An Exploratory Research Mechanism

Aemilius
Aemilius's picture
Posts: 55
Joined: 2010-07-31

Designed and Built by Emile Cole

Range of Motion Video (profile)....
http://www.youtube.com/watch?v=P_vF3...layer_embedded

Range of Motion Video (front)....
http://www.youtube.com/watch?feature...&v=E7CEwnOFnCk

I've been working on this (hobby status) on and off over the last fifteen years or so.... a 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 five to seven degrees its rate of rotation rapidly approaches about a 100 to a 150 rotations per minute over the course of just eight to ten repetitions, all while overcoming only negligible frictional resistance from the main axel (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.

A uniquely balanced mechanical arrangement, the Mechanism's motion is pendulous.... but unlike a simple pendulum which has two possible positions of equilibrium (un-stable when up and stable when down), this Pendulum, because of the way it's balanced, actually has four possible positions of equilibrium.... two un-stable positions alligned with the force of gravity (up or down vertically).... and two stable positions perpendicular to the force of gravity (positioned to either side horizontally).

The gravitational force itself is not switched or turned on and off, the influence that gravity has on the Mechanism is changed by changing the Mechanism's condition.

I'm getting the Mechanism to rotate by periodically changing its condition. The Control Lever at the rear (connected to the Calibrated Spring) is the part that's periodically moved back and forth (3 to 5 degrees approx.) and is solid or fixed to the Main Axel (white) and Sun Sprocket (gold with white center) of the Planetary Chain and Sprocket arrangement. The Planet Sprocket (black, with the Pendulum that is fixed to it) is affected through the imbalancing action of the Sun Sprocket, transmitted to it by the Chain.

There are a few differences that immediately come to mind when comparing this Mechanism to a conventional pendulum. This pendulum....

1. ....has been robbed of any natural periodicity normally associated with pendulous motion. In other words, it's rate of motion depends exclusively on the rate/frequency at which it is being periodically imbalanced.

2. ....unlike a simple pendulum which has two possible positions of equilibrium (one stable and one un-stable), this Mechanism actually has four possible positions of equilibrium (two stable and two un-stable).

3. ....does not swing back and forth in two directions like a simple pendulum with the well known accompanying periodic rise and fall of potential and kinetic energy levels as it begins, continues and ends each motional cycle.

This Mechanism swings to one side, gaining kinetic energy as its potential energy diminishes, and then, by slightly changing the condition of the Mechanism at the appropriate time, it continues its swinging motion in the same direction to the other side without losing the kinetic energy it gained. I believe that's why it begins to rotate so quickly and forcefully.

It's a pendulous Mechanism that rotates relatively forcefully at the first introduction of a relatively slight imbalancing force which is all that's necessary to begin, and then maintain an ongoing reaction to the un-changing or constant force of gravity.

The magnitude of the very slight imbalancing force delivered to the system by means of the Control Lever is sensibly comparable in every way to standing a pencil on end, holding it at the top and moving it back and forth an inch or so (exactly what I feel during testing, almost nothing), a level of applied force that should be wholly insufficient to overcome the inertia of the relatively heavy Mechanism whether at rest or in motion, nor can it account for the immediate onset of rotation.

The actual driving force needed to cause rotation of the Mechanism as a whole cannot be imparted to the Planet Sprocket by the Sun Sprocket via the Chain because the Sun Sprocket doesn't move in such a way as to be capable of imparting rotational motion to the Planet Sprocket, which leaves gravity as the only other driving force available to explain why it immediately begins to rotate in response to a slight imbalancing force delivered to the system by means of the Control Lever.

The reason no mass is explicitly stated anywhere in the analysis is because I didn't see the need. The length of a line represents the magnitude of a force and the arrow itself represents the direction of a force. For example....

The situation graphically depicted in the diagram below won't change as long as any arbitrarily stated magnitude of force for the vector A is uniformly applied as a standard. In other words.... Whether one arbitrarily states for the vector A a magnitude of force equal to two ounces or sixteen pounds the resulting diagramatically shown vector proportions won't change in any way, and the diagram will remain an accurate representation for both scenarios (two ounces or sixteen pounds). So, since any arbitrarily stated magnitude of force for the vector A will result in an identical diagram and identical vector proportions, for the purpose of analysis, there's no need to state any specific magnitude of force for the vector A in the diagram.

It's the same for all the scale drawings in the analysis below....Whenever an arbitrarily stated magnitude of force for the vector D (or any other vector in the diagrams) is uniformly applied as a standard, the magnitude of force associated with any of the other vectors in the scale drawings of the analysis can be quickly and easily derived. For example....

If the vector D is made to equal one inch and the arbitrarily stated magnitude of force associated with it is two ounces (one inch equals two ounces), then....

A.... 3/8 inch equals 0.75 ounces
B.... 3/4 inch equals 1.50 ounces
C.... 3/4 inch equals 1.50 ounces
E.... 3/8 inch equals 0.75 ounces
F.... F = C + B.... 0 ounces

If, instead, the vector D is made to equal one inch and the arbitrarily stated magnitude of force associated with it is sixteen pounds (one inch equals sixteen pounds), then....

A.... 3/8 inch equals 6 pounds
B.... 3/4 inch equals 12 pounds
C.... 3/4 inch equals 12 pounds
E.... 3/8 inch equals 6 pounds
F.... F = C + B.... 0 pounds

For the purpose of analysis the very same numerically un-adorned diagram serves to describe both of the above scenarios equally well.

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.

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.

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.

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, or.... B plus C equals F.

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....

In order to render the mechanism purturbable the sun sprocket must be free to move. When it's free to move the mechanism's equilbrium (which was stable at all points around 360 degrees when the sun sprocket was fixed) can be purturbed 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 axle as the sun sprocket. This is also the condition in which four distinct positions of equlibrium emerge. I found a video of 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 sprocked is freed to rotate (two stable and two un-stable), appearing in the same order as listed below the video. The video also shows how the mechanism can be caused to rotate as easily in one directon as the other....

http://www.youtube.com/watch?v=OoF3zUu8G9s]Images

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, un-stable equilibrium.... the mechanism can be caused to rotate by the action of the control lever from this position.
4. Pendulum up vertically, un-stable equilibrium.... the mechanism can be caused to rotate by the action of the control lever from this position.

This constitutes a perturbable form of balance that can result in immediate onset of rotation (in either direction), presented here as an animation....

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.

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 equilibrious balance 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.


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). 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 Axel (equipped with bearings), presented here as an animation....

Timing.... the stage of the analysis that illustrates the variable timing function of the adjustable Cam and Standing Lever. The diagram below shows the 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 Cam that's moving 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, presented as an animation....


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.



Douglas
Posts: 7
Joined: 2012-11-09
Re: An Exploratory Research Mechanism

I'm not clever enough to understand it, but I still think you're a genious! Coincidence Aemilius rhymes with ingenious? 

I hope everything goes well with this Aemilius. Good luck!

Blessings and good will