WO2010077158A1 - Wave energy converter and the 3-phase mechanic method - Google Patents

Abstract

This invention describes a Wave Energy Converter (WEC), which is the mechanical equivalent to a fully balanced 3-phase electrical generator, aimed to produce continuous power. By virtue of its 3-phase mechanic architecture, the WEC reacts force against himself and doesn't need any mooring system to react force against. The WEC is characterised by three equal legs (12,13,14), which are the three individual mechanical phases, all of them connected to a central articulation (1). The angle between each mechanical phase/leg (12,13,14) centre of mass (2,3,4) is exactly 120° degrees. Each leg/phase (12,13,14) must have the same inertia moment and is characterised by an equal large rigid mass (22,23,24) connected to each leg/phase (12,13,14). Only one of the three masses (22,23,24) interferes with Ocean waves, being the other two deeply submerged. Each leg/phase is connected by one of three equal springs (5,6,7) and one of three equal power-take-off dampers (8,9,10).

Description

Wave Energy Converter and the 3 -Phase Mechanic Method

Technical Field

This invention relates to Ocean Wave Energy and describes a Wave Energy Converter (WEC) , aimed to produce electricity from Sea waves, according to a very specific method, which is the heart of the invention.

Ocean waves are a known form of renewable energy. Energy, not water, flows continuously along the Ocean's surface and below. In deep water, the water particles travel only in small circles as the wave passes. This motion of water particles also happens underwater, but the particle velocity and thereby the circle radius decrease exponentially as we go deeper. In fact, it can be shown theoretically that 95.678% (percent) of the energy transport takes place between the surface and the depth of L/4, where "L" is the wavelength.

Wave energy is a concentrated form of energy. In the time- average, and just below the Ocean's water surface, the wave energy flow is typically around 2,000 to 3,000 Watts per squared meter. That is about five times denser then the wind, which is around 400 to 600 W/m² at 20 meters above the sea surface. Wave energy is 10 to 30 times denser than the solar energy flow (100 to 200 W/m²) . Hence, there are good prospects for development of commercial wave-power plants, which may in the future become significant components for providing energy to many coastal nations.

Disclosure of Invention Technical Problems and Advantageous Effects

A WEC must face many serious problems. We'll describe some of the most important problems that have been solved by this invention.

This invention describes a deep-water WEC, aimed to capture all the wave energy content. Hence, it won't work properly on shallow waters, where wave energy is not "circular" anymore. That is, in shallow water the amounts of wave potential energy and wave kinetic energy are not present in equal amounts, over the period, while they are in deep waters.

In deep water, gravity water waves are known to carry potential and kinetic energy on exactly equal amounts, being the potential energy characterised by the water up and down motion/ and the kinetic energy characterised by water particles motion parallel to the sea surface (26) .

Most of the known WEC only have one degree of freedom, up and down, or back and forth. Therefore, those devices only have one degree of freedom and they are limited to capture a theoretical maximum of 50% of the wave energy content. This invention describes a WEC with the required two degrees of freedom, vertical and horizontal, which is aimed to capture 100% of wave energy content and leave behind an ideal flat sea, in theory.

Waves produce vertical and horizontal forces, against which the WEC must react. Therefore, most of known WEC must be tight moored to the seabed (18) , either by means of pillars or by means of tensioned cables, thus providing both stability and a datum to react force against. Without such a fulcrum or an ultra reactive body (like a platform) to apply forces against, the WEC will trend to move free and very little energy can be captured. Studies of the problem concluded that the mooring costs are often larger then the entire WEC cost. This invention describes a WEC that reacts against himself, by means of its 3 -phase mechanic architecture, and doesn't need to be moored to the seabed (18), nor any secondary body. The required mooring for the WEC described by this patent of invention is to maintain geographical position only, mainly because of the electrical cable problem.

It is possible to group WECs according to their geometry as terminator, attenuator or point absorber. Terminators and attenuators trend to be very large devices, basically as large as the amount of power they are aimed to capture. On the contrary, point absorbers are by definition of very small extension compared to the wavelength. The theory behind this is that a body oscillating in water will produce waves. Thus, a good WEC must be a good wave maker, so that to destroy a wave means to create a wave that will interfere destructively with the incident wave. Absorbing wave energy for conversion means that energy has to be removed from the waves. Hence, there must be a cancellation or reduction of waves, which are passing the energy-converting device or are being reflected from it. Such a cancellation, or reduction of waves, can be realised by the oscillating device, provided it generates waves which oppose (are in counter-phase with) the passing and/or reflected waves. In other words, the generated wave has to interfere destructively with the Ocean waves. This explains the paradoxical, but general statement that "to destroy a wave means to create a wave". Hence, a big body and a small body may produce equally large waves, provided the small body oscillates with larger amplitude. The well-known solution to achieve large motion amplitudes is resonance. The obvious advantages, between a small point absorber and large oscillating body, are the costs and the WEC survivability. The WEC described by this invention is a point absorber that must work in resonance with the incident waves.

Survivability is a fundamental problem, since during storms the Ocean energy content can easily be tens of times higher the WEC nominal power. There are only two possible solutions for the survivability problem: Either it is possible to have a survivability strategy, or the WEC design must be tens of times over dimensioned. While the first can be possible or not, the second is forbidden due to the high costs involved. This invention describes a WEC that has fully controllable buoyancy and, therefore, in an extreme situation it can sink without causing any costly or additional technical problem to solve .

