(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 piston pumping at an oil extraction wellhead and consists of 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 long rod (AH). It creates in this way a balance beam ECCENTRIC, which initially was supported in 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) who becomes a projection of the point of that fulcrum (Ο') for the long 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 in mechanical equilibrium. Further, we cut longitudinally the long rod in 2 equally length rods, an split the weight of their free ends also in 2 equal parts. Then open the two newly formed long rods (AB) and (AC) with an angle (a), preferably a square angle, so that eccentric balance remain in the mechanical equilibrium (AOH), as shown in Figure 3, where (AO) is the projection of resistive force and (OH) is the projection of the active force, while long 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 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 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) such as the triangle height (AH) to have the projection of the fulcrum (O) in the Centre and the eccentric balance to be in equilibrium. When long rods approaching each other synchronously in mirror, the height (AH) increase with an additional distance (ΗΗ') and by this extension of the active force arm (OH), with additional length, from the initial open angle, it creates a unbalancing in this mechanism with an moment of force equal with distance gain (ΗΗ') and as smaller as angle alfa becomes, as big as the HH' become and the resistive force will be added with it, creating by intentional unbalance, an ascension moment 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, when free weight-carrying ends of the long rods, were in an angle position wide open (square) and when the eccentric balance was in equilibrium. Considering maximum length, when the long rods angle (a) formed in A are closing up to 0°, then the active force will increase with the length of the arm that was added to the active force and the intentional loss of mechanical equilibrium, becomes maximum 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 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 rods with short rod, rotate around the axis and where the angle (a) of long 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 rod, 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 the piston of extraction oil pumps from wells, 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 extractors arm or remotely located weights to be lifted to which classical cranes cannot reach or utilities are difficult to be built for large cranes electrical needs.

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 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 a Grade 1 lever the balance is in mechanical equilibrium when the active force (F) with its weight equivalent and equivalent resistive force (R), and its equivalent 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 the reference system as the Earth's surface and the condition of equilibrium of rotating vertical reference system (mechanical equilibrium), for a lever of balance 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: 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 a closed 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, and if we manage to improve one of the factors, i.e. frictions of the weight on horizontal sliding, it would be a whole-operation mechanism gains, turning the gained energy in this process in 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 resilient Force created with this method, on the ascending long rod's end, and which is generated by extending the distance of the point of application of force to 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 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. At this point of the State of the Artwork, this method was proposed by the same author in the application for patent no. A2015/00060, and by its international application no. PCT/RO2015/000020, which was unfortunately presented as closed system and could not be patented in that form, therefore was withdrawn, so technical solution in this script is entirely new, and only now formally submitted.

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 point of embedding and does not touch the 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 (Ο') in a vertical plane in relation to the reference grid as shown in Figure 2.

1.6 Furthermore, through a new way of development, cut the long rod longitudinally, transforming it in two rigid rods of the same length, and keeping them embedded in each of the initial embedding point by a shaft, which is also the point of action of the resistive force in the mechanism and also 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 the Earth. The free ends of the rods that carries half the weight of the original active force, should it approach and closing in, mirroring each other synchronously, one another, towards and outwards the main axis of the mechanism, which is represented in part by the short Rod, generating an angle that varies according to the distance between the weight- carrying ends of the long rods. The initial active force and the resilient force, respectively their equivalent weights, attached to the free ends of the long rods, remains constant in this mechanism.

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 rods with weight-carrying ends, at a convenient angle, which can be a square angle, and with the rod's ends caring weights, 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 rods ends, 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, where the height of the 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 (O) in the middle. The role of the initial projection of long rod, 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 rods remaining constant, since only rotating one towards the other, it can be added an additional length, that will be added to the initial length of triangle's Height to the side of the arm of active force, 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 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, it forms a balance in mechanical equilibrium. However, in order to be in equilibrium, the mechanism described above must have the two long rods open at an 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, for the projection of the active Force when long rods are open at the square angle and the projection of resistive Force towards fulcrum, are equal. Long rods remain roughly 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 rods free ends, and can be calculated mathematically, for each size of the angle of opening of the rods.

1.9 The projection of the two long rods on the central axis when those are opened in the triangle, is also height in triangle, as well as the projection of initial long rod, and the central point is equal to half the height of the initial 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 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 (Ο'), 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 value of the scalar initial triangle's Height, whereas only one of the above equivalent triangles, by well known mathematical formula:

AH = 0.5 cos a x AB

where the two long rods are considered sides of the triangle AB = AC are the length of the sides of the triangle, and a is the measure of angle BAC, and AH is the height.

