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Stable Limit Set Behavior in a Dynamic Parts
Feeder
Advisor: Dr. Kevin Lynch
Students: Michael Northrop Peng Pan
We describe a one-joint
planar arm which repeatedly throws and catches parts on its surface, and we
demonstrate that proper choice of the throw velocity and arm geometry guarantees
that the part will enter a unique recurrent motion pattern from a large set
of initial configurations. The resulting system resembles an open-loop
stable juggler of polygonal parts.
The simulation result of a
triangle part is shown in figure below. Note that the cycle has a thickness
associated with it, unlike the limit set for the approximate system where
discrete jogs are replaced by a velocity. We can also show that the system
is attracted to this cycle from a large range of initial conditions.
Left figure below is a
line drawing of our prototype experimental system. A planar part rests in
gravity on a horizontal arm. A rotating actuator contacts the arm and
rotates it clockwise about a pivot. This stores energy in a return spring.
The actuator eventually breaks contact with the arm, releasing it to spring
back and impact a mechanical stop, at which point the part breaks contact
with the arm, free falls, impacts on the horizontal arm and settles. The
actuator then comes back around and repeats the process. If the amount of
the arm deflection is small, the process approximates a sudden upward
impulse on the part.
The experimental video is
shown in the right. (Download: AVI format
MPEG4 format)
Experimental System
Publication:
Stable Limit Set Behavior
in a Dynamical Parts Feeder
Kevin Lynch, Michael Northrop, Peng
Pan
IEEE Transactions on
Robotics and Automation, Vol. 18, No. 4, August 2002
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