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Title:
METHOD OF ECCENTRIC BALANCE WITH VARIABLE PITCH
Document Type and Number:
WIPO Patent Application WO/2021/148888
Kind Code:
A1
Abstract:
Eccentric Balance with Variable Pitch Method, for improvement of the performance of a lifting mechanism, creates mechanical work, through a modified classical balance into an eccentric balance. In this way we create a balance, where eccentric variable pitch is formed by opening or closing its weight carrying free ends of long rods, and in turn, when open/close action take place, it is resembles a theoretical triangle, which have the height as the projection of axis and balance fulcrum in the middle. With this method, and adding the fact that, on long rods free-ends-caring-weights translation, the friction in the horizontal axis is dramatically reduced, due to screw principle from classical physics, and considering the long rods embedded in short rod through radial ball-bearings, being operated for synchronous rotation by a bi-directional engine, which move a cog on each of the long rods by a pinion teeth, it consumes much less energy.

Inventors:
BOTEZATU MIHAITA (RO)
Application Number:
PCT/IB2021/050002
Publication Date:
July 29, 2021
Filing Date:
January 01, 2021
Export Citation:
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Assignee:
BOTEZATU MIHAITA (RO)
International Classes:
F03G3/00; F03G7/10
Domestic Patent References:
WO2019021167A12019-01-31
WO2015051427A12015-04-16
Foreign References:
CA2569642A12008-05-24
Other References:
O.F. KABARDIN: "Fizika: Spravocnye Materialy (Physics: The Reference Materials)", 1991, PROSVESENIE, pages: 46, 51 - 53
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Claims:
(II) THE CLAIMS

By ECCENTRIC BALANCE with VARIABLE PITCH Method, for improvement of the performance of a lifting mechanisms, it is created mechanical work, through a modified classical balance into an eccentric balance with variable pitch featuring that at a classical balance’s long rod (AH), with a fulcrum in the middle, it is added a shorter rod (AO) underneath, with half the length of the long rod and having one end embedded into one end of the long rod (A) and the other end is resting on the main fulcrum (O). In this way the point of embedment (A) of the two rods, become the fulcrum of long rod (AH) which is eccentric from the main balance’s fulcrum, but it maintains the same function of support in the balance originally described, the physical main fulcrum (O) no longer supports directly the long rod, but is relative to the initial support’s projection (O') in the middle of long rod, and is the support of long rod, although eccentric. The next step is that the long rod (AH) of this eccentric balance is sectioned longitudinally in two, keeping the heads of the newly formed long rods (AB) and (AC) embedded in short rod (A) through a shaft, so that the free ends of the two rods (B) and (C) can simultaneously approach and move away from each other, in a mirror fashion, in a horizontal rotation motion, forming at embedding point (A) an angle (a), and the main axis of mechanism is still represented by short rod (AO) as shown in Figure 3, which is a top-down view. Being of a scales type, the weight at the ends at initial long rod’s balance has to be equal, so that the balance is in equilibrium, but when the eccentric balance’s long rod is sectioned longitudinally, then the weights of the two free ends to the newly formed long rods, shall be split also in two equal weights, having regard to maintain at a level equal to the balance weights acting at opposite ends of the mechanism (A = B + C), so that the entire mechanism to be in equilibrium when the newly formed long rods are opened up under an convenient angle (a), preferably a square angle. In this way an eccentric balance with variable pitch is formed, by opening or closing its weight carrying free ends of long rods, and in turn, when open / close action take place, it is resembles a theoretical triangle (ABC), which have the height (AH) as the projection of axis and balance fulcrum (O) in the middle, see Figure 3, and the long rods opened in a convenient angle (a) so that the theoretic triangle’s height (AH) to satisfy the requirement of balance’s static equilibrium, respectively (AO=OH), that will place the gravity centre of ABC in the middle of its height AH. When long rods synchronously approaching each other in the mirror, the height (AH) increase with the additional length (HH') and, due to extending of the projection of active force (OH) with additional length, from the initial open angle, it creates an additional force proportional with the added length (HH’), in this way intentionally unbalancing the forces in the scales with an moment of active force descendant to the point (H') and the resistive force become ascendant at opposite end (A) proportionally, with same momentum amount. With this method, and adding the fact that on long rods free-ends-caring-weights translation, the friction in the horizontal axis is reduced due to screw principle from physics, and considering the long rods embedded in short rod through radial ball-bearings, being operated for synchronous rotation by a bi directional engine, which move a cog on each of the long rods by a pinion teeth, and that it consumes much less energy, we succeed to demonstrate the mechanical momentum added value by creating an additional length of one forces arm in the balance, not by sliding, but by rolling the weights on horizontal plane, to reduce friction.

