Designed and Constructed by Emile Cole
A balanced mechanism that immediately begins to rotate in either direction with an imbalancing displacement of as little as one degree. With repeated periodic displacements of as little as three to five degrees its rate of rotation rapidly approaches about 100 to 150 rotations per minute over the course of just eight to ten back and forth repetitions, all while overcoming only negligible frictional resistance from the Main Axle (equipped with bearings). It may have some applications for extracting rotational motion more efficiently from wind and wave and maybe a couple of other things too.... or it may just be a work of art.
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Range of Motion Video (profile)....
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A uniquely balanced mechanical arrangement, its motion is pendulous. But unlike a simple pendulum which has two possible positions of equilibrium (stable when down and unstable when up), this Pendulum actually has four possible positions of equilibrium.... two unstable positions aligned with the force of gravity (up or down vertically).... and two stable positions perpendicular to the force of gravity (positioned to either side horizontally). In all the diagrams the length of a line represents the magnitude of a force and the arrow itself represents the direction of a force, so no mass is explicitly stated anywhere in the numerically unadorned vector analysis.
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A balanced mechanism that immediately begins to rotate in either direction with an imbalancing displacement of as little as one degree. With repeated periodic displacements of as little as three to five degrees its rate of rotation rapidly approaches about 100 to 150 rotations per minute over the course of just eight to ten back and forth repetitions, all while overcoming only negligible frictional resistance from the Main Axle (equipped with bearings). It may have some applications for extracting rotational motion more efficiently from wind and wave and maybe a couple of other things too.... or it may just be a work of art.
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Range of Motion Video (profile)....
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Range of Motion Video (front)....
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A uniquely balanced mechanical arrangement, its motion is pendulous. But unlike a simple pendulum which has two possible positions of equilibrium (stable when down and unstable when up), this Pendulum actually has four possible positions of equilibrium.... two unstable positions aligned with the force of gravity (up or down vertically).... and two stable positions perpendicular to the force of gravity (positioned to either side horizontally). In all the diagrams the length of a line represents the magnitude of a force and the arrow itself represents the direction of a force, so no mass is explicitly stated anywhere in the numerically unadorned vector analysis.
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This constitutes a perturbable form of balance that can result in immediate onset of rotation in either direction from either of the two possible positions of unstable equilibrium, when the Pendulum is up or down vertically.
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Acceleration....
The
diagram below illustrates both the direction and magnitude of the
forces arising from the various moving parts of the mechanism
individually and shows (FIG. 4) how they ultimately cancel each other
out.
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FIG. 1 - Schematic representation of the Chassis.
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FIG.
2 - The Chassis is fixed in this schematic. The diagram shows the
downward force A of the Pendulum and the resulting force B on the
Planet Sprocket.
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FIG.
3 - The Sun Sprocket is fixed in this schematic. The Chassis and the
Planet Sprocket are free to rotate. The diagram shows the downward
force D of the Planet Sprocket. The force C on the Planet Sprocket is
the result of the force D after the force E from the oppositely
situated Counter Weight (fixed to the chassis) is subtracted, or.... D
minus E equals C.
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FIG.
4 - The Sun Sprocket is fixed in this schematic. The Planet Sprocket
with its attached Pendulum and the Chassis are free to rotate. The
equal and opposite forces B and C acting on the Planet Sprocket
effectively cancel each other out, or.... B plus C equals F.
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A series of schematic diagrams (below) show how the equal and opposite forces B and C cancel each other out at various points around 360 degrees (the Sun Sprocket is fixed for this part of the analysis), presented here as an animation....
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A series of schematic diagrams (below) show how the equal and opposite forces B and C cancel each other out at various points around 360 degrees (the Sun Sprocket is fixed for this part of the analysis), presented here as an animation....
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2.
Pendulum horizontal to the right, stable equilibrium.... the mechanism
can't be caused to rotate by the action of the Control Lever from this
position.
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3.
Pendulum down vertically, unstable equilibrium.... the mechanism can
be caused to rotate by the action of the Control Lever from this
position.
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4.
Pendulum up vertically, unstable equilibrium.... the mechanism can be
caused to rotate by the action of the Control Lever from this
position.
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Pendulum up....
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Pendulum down....
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Pendulum down....
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This constitutes a perturbable form of balance that can result in immediate onset of rotation in either direction from either of the two possible positions of unstable equilibrium, when the Pendulum is up or down vertically.
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Acceleration....
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Timing.... the variable timing function of the Adjustable Cam and Standing Lever. The animation below shows the Adjustable Cam that's located directly behind the Sun Sprocket. It's fixed to the Chassis and rotates with it. The Standing Lever (visible in the videos as a second lever moving back and forth in front of the Control Lever) and the corresponding position of the Adjustable Cam that's driving it are depicted to the left. The Planet Sprocket with its attached Pendulum, the Chassis and the Sun Sprocket are all free to rotate in the following schematic diagrams....
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A
problem then arises as a direct result of the Sun Sprocket being freed
to rotate for the purpose of perturbing the mechanism's equilibrium via
the chain. The varying forces arising from changing mass distribution
during rotation that were formerly transmitted directly to the stand
when the Sun Sprocket was fixed now come to bear on the Control Lever
instead. The diagram (below) shows the downward force D on the Planet
Sprocket. The force H on the Sun Sprocket is the result of the force D,
and the force I on the Control Lever is the result of the force H. The
Mechanism is not balanced or in equilibrium in this diagram because
there is no equal and opposite force to counter the force I.
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That's
where the Calibrated Spring comes in.... it's mounted on the back of
the Mechanism (depicted to the right in the diagram below). The lower
end X is fixed to the stand the Mechanism is mounted on. The upper end Y
is connected to the Control Lever. The diagram (below) shows how the
equal and opposite forces I and J effectively cancel each other out and
equilibrium Q is the result, or.... I plus J equals Q. The
Mechanism is in a state of compensated equilibrium, the sum of all
forces acting on the Control Lever is zero.
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I want
to minimize the magnitude of the input force needed to perturb the
system.... the Calibrated Spring variably compensates for and cancels
out the varying force coming to bear on the Control Lever due to
changing mass distribution. The sum of the equal and opposite forces I
and J coming to bear on the Control Lever equals zero at all times
during rotation as shown (below).
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This constitutes a
compensatory form of balance. It reduces the input force needed to
cause immediate onset of rotation to the level of that needed to
overcome only frictional resistance from the Main Axle (equipped with
bearings), presented here as an animation.... .
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Timing.... the variable timing function of the Adjustable Cam and Standing Lever. The animation below shows the Adjustable Cam that's located directly behind the Sun Sprocket. It's fixed to the Chassis and rotates with it. The Standing Lever (visible in the videos as a second lever moving back and forth in front of the Control Lever) and the corresponding position of the Adjustable Cam that's driving it are depicted to the left. The Planet Sprocket with its attached Pendulum, the Chassis and the Sun Sprocket are all free to rotate in the following schematic diagrams....
By
linking the Standing Lever to the Control Lever the mechanism's
position can be synchronized with the position of the Control Lever at
all points around 360 degrees.
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