Wave power considered on both directions or degrees of freedom: vertical (for wave's potential energy) or horizontal (for wave's kinetic energy), both are a sine squared function of time that will be zero twice per wave period, not continuous power. Nevertheless, at the end of the energy conversion chain, the electrical power to be fed to the grid must be continuous power. Therefore, some means of intermediate energy storage are required. This problem will raise obvious issues on efficiency and additional costs. Since power is equal to force times velocity, and we know that waves force and velocity are both sine functions of time, at best we can get an unavoidable sine squared function of time, for power on each degree of freedom. This sounds like a problem impossible to solve and, so far, no known WEC had solved the problem. To solve the problem one must notice that potential and kinetic energy of waves are always 90 degrees out -of-phase, which means that if power due to potential energy changes is a sine squared function of time, then power due to kinetic energy changes must be a cosine squared term. By trigonometry, we know that a sine squared plus a cosine squared is equal to one, thus a constant. Hence, theoretically, only a two-degree of freedom WEC, perfectly tuned, can produce continuous power. This patent of invention describes a fully balanced 3 -phase mechanic that can be tuned to produce continuous power, without the requirement of any intermediate means of energy storage. The said 3 -phase mechanic architecture is the most important breakthrough, that made possible to work a WEC that reacts force against itself and requires no reference point, so that it will naturally moves vertically and horizontally 90 degrees out- of-phase, as required. Sun and Moon tides are a big problem for a tight moored WEC, which requires a fixed point to react against. The size of the average tide can be larger then the WEC maximum power- take-off amplitude. That fact increases the load over the mooring system. The WEC described by this invention is not influenced by tides, since requires no mooring nor has any fixed point of reference.

Besides the above-described problems, some other secondary and derived problems have been solved by this invention. For instance, the WEC described by this invention has:

- Virtually no amplitude limitations, nor any other constrains like a mooring or a reference point.

- The WEC can work as a terminator (out-of-resonance) , almost completely submerged, in case of very high wave heights, so that waves will pass above it and only interfere partially.

- No volume changes on the WEC geometry exist during its motion and, therefore, it avoids secondary forces radiated to the surrounding water, due to buoyancy/gravity changes.

- Easy tuning by means of mass solely, which means that we can use a single set of mechanical and buoyancy springs, with a fixed and constant springiness and, even so, achieve a broad band or full spectrum bandwidth, just by means of adjusting the entire system mass.

- The power-take-off spring system doesn't have to balance gravity forces, since all submerged part have neutral buoyancy and no buoyancy/gravity changes exist during the WEC motion, contrary to some WEC that require an equilibrium point to be set by the WEC internal spring system.

- Complex conjugate control is the working mechanism of the entire system, by definition. Power can be delivered to the Ocean by means of latching the power-take-off and, therefore, let the energy stored on previous mass motion to be transferred to the Ocean instead of the power-take-off. Or else, the power-take-off can be turned loose and the waves will deliver energy to increase the WEC motion amplitude.

Background Art

No prior art is known, since no known Wave Energy Converter (WEC) have so many simultaneous advantageous characteristics like the one here described. Namely:

- Being a deep water WEC;

- Two degree of freedom (vertical and horizontal) for potential and kinetic wave energy capture (100% energy capture) .

- No tight mooring is required for the WEC, nor any reference point exists.

- It is a point absorber, to maximise power capture.

- It is a fully balanced 3 -phase mechanic, aimed to produce energy continuously without any additional storage equipment.

- The entire WEC can be submerged for survivability. - It has virtually no amplitude limitations, nor any other constrains like a mooring or a reference system.

- The WEC working mechanism requires no volume changes on its geometry.

- Constant springiness and tuning by mass adjustment solely.

The WEC power-take-off spring doesn't have to balance gravity forces, since no buoyancy/gravity changes exist.

- Complex conjugate control is the basic working mechanism.

Technical Solution and Main Advantageous Effects

The technical solution to create a WEC with two degree of freedom that requires no mooring, nor any fixed point of reference, is the WECs fully balanced 3 -phase mechanic architecture, that provides means for the WEC to react forces against itself and also to produce power continuously. A 3- phase mechanic means the existence of three inductive loads (three masses) , three capacitive loads (three springs) and 3 resistive systems (three power-take-off for damping) all of which displaced 120 degrees one from each other in a full circle, in a manner perfectly equivalent to every electrical 3 -phase generator winding, whose displacements (the electrical current) describe equal sinusoidal waves displaced 120 degrees one from each other in time.

In order for a fully balanced 3 -phase mechanic to work, it is required that equal external forces be applied to every mass, spring and damper system, exactly 120 degrees out-of-phase. Therefore, the basic geometry of a WEC according to this patent of invention is unique.

This patent of invention describes a complete and detailed method and such method is the technical solution himself.

The main advantageous effects are the possibility to capture up to 100% of wave energy, instead of the usual 50% limit. Also the fact that the WEC reacts forces against itself and requires no mooring system to react forces against. Finally the continuous production of power at a constant value, instead the usual sine squared function that limits any WEC with a single degree of freedom.

Brief Description of the Drawings

- Fig.l shows a general and highly schematic view of the "Best Mode of Carrying Out the Invention" .