Description:
METHOD OF ECCENTRIC BALANCE WITH VARIABLE PITCH

(I) THE DESCRIPTION

1.0 The invention relates to a method for improving the work through an ECCENTRIC BALANCE with VARIABLE PITCH, applicable to a mechanism, as a lifting element using minimum energy for cranes or as the swinging beam at an oil extraction wellhead and consists of a mock-up device to describe a process that produces an improvement in mechanical work by means of a new construction method of a classic balance, namely the addition of a short rod (AO) under initial scale’s long rod (AH) so that the short rod will be supported on the fulcrum in the centre of balance at one end (O) while the other end will be bonded with one end of the initial scale’s long swinging rod (AH) It was created in this way a balance beam ECCENTRIC, which initially was supported in its centre on the fulcrum of balance, now rests with one end embedded in the short rod which in its turn rests with the other end on the central fulcrum of the balance (O) which becomes a projection of the point of that fulcrum (O') for the long swinging beam, so the balance became eccentric. We consider equal weights at the ends of long rod (AH), which is embedded in the short rod, so that the mechanism is kept in mechanical equilibrium. Further, we cut longitudinally the swing long rod in 2 equally length rods, and split the weight of its free ends also in 2 equal parts, then open the two newly formed swing long rods (AB) and (AC) with an angle (a), preferably a square angle, in such way that eccentric balance remain in mechanical equilibrium (AOH), as shown in Figure 3, where (AO) is the projection of resistive force arm and (OH) is the projection of the active force arm, while long swinging rods remaining embedded in short rod from one of their ends, but through a shaft to enable their rotation on the horizontal plane, having attention to maintain all weights from this mechanism at an equal level so that the balance weights acting at opposite ends of the mechanism to be A = B + C. In this way we create an eccentric balance with variable pitch, where the free weight carrying heads of long swinging rods, can approach and departing synchronously from one another in mirror fashion, horizontally relative to the reference plane which is the Earth's surface at an angle (a), as well as relative to the main axis of the mechanism, represented by the short rod, to which are referred all the projections of the forces. Through their rotation, long rods forms a projection as the height (AH) of the theoretical formed triangle (ABC) as can be seen from top to bottom in Figure 3, relative to projection on the axis of balance, this angle is open by initial position in a convenient way (square angle) such as the triangle height (AH) to have the projection of the fulcrum (O) in the Centre and thus making the eccentric balance to be in equilibrium. When long swinging rods approaching each other synchronously in mirror, the height (AH) increase with an additional distance (HH') and by this extension of the active force arm (OH), with additional length, from the initial open angle, it creates an unbalancing in Eccentric Balance with descending moment of active force in point (H’) with an moment of force equal with arm’s distance gain (HH') and as smaller as angle (a) becomes, as big as the HH’ become and an ascending moment of resistive force acting on the opposite end (A) proportional with the additional distance added to the total height of the triangle dynamically created, compared to the initial triangle’s height, when free weight-carrying ends of the long swinging rods were in an angle position wide open (square) and when the eccentric balance was in mechanical equilibrium. We consider a maximum added length, when the long swinging rods angle (a) formed in A are closing up to 0°, then the active force will increase with the measured length of the arm that was added to the active force’s arm and the above described intentional loss of mechanical equilibrium, becomes ascending force in favour of resistive force and will be able to lift such a weight equal to the force added by the additional arm's length. This improvement in performance of the mechanical work resulted, also manifests because of minimizing the friction in the horizontal plane, by synchronous rotation of long swinging rod weights around the axis, understood from the known theory of the screw type rotation in horizontal planes, in which the embedded end of long swinging rods with short rod, rotate around the axis and where the angle (a) of long swinging rods is adjustable by the action of a bi-directional synchronous electric motor, which handles a corrugated rod attached to each of the long rods. Since the forces are applied to this eccentric balances are generated by the size of some scalar weights applied to the long swinging rods, this new process is contained in the field of classical mechanics. The technical problem that this process proposes to solve, it is to lift weight or handling a swinging beam of extraction oil pumps from wells up-down, because of using a lower operating cost for equipment located far from the utility networks, capable to provide permanent high power for the operation of wells oil pump extractor’s swinging beam.

