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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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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. 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.
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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In order to render the mechanism perturbable the Sun Sprocket must be free to move. When it's free to move the mechanism's equilibrium (which was stable at all points around 360 degrees when the Sun Sprocket was fixed) can be perturbed via the chain by a slight change in the position of the Sun Sprocket by means of the Control Lever, which is fixed to the same Main Axle as the Sun Sprocket. This is also the condition in which four distinct positions of equilibrium emerge. An older model (balanced the very same way as the current model) that clearly demonstrates the four possible positions of equilibrium that arise when the sun sprocket is freed to rotate (two stable and two unstable), appearing in the same order as listed below the video, also shows how the mechanism can be caused to rotate as easily in one direction as the other....
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1. Pendulum horizontal to the left, stable equilibrium.... the mechanism can't be caused to rotate by the action of the Control Lever from this position.
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.
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.... 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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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....
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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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