- Fig.2 shows the same view of Fig.l, but it was meant to explicitly show each mechanical phase (12,13,14) separately. We also call "three entire legs" (12,13,14) to each of the three mechanic phases (12,13,14) that compose de WEC. - Fig.3 shows exactly the same WEC of Fig.l, with the large three masses (22,23,24) fully expanded. Which means, the three WEC phases (12,13,14) are at its maximum inductive reactive value, aimed for the more energetic long waves, with smaller frequency.

- Fig.4 is equivalent to Fig.1,2, 3 and shows a more detailed schematic view of the "Best Mode of Carrying Out the Invention" , specifically taking into consideration also the best mode of carrying out an oil-hydraulic power-take-off damper (8,9,10) system.

- Fig.5 shows exactly the same WEC of Fig.4, but it was meant to explicitly show each phase (12,13,14) separately.

- Fig.6 is equivalent to Fig.1,2, 3, 4, 5 and shows another way of carrying out the spring (5,6,7) and power-take-off (8,9,10) system of the WEC, now in a star like geometry instead of the previous delta like geometry.

- Fig.7 is meant to be a presentation of the mathematical model of the entire WEC, which is aimed only for mathematical proposes, not the description of the invention. Fig.7 also shows a highly schematic view of the WEC, which is used later in Fig.11, 12, 13, 14,15, 16 for the sake of simplicity.

- Fig.8 is meant to be a presentation of the mathematical model of the 3 -phase mechanic harmonic oscillating system, aimed only for mathematical proposes, as previous Fig.7.

- Fig.9 shows one of several possible mechanisms required to achieve variable mass and variable inertia moment of the upper buoyant large mass (22) , based on a spherical or cylindrical shape.

- Fig.10 is similar to Fig.9. The only difference is that Fig.10 refers to the lower large masses (23,24) mechanism to achieve variable mass and inertia moment.

- Fig.11 is a highly schematic view of WEC cinematic motion and is not particularly important for the invention description.

- Fig.12 is a highly schematic view that shows the general configuration that a WEC, according to this patent of invention, should have in order to be fully independent of waves directionality. The shape is a geometric tetrapod, also known as the breakwater shape. - Fig.13 is very similar to Fig.12 and also is an highly schematic view that shows the second possible spring/damper configuration that a WEC, according to this patent of invention, should have in order to be fully independent of waves directionality. The shape is again a geometric tetrapod.

- Fig.14 is highly schematic and shows an imperfect mode of carrying out the invention.

- Fig.15 is highly schematic and shows another imperfect mode of carrying out the invention.

- Fig.16 is highly schematic and shows one more imperfect mode of carrying out the invention.

General Description of the Invention

We believe it's required a general description of the method, which is the heart of this invention and directly leads to the "Best Mode of Carrying Out the Invention" .

The art of wave energy capture is the art to balance the mass, the springiness and the damping of the entire WEC, which forms the WEC internal mass-spring-damper system that must react as a whole against the wave. Any unbalance will cause losses. All efforts have been made in order to achieve a fully balanced system, relative to the central articulation (1) of the WEC.

The most important point of the entire invention is the equilibrium of angular momentum around the WEC central articulation (1) .

Basically, waves carry an inductive mass of water that will induce the action against which the WEC must react. Within the entire WEC, with no exceptions, every mass or every inductive effect, every spring or capacitive effect, and every damper or resistive effect, must be in perfect 3 -phase balance around the WEC central articulation (1) .

Herein Ocean waves are thought to be sinusoidal waves, made of a given mass of water under macroscopic rotation that carries energy. Such energy can be regarded as: E = 1/2 I ω², being "I" the total inertia moment of the displaced water, made up of the sum of a infinite number of water particles that actually rotate at a given radius at macroscopic scales. The actual Ocean wave frequency is "ωⁿ . Therefore, we regard an Ocean wave as a rotating vector of constant amplitude (an Eulerian description) , in agreement to the well-known "Linear Airy Wave Theory" and all laboratory experiments.

This view of Ocean waves is somehow new, or different, from the general and usually meaningless description. Our claim is that energy of each individual wave is E = l/2Iω², which also can be written as E = 1/2 m r² ω², being "m" the value of the total mass made of the sum of an infinite number of particles, and "r" the average radius of the circle described by the sum of all those particles. This might sound bizarre, nevertheless it was found to be the best way to describe the Physics of this invention, because the equilibrium of the entire WEC, as a whole, resumes to a balance of the total angular momentum (mr²ω) over time.

A perfect 3 -phase equilibrium of the WEC means that the total angular momentum of the entire system must be instantaneously conserved. Here, the entire system is composed of the WECs oscillating mass-spring system, the WECs internal damper system, and the external waves action. Those skilled on wave energy capture already know that a WEC must have a resonant mass-spring system, oscillating de-coupled from the waves and the WEC damping system. This means that WECs mass-spring system "angular momentum" is always zero over time, and that wave's force {from the actual passing wave) must cancel out with WECs damping resistive force. The wave force depends on wave amplitude on a wave-to-wave basis. This is equivalent to say that the internal energy (mr²ω²) of the entire WEC must be conserved, while the wave energy must be directly transferred to the WEC power-take-off damping (8,9,10) system.

Notice this patent of invention describes a kind of "rotating WEC system" based on a "rotating wave" description. That's why we must refer to "angular momentum", instead of simply stating "momentum" (mass times linear velocity) , which should be more appropriate for any linear description.