1.1 We know in principle, that the levers are simple mechanisms consisting of a rigid body, usually in the form of the rod, in which acts three forces (the fulcrum, active force and resistive force) and that can create a balance of forces, perpendicular to the reference system, i.e. the Earth's surface. Levers can be arranged by Grades, depending on the position of the fulcrum relative to lever’s Rod Grade 1 , namely balance or scales, with the rod positioned on fulcrum, half of the distance between the point of active force application and the point of resistive force application on the balance’s rod We are referring to a new method to build a Grade 1 Lever.

1.2 It is known also that in a Grade 1 scales, the balance is in mechanical equilibrium when the active force (F) with its weight equivalent and equivalent resistive force (R), and its equivalent in scalar weight, are equal, and the distances between the points of application of these forces relative to the fulcrum, respective active force’s arm (bF) and resistive force’s arm (bR), are also equal. We consider as reference system as the Earth's surface and the condition of equilibrium of rotating vertical against the reference system as mechanical equilibrium, for a lever of balance Grade 1 type, leverage is expressed by that the moment of active force (MF) towards fulcrum is equal to the moment of resistive force (MR), expressed in formula MF = MR, where active force FA = F bF and resistive force MR = R bR. By this relationship, it is understood the well known law of levers, in the form of Balance- type Grade 1 : F bF = R bR.

1.3 When, in the case of a classical Scales, arm length of active Force is increased (bF), which is the arm length from the fulcrum to the point of application of active Force, without changing the size of the equivalent weight and the arm length for the application point of the resistive force (bR) and equivalent weight resistive Force remain constant, then the active Force will increase proportionally with the length that was increased active force’s arm, and becomes descending relative to the reference plane, thus generating an intentional loss of mechanical equilibrium in favour of resistive Force, that will be able to lift such a weight that equals the upward force added to the resistive force (R) by descending active Force (F), see Figure 1.

1.4 Without intended to demonstrate that the mechanical advantage is equal to 0, under a system that requires the translation of the weight along the length of the rod, further from the middle fulcrum, which require as much additional energy gain through the length of the active Force’s arm added, due to the frictions in the system, and knowing that in an isolated system, energy is not lost but is transformed in accordance with the laws of physics, the demonstration would have no practical gain. But, if we cosider this system of forces, as open system, with energy input from outside the system, in a form of a bi-directional motor, and if we manage to improve one of the factors, i.e. frictions of the arm’s caring weight on horizontal sliding, it would be a whole-operation mechanism gains, turning the gained energy in this process in improved mechanical work, within the same system. Therefore, we will use a new method to move the point of application of active Force on the arm's length of this force, i.e. the equivalent weight in physical terms, adding an additional length of the arm active force and minimizing friction on plane surfaces, by moving the weight almost without friction, due to the well-known screw theory for rotating around a shaft, intentionally generating steady loss in mechanical equilibrium, with the intention of using added resistive Force created with this method, on the ascending long swinging rod’s end, and which is generated by extending the distance of the point of application of force on the lever relative to the fulcrum, and to create through this action of extending the active Force’s arm, a mechanical work which moves downward at the opposite swinging rod’s free end, for practical purposes without the use of weights to add to active Force as a source, which is applicable in a new model of a crane or a Piston’s arm, to lift and manipulate weights, using only initial weights applied in the balance, without changing the physical size of respective weights, neither changing the initial length of the long swinging rods. In the actual stage of technology, with reference to this Artwork, this method was only proposed by same author in application for patent no. A 00520-2017, and by its certified priority IA no. PCT / IB2018 / 055488, and published by reference no. WO / 2019 / 021167, which was unfortunately presented at conclusions without a solid demonstration of Industrial applicability, according with the Report from IPEA / RU and respectively could not be patented in that form, therefore was withdrawn at end of period, so technical solution in this script is new, and was formally submitted to the local bureau OSI under reference number A 00020-2020, dated 20-01-2020 for intent of Certification of Priority with that date.

1.5 The object of this invention is the method of creating a mechanism that enhances the work, and refers to a classical balance, whose long rod having added another rod twice shorter than long rod, underneath the long rod and which short rod has one end embedded to one side of long rod and rests on the balance’s fulcrum at the other end, so the long rod remains suspended only in the point of embedding and does not touch balance’s fulcrum.

