about half a degree of freedom. I have done some research and have founf nothing on this (...) (22 years ago, 24-Nov-02, to lugnet.build.mecha, lugnet.technic, lugnet.robotics)
|
Message is in Reply To:
| | Re: articulation points?
|
| (...) 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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