The above resumes the basic "working mechanism" of the WEC described by this patent of invention. The working mechanism is that the 3 -phase harmonic system (with zero damping) once excited will oscillates permanently as a de-coupled system. Within such system, the energy is conserved at every instant, like every mass-spring system without friction. If energy is conserved instantaneously, then obviously angular momentum is instantaneously conserved too. Due to the build-in symmetry of a 3 -phase architecture, it can be shown that total amount of angular momentum (and thus energy) equals to zero.

The above should have some obvious consequences. If the total amount of angular momentum of the entire WEC is zero, over time, then the centre of mass (11) of the entire WEC cannot have any kind of rotation, but only a pure translation back and forth around some direction. In fact, after a fully abstract mathematical work, made in order to derive the WECs phase (12,13,14) motion on a drawing, the solution presented Fig.11 shows that the entire WEC centre of mass (11) doesn't rotate, but moves in a line back and forth along the waves horizontal direction. Such linear horizontal motion is normal to exist on every floating massive body as a whole. We believe that's because along the horizontal direction there's no "water springiness", thus no possible resonance effect.

By virtue of the WEC central articulation (1) , the waves force acts directly, and divides on equal parts, over all the three entire legs (12,13,14) centre of mass (2,3,4). The wave's force over each centre of mass (2,3,4), or over each mechanic phase, will found each centre of mass (2,3,4) on a delayed position, of exactly 90 degrees on a circle, because the 3 -phase mechanic system is in resonance with wave's frequency. Hence, the force over any of the three centre of mass (2,3,4), induced by the waves, will have a maximum value exactly when the velocity of the centre of mass (2,3,4) is a maximum too, which means that force and velocity are in-phase during a wave period, as they should.

The power-take-off damping (8,9,10) system has to absorb all the wave's force at a given velocity, for a given input power, being the velocity "v" dependent on the WEC motion maximum amplitude "5_maχ" and frequency "ω" as usual (v = ømax r ω) , being "r" the distance between the damper (8,9,10) application point and the WEC central articulation (1) . It is fundamental to capture the exact wave power amount, in order to leave the 3-phase mass-spring oscillating harmonic system free, meaning de-coupled and thus oscillating at its previous constant amplitude.

Any unbalanced situation causes the entire WEC to rotate as a whole, which is allowed but not desired and wouldn't happen under optimum conditions. We must adjust the power-take-off to capture the exact wave height amplitude (the actual wave energy content) , to avoid WEC rotation as a whole, clockwise or counter-clockwise, depending on which side the unbalance is: To much wave induced force, or to much WEC reactive force. Notice that this trend to rotate can be of great help on the WEC survivability strategy.

We believe the best mode to describe this invention are the two following statements: - If deep water Ocean waves are equivalent to a rotating vector, hence Ocean waves look like the motion of the magnetic field build-in the rotor of an electrical generator. The rotating excitation field build on the generator rotor's surface is the primary action that causes electrons to flow on stator windings. Likewise, the water rotating vector is the action against which the entire WEC must react ;

- Hence, the entire Wave Energy Converter (WEC) must be the mechanic equivalent to a stator of a 3 -phase electrical generator, including a balanced external load that short-circuits the generator stator terminals.

Moreover, since an electrical generator produces continuous power at a constant value, the WEC claimed by this patent of invention also produces power continuously at a constant value. This must happen per each individual wave, which means during a time interval equal to the wave period.

This last statement requires that each individual wave must deliver power continuously, at a constant value, per each wave-cycle. Hence, a wave must be a rotating vector of constant amplitude that could deliver energy continuously during its time period. Mathematically, this can be expressed in terms of angular momentum as: mr²ωsin²{ωt) + mr²ωcos²(ωt) = mr²ω = Constant

The insight and background come up to the inventor by means of his other patents WO 2004/109140 and WO 2004/109139, which required a great deal of effort to understand the true nature and the working mechanism of a 3 -phase electrical motor/generator.

More recently, inventor's patents number WO 2008/097116 and WO 2008/097118, refers the work done on an attempt to build a 3 -phase mechanic for a single degree of freedom WEC. At the time, no mathematical solution was found, because we've concluded it is physically impossible to achieve a 3 -phase architecture based only on a single degree of freedom. We must notice that, by nature, a 3 -phase architecture is like a rotation and at least two degrees of freedom are required to describe a rotation.

An electrical generator has a fully balanced 3 -phase architecture. Likewise, the WEC described by this patent also has a fully balanced 3 -phase mechanic architecture. That's why we've started by saying that equilibrium is the most important matter. From the electrical field, it's well known that only a fully balanced 3-phase architecture can provide a smooth running and the best energy conversion efficiency.

This patent of invention describes the mechanical equivalent of a 3 -phase stator of an electrical generator plus its balanced electrical load. Hence, we will often refer to the WEC, and/or the method herein described, as being a fully balanced 3 -phase mechanic.

A fully balanced 3 -phase electrical generator (including its load) comprises three equal inductors (meaning the generator coils inductive reactance) , three equal resistive loads (the electrical load that consumes real power) and three equal load capacitors (for power factor correction of generator coils plus all line and load inductive reactance) . Inductors and capacitors must be the complex conjugate of each other, as a function of the electrical frequency. That is a resonant electrical system. Complex conjugate and resonance are known to be synonymous and that ' s why the WEC must be a point absorber working at resonance. Notice that, at full efficiency, an electrical generator works in perfect resonance too, usually known as impedance match.