In principle, the mechanism acts exactly the same forces described originally from classical balance, and weights are added to a long rod when it is in mechanical equilibrium, with the difference that the fulcrum of balance becomes eccentric and the long rod is no longer supported directly on its initial fulcrum (O) but on its projection (O') in a vertical plane in relation to the considered reference system (the Earth Surface), as shown in Figure 2.

1.6 Furthermore, through a new way of development, cut the long rod longitudinally, transforming it in two rigid swinging rods of same length, and keeping those embedded each, in the initial embedding point by a shaft, which is also the point of action of the resistive force in the mechanism and thereafter dividing the value of active Force from this mechanism, i.e. the weight of the operating leverage, in two weights of equal size, which we attach at the free ends of these newly formed rods. Both longer rods will be able to rotate the angular and parallel to the reference system, which is the surface of Earth. The free ends of the rods that carries half the weight of the original active force, should depart and closing in, mirroring each other synchronously, towards and outwards the main axis of the mechanism represented in part by the short Rod, generating an angle that varies according to the distance between the weight-carrying ends of the long swinging rods. Initial active force and resistive force, their equivalent weights and respective arm length, remains constant always.

1.7 This process of achieving mechanical advantage has the benefit that we can adjust the mechanical equilibrium in the above described mechanism, opening up the two long swinging rods with weight-carrying ends, at a convenient angle, which can be a square angle, and with the rod’s ends spaced at equal distances relative to the main axis of the mechanism, so that the mechanism is in mechanical equilibrium relative to the reference grid that is the Earth's surface, so that resistive force, i e. its equivalent weight, is equal to the two halves representing the active Force, even though the long rods are kept in an open-angle, and Active Force is represented by two halves of long swinging rods with weights at the free ends, then the projection of the two halves of forces representing the active Force and the resistive Force projection, must cancel each other, creating Mechanical Equilibrium in this mechanism. Seen from above the mechanism will resemble an isosceles triangle, and in theory the centre of gravity for an isosceles triangle is one third from basis and two thirds from peak, but in practice and by experiment, when weights are applied to points described above here, then the centre of gravity can be adjusted until the height of the said triangle is half represented by Active Force projection and its arm, and the other half is represented by the resistive force and its arm and with the fulcrum (0) in the middle. The role of the initial projection of long rods, is to show the difference in distance, where free weight-carrying ends of the two newly formed long rods, will approach synchronously, they form a variable- angle, by synchronous approach to main axis, which also represents the height of this theoretical triangle - Height that will increase proportionally with the decreasing of the angle, but the chosen length of the long swinging rods remaining constant, since only rotating one towards the other, will add an additional length to the initial height length of triangle’s to the side of the arm of active force, i.e. on the side of free ends, thus forming an ECCENTRIC BALANCE with VARIABLE PITCH, as shown in Figure 3.

1.8 Results that, on the one hand, when the measure of the angle described above is zero, i.e. when the two rods are closest to the main axis of the mechanism, or joined together, is created maximum additional length to the Active Force arm, respectively the maximum surplus of ascending Resistive Force at the opposite end of the ECCENTRIC BALANCE WITH VARIABLE PITCH and on the other hand, when the angle is open until a sufficient distance between free weight-carrying ends, the height of the triangle formed by the projection of two long rods, divided into two parts of equal length, forms a balance in mechanical equilibrium, with its height length equally distributed on one side and the other of fulcrum (O’). Flowever, in order to be in equilibrium, the mechanism described above must have the two long rods open at an calculated angle wide enough, and a square angle is recommended as ideal for this modality of implementation, and the length of the long rods shall be selected from the start of construction of the device, so that the height of the triangle described theoretically, must have equal lengths related to fulcrum, when long rods are open at the square angle and the projection of resistive Force and active Force towards fulcrum, are equal. When in mechanical Equilibrum, the long swinging rods remain parallel to the surface of the Earth, which is considered as reference system. Additional length to the height of the triangle described above, is gained by synchronously closing/opening of the long swinging rod’s free ends, and can be calculated mathematically, for each size of variable angle opening of the said rods, even to degrees or less. 1.9 The projection of the two long rods on the central axis, when those resemble a triangle, is also height in that triangle, and tits central point is equal to half the height of the said triangle, and represent the projection of the fulcrum of the lever. Ideal for theoretical demonstration of the solution, we will consider the triangle described above as isosceles rectangular triangle and because the sides, respectively the long swinging rods in the mechanism, are open at the same distance from the central axis of the mechanism, and we need to find the length of the long rods mechanical equilibrium, when open at the convenient angle, the projection of the resistive force’s arm meaning that from (A) to fulcrum balance projection (O) or (O'), must be equal to the active force arm projection, respectively ends of the long rods (H) that carries half the weight for rebalancing each, in points (B) and (C). The height of this initial triangle, is calculated trigonometrically, as being equal to the numeric value of the cosine of the half angle formed by the of rods and described above, multiplied by the length of one of the two long rods regarded as sides, because the height in an isosceles triangle is also bisector and divides the triangle in two equivalent rectangular triangles AHB and AHC as shown in Figure 3