The formula above is met, since the triangle is isosceles, the sides being the two long rods, and the height is also bisector of triangle and divide it into two rectangular equivalent triangles, where common side represents the height of initial triangle, i.e. the angle from the top of the triangle is divided initially into two angles of equal measure. Therefore it is sufficient to compute only one of rectangular triangles thus formed, in order to find out the value of the HEIGHT of the initial triangle, and half the Cartesian value of the angle alpha. As the angle in closing in by synchronous approach of the free ends of the two long rods, angle alpha 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 (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 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, through the screw principle of rotation in the horizontal plane of the free weight-carrying 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 generate a upward resistive force at the meeting point of the two long rods, equivalent with all additional length gained at the other end of the mechanism. So the additional length mathematically depends on the size of the angle formed by the synchronous rotation of the long rods and by applying additional length relative to the point of initial application, in order to make the translation of the application of 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 by rolling mode, 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 endearing weights of long rods with an initial impulse. 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 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 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 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 rods long synchronous approaching 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 the 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/t. Where (F) is the scalar size of the force acting on the free ends of the 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 alpha angle sizes, which is a result of moving of free weight-caring ends of long rods.

1.10 Conclusion is that we have demonstrated the process in terms of theory that horizontal rotation of long 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 reference plane, which is the surface of the Earth, and the mechanical work of active force and resistive force in this balance, is the force multiplied by the length of arm force's projections gained as excess length and to obtain this is needed an impulse from the outside of the system, in order to move by rotation towards each other, those long rods in horizontal plane, so it is an open system.

1.11 With this conclusion, we move on to creating a mechanism for type crane or piston 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. The force required for this moment of force is calculated mathematically and is equal to the mechanical work required for the translation of both free weight-carrying heads of the long 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.

To give an example of this practical application of methodology, in terms of physical lookout, and without necessarily scaling the picture of 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 rods (B, C) and free ends that initial carrying weight of the 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 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 is equal to 1 (one) meter:

From above theoretical demo, the initial angle BAC = 90°, for half of this angle (cos 0.5 a): so we have cos BAH = AH/AB = > cos 45° = 1 m / AB = > AB - 1.4142 m

The final result is that the length of the long rods, to install in mechanism, to which the Eccentric Balance to be in mechanical equilibrium at maximum open angle of 90° is equal with 1.4142 m. But the 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' = AH7AB = > cos 30° = AH'/ 1,4142m = > AH '= 1,2232m, and this additional gained distance is for an angle 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 when 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, respectively 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 multiplied 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 the momentum necessary to close or open the free ends of the weight- carrying rods, in order to assess all mechanism consumptions, using 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 on the lubricated steel on steel, is equal with μ= 0.002 (because rotation around the axis by an embedded ball bearing, where the balls don't slide but roll). Calculation, under most stringent condition of lubricated 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 = rFsina I t, 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 close at 30° and open back to 90° to the free weight-carrying ends of long rods, therefore for the above case: we have M = rFsina / 1 => M = 1 m*100N*1 / 4s therefore the size of the scalar momentum is 25Nm/s at a maximum friction coefficient (for most stringent theoretical case) when μ = 1. 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 that the initial torque is multiplied with real friction which is μ= 0.002 as we considered the equivalent of railroad steel wheels rolling on steel rails (with no lubrication), and we also considered a continuous maximum torque applied, as well as the need of a limitation stopping pin, at the opposite side of the corrugated rack (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 = 0.2Nm/s and even in the most stringent case the rest of 19,71 Nm/s up to 41,40 Nm/s, would be our Mechanical advantage, whereas in the ball bearing case, this kinetic friction coefficient becomes negligible, even more. This mechanical advantage, in this particular case study, has the results that demonstrates mathematically, how can be lifted up / down a weight of 2 Kg to 4 kg, and manoeuvring it around, using less than 0,2 Kg/force mounted into a synchronous bidirectional electric engine.

This calculus stating that any other scalar size of weight, additional increases this Mechanical Advantage, by calculation formulas, and proves that we succeed to change the moving weights further from the fulcrum, by rolling ball bearings and not sliding the weights. Mechanical advantage can be improved even more, because the weight lifted (1) from the reference plane, may be lowered back through its own weight, used as counterweight balancing the rotation in the vertical plane or as a weight rebalancing mode, so no additional energy would be used, thus increasing even more the mechanical advantage, but this application is only to a piston method.