Build within the stator of a good electrical generator, each of the three electrical phases are fed by a single passing sinusoidal potential, which is the magnetic force induced by the generator rotor, equivalent to a rotating vector. Each stator phase is geometrically de-phase 120 degrees one from the other. The source of force is the generator rotor carrying one single potential wave (a rotating vector) . Such rotor wave drawn on the rotor surface applies simultaneously over all the three electrical phases at the same time, but the peak force of the sine wave, seen per each phase, is geometrically de-phased exactly 120 degrees. It is the wave drawn on the generator's rotor (the rotating vector drawn by the rotor excitation magnetic field) combined with the stator 3 -phase architecture, via the air-gap, that makes the fully balanced 3 -phase electrical system.

Likewise, the WEC described by this patent of invention comprises three large rigid masses (22,23,24), which are the inductors, three large power-take-off systems (8,9,10), which are three hydraulic resistive systems that produce the real part of the load, and three large spring systems (5,6,7), which are the equivalent to the power factor correction capacitors.

The hard to understand is how we are going to fed external sinusoidal force, of equal amplitude, equally by each of the three mechanical phases (12,13,14) that compose the WEC, de- phased exactly 120 degrees. According to Fig.1,2 ,3,4, 5, 6 accompanying this patent, only one phase clearly interferes with the waves and, therefore, directly receives external force from the waves. How do other phases receive wave induced force?

The central articulation (1) of the WEC provide means for the wave's external force to reach all the WEC phases, in equal amounts and, by geometry, de-phase exactly 120 degrees one from the others, all done by means of the specially chosen and unique geometry we claim.

A fully balanced 3 -phase mechanic, as claimed by this patent of invention, requires that only one entire leg (12,13,14) receive energy from the waves. The force transmission between legs is done by means of the central articulation (1) and the cinematically de-coupled parallel system, composed of three equal springs (5,6,7) and three equal power-take-off dampers (8,9,10) systems. Hence, two of the legs centre of mass (2,3,4) must be deep submerged and out of waves reach. Around 4,3% of the wave energy exist at a depth of one quarter the wavelength, which is well above the viscous losses. Likewise, still about 20% of wave energy exists at a depth of one eighth the wavelength, which will be around 25 to 30 meters, if we what to capture very long waves (of 12 seconds period) in a fully balanced 3 -phase control.

Fig.2, 5 show all the three entire legs (12,13,14) separated. Each of those three legs (12,13,14) is one of the WECs three mechanical phases (12,13,14), whose centre of mass are points (2,3,4) .

Finally, we must recall that:

Absorbing wave energy for conversion means that energy has to be removed from the waves. Hence, there must be a cancellation or reduction of waves, which are passing the WEC device or are being reflected from it. Such a cancellation or reduction of waves can be realised by an oscillating device, provided it generates waves which oppose (are in counter- phase with) the passing and/or reflected waves. In other words, the generated wave has to interfere destructively with the incident waves and, therefore, absorption of wave energy from the sea may be considered as a phenomenon of wave interference .

This explains the paradoxical, but general, statement that: "To absorb a wave means to generate a wave", or, in other words: "To destroy a wave is to create a wave", hence "A good WEC should be a good wave maker" . This should give us a precise understanding of the motion that a massive body (22) must have.

Detailed Description of the Invention

This "Detailed Description of the Invention" concerns the "Best Mode of Carrying Out the Invention". Later we'll describe and comment some imperfect modes of carrying out the invention.

This invention is based on Physics, equilibrium and geometry. We've also developed the basic mathematics, for static, dynamic and cinematic models, as shown Fig.7, 8 for instance.

According to the previous "General Description of the Invention" , the "Best Mode of Carrying Out the Invention" is a fully balanced 3 -phase mechanic, which must be equivalent to a complex conjugated load applied to a fully balanced 3- phase electrical generator. There's a total equivalence between a loaded 3 -phase electrical generator and the 3 -phase mechanic method described by this patent of invention.

Fig.1, 2, 3,4, 5, 6 show the fully balanced 3-phase mechanic, which comprises a central articulation (1) , three long rigid legs (12,13,14), each leg carrying one of the three large rigid masses (22,23,24), plus one of the three spring (5,6,7) systems and one of the three power-take-off damping (8,9,10) systems .

The centre of mass of the entire leg (12,13,14) is a point, which is shown by numbers (2,3,4) in all relevant Figures. The centre of mass (2,3,4) of each entire leg (12,13,14) and the centre of mass (11) of the entire WEC, are very important points that help us to describe and understand the invention.

Each of those said rigid legs (12,13,14) are what we call a mechanical phase (12,13,14). Fig.2, 5 show the said three legs (12,13,14), which are the three mechanical phases (12,13,14), separately .

Each of the entire legs (12,13,14) have one leg structure (19,20,21), which as one extremity firmly connected (by means of a bearing) to the central articulation (1) , while the other leg structure (19,20,21) extremity is firmly connected to a large solid mass (22,23,24), most of that large rigid mass (22,23,24) is seawater that fills-in the rigid volume.