In this way we can find out the scalar value of the initial triangle’s Height, whereas only one of said equivalent triangles will give that sufficient result, by well known applied formula to our case:

AH = 0.5 cos a x AB (where 0.5 is multiplied with the Cartesian value of “cos a”) where the two long swinging rods are considered sides of said triangle and AB = AC are the length of these sides, and a is the measure of angle BAC of said triangle, where AH is the height into theoretically formed triangle ABC.

The formula above is met, since the triangle is isosceles, the sides being the two long swinging rods, and the height is also bisector of said triangle and divide it into two rectangular equivalent triangles, where common side represents HEIGHT of initial triangle, i.e. angle from top of triangle is divided initially into two angles of equal measure. Therefore it’s sufficient to compute only one of rectangular triangles formed, in order to find the value of the HEIGHT of initial triangle, by half of Cartesian value of angle (a). Closing-in the said angle by synchronous approach of the free ends of the two long swinging rods, angle alpha’s value decreases, hence the Cartesian value of the cosine increases proportionally, and therefore HEIGHT of initial triangle increases.

This is achieved by the above formula for triangle taken into account, until such time as the measure of the angle alpha, which is the variable angle BAC, becomes zero, i.e. when the value will be cos 0° equal to 1. From the total gained value of height, we deduce the initial value of the height of the triangle, it follows a surplus of mechanical work of the active arm length relative to the initial Height. So, every smaller angle results in greater extent of the length in triangle’s Height, and also additional length to active Force’s projection on the axis, added to active Force arm’s projection of the mechanism. Note that, when the angle is entirely closed, i.e. when it has zero value, we have maximum additional length added to active Force’s arm and practically, due to horizontal translation of the free ends of rods approaching up to unify and of negligible friction from the embedded shaft of the ECCENTRIC BALANCE WITH VARIABLE PITCH, due to the screw principle of rotation in the horizontal plane of the free weight-carrying swinging rods, we can create a mechanism described with an added value along the Active Force’s arm, without changing weights acting in this mechanism, and without changing the length of arms, and to generate a upward resistive force at the meeting point of the two long swinging rods, equivalent with all additional length gained at the other end of the mechanism. So the additional HEIGHT length, mathematically depends on the size of the angle formed by the synchronous rotation of the long swinging rods and so, by applying additional length relative to the point of initial application, in order to make an additional distance relative to the initial projection of point (H), using less energy for mechanical rotation-translation in this case, and substantially less for pushing weights on a horizontal plane through direct horizontal friction, because through the screw principle, rotating around a shaft, the friction is much smaller than sliding weights along the force’s arm on a horizontal plane.

See further Forces moment (L) = (moment of inertia)*(kinetic acceleration):

To try to understand this relationship much more precisely, let's imagine that one hit the free end-caring weights of long swinging rods with an initial impulse from outside towards inside as represented in Figure 3. This can be done manually or by a bidirectional motor synchronous, handling a corrugated rack attached to each of long rods to close-in their angle. We know that the initial moment of inertia of the weight-carrying rods is zero, respectively the rods are at rest, when the eccentric balance is in equilibrium. We know also and that orbital angular momentum (L) for a particle, is a pseudo-vector r*p, a direct product of the position vector of the particle r (relative to a specific origin), and its mechanical momentum p=m*v. Consequently, to transfer the kinetic moment generated by hit-closing in the angle Alpha at a given speed, we have: mvr = ± L (depending of rods position towards the main axis), where the plus sign or minus sign, in the view of the “Screw Principle” related to a horizontal plane, indicates if angular momentum tends to create a movement of rotation in clockwise direction or in the opposite direction of free weight-carrying ends of long swinging rods towards the axis, and we can define (r) as a point on the arc of a circle described by the free ends of the long swinging rods, as synchronous approaching or departing one-another. This equation can be applied more generally, provided that (L) should include only those parts of the force, perpendicular to the radius of the line, according to the “Right Hand Rule of Screw” at horizontal rotation, and net amount of Momentum is M = dL/dt. If we take into account the well-known formula of mechanics, kinetic momentum is L= rFsina, applied for a period of time, the net momentum will be M = rFsina / 1. Where (F) is the scalar size of the force acting on the free ends of the swinging rods projection, calculating the constant weight at the rod’s end, where (r) is the scalar length of a rods, and (sin a) is derived from the angle of the long rods for each of the variable angle “alpha” sizes, which is a result of moving of free weight-caring ends of long swinging rods.

