Subject:
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Degrees of Freedom - an introductory tutorial
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Newsgroups:
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lugnet.robotics
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Date:
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Thu, 6 Jan 2000 21:08:26 GMT
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Viewed:
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589 times
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In kinematics there is a concept called "degrees of freedom." It's usually
abbreviated "DOF." A degress of freedom is one axis of physical movement (this
discussion is restricted to real motion - virtual degrees of freedom won't be
discussed).
If you imagine a Cartesion coordinate system, with an X, Y and Z axis system,
all perpendicular to each other, then translation along any axis represents a
single degree of freedom. It includes translation in both the positive and
negative directions, but not rotation. Rotation about an axis is a totally
separate DOF. For example, if you had a gear in the YZ plane, it would rotate
about the X axis. If it were properly attached, it wouldn't translate.
That means that there are six independent degrees of freedom for every
independent part. These are usually called the "rigid-body" degrees of
freedom, representing motion of the center of gravity of the part.
Usually when degrees of freedom are discussed, independent degrees of freedom
are meant. One important thing for us is that each separate motor driven by
the RCX or an external battery-box is a single degree of freedom control.
A single DOF is not a vector quantity. It typically doesn't have magnitude,
only direction. Vector descriptions of the motion are based on a study of the
degrees of freedom.
It should be noted that a single DOF isn't restricted to a cartesion
coordinate system, but could be translating or rotating in any single
direction. It's the independence of the motion which is important.
The next kind of degree of freedom is a "coupled" degree of freedom. This is
where there are secondary motions which are fully attached to an independent
DOF. An example of this is a differential drive, with one leg ratcheted, so
that a 'bot will go forward straight, but turn while backing up. The second
DOF is the turning rotation, but it's not independent; it's coupled to the
translational DOF. Thus you get it with no extra motor. But note that if you
lift away the ratchet, the coupled degree of freedom disappears. However,
lifting away the ratchet requires another independent degree of freedom.
Sometimes, particularly in precision optical equipment, it is necessary to
ensure that motions from one part are cleanly transferred to another, without
strains or disturbances from thermal expansions, for example. This is done by
attaching the two parts with a "kinematic" interface. A kinematic interface
transfers only the six "rigid-body" DOFs from one part to the other. Often
this is harder to do than it appears. Although kinematics is a general study
of motion, a "kinematic" interface is a very particular thing.
I hope this helps in thinking about what you want your devices to do.
Regards, Dave Paule
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