So far, such system above doesn't hold in any particular position, nor assumes any configuration in space, nor has any specific shape. The entire WEC acquires some rigidity, and thereby a shape over time, by means of three pre-tensioned springs (5,6,7). Each one of those springs (5,6,7) is connecting two of the previous said legs (12,13,14) and each leg (12,13,14) is connected by two different springs (5,6,7). This is equivalent to say that the entire spring system (5,6,7) assumes a triangular shape, with a leg (12,13,14) connected on every corner. The springs (5,6,7) are connect via an articulation, as usual, to avoid unwanted bending stresses.

Likewise, each damper (8,9,10) of the three power-take-off damping (8,9,10) systems are to be connected (by means of an articulation too) on two consecutive legs (12,13,14), exactly like the three springs (5,6,7) connect. Therefore, the spring (5,6,7) and power-take-off (8,9,10) systems work in-phase and work in parallel, but they are not necessarily parallel.

Basically, only the spring (5,6,7) system provides some rigidity for the entire WEC. The WEC power-take-off (8,9,10) system is a pure damper that, by definition, only reacts against velocity and should be displacement indifferent.

The springs (5,6,7) are to be pre-tensioned, either all three springs (5,6,7) loaded at traction, or all three springs (5,6,7) loaded at compression, it doesn't matter as long they are tensioned the same way. What matters is that the pretension must be such that the pre-tension displacement of the spring (5,6,7) is well above the working maximum nominal amplitude of the spring (5,6,7). Also very important is that all springs have exactly the same springiness coefficient, exactly the same pre-tension, and the angle between the entire legs (12,13,14) is exactly 120 degrees over a circle. That's for perfect equilibrium.

The springiness coefficient of a spring (5,6,7) is the value of force the spring (5,6,7) generates divided by the elongation of the spring.

There's a perfect 3 -phase balance only if the angle between each of two consecutive entire legs (12,13,14) is exactly 120 degrees, at the WEC equilibrium position. 120 Degrees is equal to 2pi/3 radians = 2.0943951023932 radian. The said equilibrium position is the configuration assumed by the WEC, or the shape of the legs/phase (12,13,14) system, when there are no external forces applied to the WEC, nor any previous motion of the legs (12,13,14) exists. To be more precise, we claim that the angular distance between the centre of mass (2,3,4) of each entire leg (12,13,14) is exactly 120 degrees on a circle, relative to the central articulation (1) , as shown Fig .1,2,3,4,5,6. For perfect equilibrium too, all the three entire legs (12,13,14) have exactly the same inertia moment relative to the central articulation (1) . The inertia moment is the total mass of the entire leg (12,13,14), placed at the centre of mass (2,3,4), times the square of the distance between the central articulation (1) axis to the centre of mass (2,3,4).

The total mass of each entire leg (12,13,14), or each mechanical phase (12,13,14), which can be placed at the respective centre of mass (2,3,4), is the mass of the respective leg structure (19,20,21), plus the respective large rigid mass (22,23,24), which is connected to that leg structure (19,20,21), plus the mass of one-third of the entire spring (5,6,7) system, plus one-third of the power- take-off (8,9,10) system mass, plus the so-called "water added mass", which is the mass of surrounding water that has to be moved (or accelerated when a rigid volume moves) as a function of the volume and the shape of the entire leg (12,13,14), plus one-third of the central articulation (1) mass too, which also includes one-third of the central intermediate structure (27), or (28,29,30), depending on Fig. 2 or Fig.6 for a delta or star configuration.

Likewise, the power-take-off (8,9,10) damping system must be made of three equal dampers with equal damping coefficients. The damping coefficient is the value of the force the power- take-off damper generates divided by the power-take-off internal velocity, that results from the relative motion of the legs (12,13,14) connected to the extremity of each individual power-take-off damper (8,9,10).

Fig.6 show another obvious manner to apply the spring (5,6,7) and/or the power-take-off damping (8,9,10) systems. In order to achieve some rigidity between the three legs (12,13,14) and thereby to assume a particular shape, each one of the three springs (5,6,7) can have one extremity connected to a point articulation (31,32,33), that receives motion from the relative motion of two consecutive rigid legs (12,13,14), and the other extremity connected to the central articulation (1) . Relative motion from two consecutive legs (12,13,14) must be obtained by means of fully symmetric articulated rods (28,29,30), via fully symmetric articulations (34,35,36) on each leg (12,13,14), as shown Fig.6.

Likewise, the power-take-off damping (8,9,10) system could connect exactly as the previous spring (5,6,7) system. This is equivalent to say that the spring (5,6,7) system, or the damping (8,9,10) system, both could assume a star like shape, according to Fig.6, instead of the previous delta-triangular shape described by Fig.1,2, 3, 4, 5. in the case of Fig.6 the power-take-off damper (8,9,10) - the dashpot - must be placed behind, or above, the springs (5,6,7), in which case only one (the spring or the damper) can be shown in Fig.6.

The obvious and the most suitable power-take-off damping (8,9,10) system for this invention is the double sided oil- hydraulic cylinder, all of which are represented in Figures as dashpots. Double sided oil-hydraulic cylinders have two different oil chambers with different areas and, therefore, different pressure and different flows. Those pressure and flow differences are bad for equilibrium and we need a perfect equilibrium, no matter which is the sense of motion.