1.10 Conclusion is that we have demonstrated the process in terms of theory that horizontal rotation of long swinging rods produce mechanical work to a downward force at one end and an upward Force to the other end of the mechanism main axis, applied relative to the Earth’s plane, and the mechanical work of active force and resistive force in this balance is the force multiplied by the length of swinging arm force’s projections gained as excess height length and to obtain this, is needed an impulse from the outside of the system i.e. bi-directional motor, in order to move the rods by rotation towards each other in horizontal plane, so it is a non-isolated system.

1.11 With this conclusion, we move on to creating a mechanism for type of a crane or as a piston arm, that can lift weights by applying the methodology of construction and the formula previously used for theoretical calculations, which are used for opening or closing free ends of the long rods, manually, or via a bi-directional synchronous motor handling a cog attached to each of the rods. This force is calculated mathematically and is equal to the mechanical work required for the translation of both free weight-carrying heads of the long swinging rods, considering that the effects of friction on the shaft are very low, due to principle of screw from classical physics, for rotation around a horizontal axis, and is publicly tabulated in tables for different type of materials.

To give an example of this practical application of methodology, in terms of physical lookout, and without necessarily scaling the picture of hereabove presented invention, see Figure 4.

1.12 Using further notations from Figure 3 as the most representative, in a mechanism the short rod (AO) is 0.5m and with an active force and a resistive force whose initial sizes are 90N each, we need to calculate the length of the long rods (AB = AC), before their installation in the mechanism, which must be in mechanical equilibrium when open state by a square angle. Because the rods are rigid and made of lightweight composite materials, still adding to the initial Active and resistive Force equivalent weights, distributed evenly lengthwise 10N as equivalent weight of rods on their length, on each side of the force’s arms. We know that active torque is equivalent with the resistive torque of 100N * 0,5m = 50Nm each side and that the force is divided into two free weights attached at the ends of the long swinging rods (B, C) and free ends that initial carrying weight of the swinging rods are positioned at an angle of 90° located at the point of embedding shaft with the short rod noted with (A), and we wish to calculate also the additional length of the projection of the active force arm resulting from the various measures of opening/closing long swinging rod’s angle. Using the Figure 3 notations again, we have: In the isosceles triangle ABC we have AO = 0,5 m as resistive force’s arm projection (the short rod) and OH = 0,5m as active force’s arm projection, so we have the height of triangle AH =1m as the original scalar measure, with the mechanism in mechanical equilibrium. To have this mechanical equilibrium there must be a torque AO = OH = 0,5 m * 100N = 50Nm. So, in rectangular triangle ABC, where AH it is the height and is also bisector, it generates two identical triangles. Take the right-angled triangle ABH as half of the triangle ABC and consequently, in triangle ABH the angle BAH = 45°, and the common side AH = 1m, and AH is common in two equivalent triangles ABH and ACH, but AH is also the HEIGHT of the triangle ABC and we set this length of AH to be equal to 1 (one) meter:

From above theoretical demo, the initial angle BAC = 90°, for half of this angle (cos 0.5 a): where cos BAH = AH/AB = > cos 45° = 1m/AB = > 1.4142 / 1 - AB (scalar value is meters). The final result is that the length of the long swinging rods to install, and at which the Eccentric Balance to be in mechanical equilibrium at maximum open angle of 90°, is equal with 1.4142 m = AB = AC