To achieve perfect oil -hydraulic power (pressure times flow) equilibrium the solution is shown Fig.4. We must use two oil- hydraulic cylinders for each mechanical phase (12,13,14), one each side of the leg structure (19,20,21) .

According to Fig.4, 5 there are two oil-hydraulic cylinders per each mechanical phase (12,13,14), so that no matter which is the relative phase motion we always get equal balanced oil -hydraulic power (pressure times flow) per each mechanical phase (12,13,14) . We also need to use an intermediate structure (27), between each leg (12,13,14), to achieve the desired oil -hydraulic power equilibrium.

In order to capture energy from waves, at least one of the large rigid masses (22,23,24) must severely interfere with the Ocean waves. Otherwise no energy can be captured.

We've started the study and development of this invention to consider that two large buoys, which are in fact two of the three large rigid masses (22,23,24), could float and directly interfere with Ocean waves. Our aim was to find the distance between such two buoys (22,23,24) that could produce a fully balanced 3 -phase architecture, based on some theoretical hypothesis. Our conclusion was that such distance, between the two floating buoys (22,23,24), must be equal to the wavelength. A wavelength distance is equivalent to a zero distance, which means that wave's force over two buoys (22,23,24) must be equal and in-phase.

While the 3 -phase architecture can work for any distance between two capturing buoys (22,23,24), and we can also find solutions for the equations of motion of the forced system, it is impossible to achieve continuous power at a constant value. When two buoys (22,23,24) capture energy from waves, the total power generated over a period will be delivered as a sinusoid, with more or less amplitude, whose minimum value could be more or less close to zero. Based on these conclusions, it becomes clear that those are imperfect modes of carrying out the invention.

Since a zero distance, or a distance equal to the wavelength are both not feasible, we've concluded that only one single large rigid mass (22,23,24), or one buoy (22), must interfere with waves. Therefore, the other two large rigid masses (23,24), including all other masses connected to the respective entire legs (13,14), must be in a position so deep underwater that no significant energy of the waves could be transferred to them.

Therefore, while the three large rigid masses (22,23,24) must be equal and the respective centre of mass (2,3,4) of each entire leg (12,13,14) must be placed exactly at the same distance from the central articulation (1) , the truth is that one large mass (22) behaves differently from the other two masses (23, 14) .

The large rigid mass (22) , which is the only one that must interfere with Ocean waves, is a buoy that floats and produces a very important buoyancy springiness effect. While the other two large rigid masses (23,24), which shouldn't interfere with Ocean waves, are neutral buoyant bodies. A neutral buoyant body is an underwater body that neither floats, nor sinks. It must be almost composed of surrounding water and it will be a body whose volume generates a vertical buoyancy force that exactly cancels out the downward gravity force, defining what is called a neutral buoyant body.

The large rigid mass (22) that interferes with waves also is a neutral buoyant body, if placed on still waters (26) and if no previous vertical motion exists. If there are incident waves, or any previous vertical motion of mass (22) , then a spring effect occurs, due to an unbalance between the vertical buoyancy force and the downward gravity force. That occurs because there is an enclosed air volume (37) on the top of the large rigid mass (22) , which defines the neutral buoyancy point, or the static equilibrium point, of the entire WEC. The entire WEC mass and the springiness coefficient, created by the air volume (37) and the cross- section area of the mass (22) at still water level (26) , define an important harmonic oscillating system that we'll describe later.

As stated, neutral buoyancy is theoretically the best mode of carrying out the WEC entire legs (12,13,14), or the WEC mechanical phases (12,13,14). Nevertheless, a total neutral buoyant WEC will assume any spatial position, and not necessarily the vertical position as shown Fig.1,2 ,3, 4, 5, 6. Therefore, the entire WEC, and each individual WEC phases (12,13,14), they cannot be totally neutral buoyant. They must carry some minimum gravity mass, to create a downward force that could keep the WEC position vertical, as shown in all the said relevant Figures . Such minimum gravity force must be balanced by the spring (5,6,7) system pre-tension.

Therefore, the spring (5,6,7) system pre-tension also cannot be exactly the same in all the springs (5,6,7), as previously stated. Nevertheless, any pre-tension differences will be only required to adjust the required 120 degrees angle, between entire legs (12,13,14). The only propose is that to keep the vertical orientation of the entire WEC, as stated.

The result of a very small gravity effect, of WEC entire legs (12,13,14), to create a minimum downward force, will cause a small difference between the still water level (26) and the greyed water level inside the large mass buoy (22) , as shown in all Fig.1,2, 3, 4, 5, 6.

Besides that, all the three large rigid masses (22,23,24) must have some important characteristics. The first important characteristic is that any geometry underwater produces what is known as an added mass, also known as hydrodynamic mass, and is due to underwater motion of an additional mass of water that has to be accelerated whenever the underwater body moves. Such added mass is a mass that must be added to the actual mass of the moving body, no matter the body velocity, but only body's acceleration. Experiments have shown that, in resonance the added mass is the tabulated value for a given geometry, which is roughly equivalent to the mass of the volume of the body if it was made of surrounding water. Since the rigid masses (22,23,24) are mostly made of water, that fill-in the rigid volume, the external added mass effect doubles the actual gravity mass of the geometric volume.

For a perfect equilibrium of the three WEC phases (12,13,14) it becomes clear that all three large rigid masses (22,23,24) must create the same added mass effect, which means that the volume and geometry moving underwater must be geometrically identical, even if sometimes a more aerodynamic shape could look more appropriate to avoid viscous drag loses.