But pitch angle is variable, so in order to find length of height AH' at the angle B’AC’ = 60°, for half of this angle, we have cos BAH' = AH’/AB = > cos 30° = AH' / 1,4142m = > AH' = 1,2232m, and this additional gained distance is for intermediary angle a size of 60 degrees. For the angle BAC = 0° additional distance added as mechanical advantage to the system will be of 0, 4142m for the benefit of the active force, which become descending since the free weight-carrying rods are total closed to the main axis, and because cos 0° = 1 then the active force is multiplied by the length of the arm active force OH' respectively maximum distance AH' is equal with AB original length. Finnally we demonstrate that maximum additional lenght added to OH by HH' is 0,4142m => 82,84% added to initial lenght of 0,5m. The result is that the maximum active force added is 0.4142m x 100N = 41,42Nm or when free weight-carrying heads of long rods are closed completely, while the initial torque angle opened at 90° was of 50Nm on either side of the projected support (O), keeping the mechanical equilibrium in balance of forces, respectively OH which is the active force and AO which is resistant force arm, that moment shall be maintained and increased by the additional arm-length increased with standard weight, which is 41,42Nm in favour of Active Force By this action we manage to unbalance intentionally eccentric balance in favour of the active force, which becomes a descending force, through additional length from the active force arm of the OH in OH' with 82.42%, transforming the resistive force into an ascending force with the same amount of mechanical work gained which is 82.84% from the initial, when the mechanism was balanced.

We must calculate also momentum necessary to close or open the free ends of the weight - carrying rods, in order to assess all device’s consumption, by above formulas, as follows: For BAC = 90° means that the mechanism is at the maximum alpha angle opening when the mechanism is in mechanical equilibrium, and we know that AB = 1,4142m and AH = 1,00m means the maximum open ends distance shall be BC = 1,9996m which we can easily round at 2,00m because when is used by trigonometric formulae the half triangle is also isosceles, then AH = BH = 1,00m. Maximum momentum necessary to move synchronously the long rods towards main axis until closing at maximum the angle BAC = 0°, and departing to the maximum angle BAC = 90°, whereas the friction at embedded support in the shaft (A), has a specification that include a ball bearing for horizontal rotation, the computing is made for the torque needed with addition of friction by the principle of screw from classical physics, even if the friction coefficient is 0.0001 on the lubricated steel on steel (because rotation around the axis by an embedded ball bearing, where the balls don't slide but roll). Calculation, under stringent condition of steel on steel, using Figure 4 quotes and above formulas, is as follows: We have constant mass, so the torque required for the rotation of long rods, in accordance with the formula chosen above M = r F since / 1, where a = 90° initially and is decreasing by the variable pitch, but we still consider the initial (for calculation of most stringent conditions) and r = 1m and F = 100N, and we set the time at 4 seconds (by convenient motion default setup to cover both directions), to maximum close open back to 90° to the free weight carrying ends of long rods, and where the value of angle alpha decreases with 22.5° every second, therefore for the above case: we have M = r F sina / 1 => M = 1,4142m*100N*1 / 4s therefore the size of the scalar momentum is 35,35Nm/s calculated as Kinetic Moment. Because we have very small friction, and long rods are encased in small Rod by ball bearings radial-thrust that rotate around the axis, there is need only the initial impulse for a second, and a limitation stopping pin, at the opposite side of the corrugated racks (4) to stop the synchronous engine’s (6) pinion teeth (5) and reverse back to initial state. So we have 100Nm/s * 0.002 => M = 0.02Nm/s and even in the most stringent case the rest of 41,42 Nm/s, of which we subtract the initial amount of impulse needed to close the rods, we are left with an optimization of the force in the system, of min. 14.7% contribution to mechanical work of this method in the presented mechanism, which is handled by weights with scalar sizes, and not by the action of gravitational forces, stating that any scalar size of additional weight, increases this percentage value, as well as any other type of closure of the weight bearing ends of long rods. The mechanical advantage could be further improved by opening the angle between the rods back to 90°, through the bi-directional motor, in this way the mechanism acts as a piston’s arm, for example for oil extraction wells, for which, due to the areas of Extraction located in remote geographical areas and away from utility networks, in many cases the energy required to operate the piston of extraction pump, is difficult to transport, and requires low energy consumption for a long time and a lower cost of operation. Hence the industrial applicability of this method of reducing energy consumption through an optimized mechanism for manoeuvring the oil well rocker at the extractor pump would be our Mechanical Advantage, whereas in the ball bearing case, this friction coefficient becomes negligible, leading to a very low energy consumption and low costs.