The total mass of the WEC, placed at the respective centre of mass (11) point, is very important too. Since no mass or added mass effect must be ignored, the total WEC mass is simply the triple of the mass of each entire leg (12,13,14), or each mechanical phase (12,13,14). This means that every mass, or added mass, must be assigned to a mechanical phase (12,13,14) of the WEC, as shown Fig.2, 5. Another important characteristic of the three large rigid masses (22,23,24) is that we can change the actual mass value, by means of filling in or expelling out some of the surrounding seawater. This is required because we want to tune the WEC with waves frequency, like if it was a radio antenna, in resonance with the incident waves.

The ideal WEC should be made of a material whose density equals that of the surrounding water, so that it could be fully filled of surrounding water, except the required air volume (37) as explained. Therefore, it would become ideally neutral buoyant. In reality, since the WEC is to be made of steel and many other materials, we will fill the large rigid masses (22,23,24) and all other possible volumes with surrounding water, but we have to leave some air chambers elsewhere, all around, so that the entire WEC becomes neutral buoyant in still waters.

Besides that, one must not forget that a fully neutral buoyant WEC won't assume the vertical position, as we want. Therefore, as already explained, some minimum gravity downward force is needed to keep a vertical orientation as shown Fig .1,2,3,4,5,6.

Then, if we are to capture waves whose frequency could range from 0.5 rad/s to 1.0 rad/s, we must be able to change the WEC total mass exactly four times, if we are to keep the same springiness coefficient. Meanwhile, we still must keep all neutral buoyant characteristics as previously described.

Obviously we can change the springiness coefficient too, but we've choose the spring systems to have a fixed value, due to technical difficulties to achieve variable springiness of a spring, no matter the type of that spring, like a floating buoy, an helical steel spring, a double sided gas pressure cylinder, whatever. Besides that, the spring must be linear along all the motion amplitude. Therefore, we believe that a variable linear spring is even much harder to achieve. Hence, our aim is to use some basic springs, namely:

- For the 3 -phase mechanic we are to use helical steel springs (5,6,7), which are linear, don't harm, are fully efficient and last long, instead of costly double sided gas pressure cylinders, which generate heat, losses and won't last to long.

- For the buoyancy spring, build-in the motion of the large mass (22) , we are to use a buoy whose cross-section around the still water level (26) is constant, along all the vertical mass (22) motion amplitude. Hence, the tuning of the WEC is to be made by means of variable masses (22,23,24), as a function of the waves frequency (or period), so that masses (22,23,24) and springs (5,6,7), including the large mass buoy (22) springiness, are the complex conjugate of each other and the WEC works in perfect resonance, like an antenna, capturing the incident waves .

Variable mass is also a somehow costly solution, but we believe that we cannot capture all the wave energy content if we don't face the waves with a machine with enough mass, or else, if we use a much smaller mass and we don't face the waves deep enough to cover all the underwater wave energy extend. At least one of the previous conditions must be full filled, or else some wave energy would escape without being captured .

Nevertheless, one should notice that a small gravity mass body that covers a large distance in depth would add a lot of added mass too. The added mass is equal to the square of the characteristic distance per distance unit. Moreover, the well-known wave energy content, as a function of the period and wave-height, clearly shows that more powerful waves always involve more mass. Hence, want it or not, the problem is always about mass and one cannot overlook the mass issue. Actually, we believe that it's the entire WEC mass the variable that better defines the nominal power of the WEC.

By virtue of the fully balanced 3-phase mechanic (12,13,14) architecture, it can be shown that the total sum, over a period, of displacement, velocity and acceleration, all of them are constant values. Similarly, in a 3-phase electrical generator, the sum of the three voltage sinusoids and the sum of the three current sinusoids are a constant value too. Therefore, the maximum nominal power of the WEC will be the total WEC mass (plus the total added mass) times the maximum acceleration times the maximum velocity.

Since waves frequency is a given value, it will be the WEC maximum amplitude that defines the maximum acceleration and the maximum velocity. Due to the usual mechanical constrains, any WEC maximum amplitude is always a limited value, so that velocity and acceleration also are limited values. Then, it is the WECs mass the remaining parameter that we have to increase, if we want to capture waves with more power content. Above the WEC maximum nominal power, which is characterised by its total mass and its maximum motion amplitude, the WEC described by this patent of invention will simply rotate as a whole and will survive. The development of this patent of invention showed us that, not only the mass value is important, but also it's very- important the angular momentum value, of each three entire legs (12,13,14) around the central articulation (1) axis. Therefore, we need variable mass and also variable angular momentum, exactly on the same amount. If we are to tune the WEC to capture wave frequencies ranging from 0.5 rad/s to 1.0 rad/s, then the required variation will be four times the WEC total mass and four times the angular momentum. Since total mass and angular momentum have to change exactly the same amount, that implies the radius distance cannot change, between the centre of mass (2,3,4) and the central articulation (1) axis.

The tuning of the resonant frequency is always a difficult task, for any WEC. We need to adjust the square root of the springiness-mass ratio and, in the case of the WEC described by this patent of invention, it looks very difficult to achieve variable springiness of a floating buoy (22) and, from the Physics point of view, variable mass is better. Hence, we had to study and develop means to achieve variable mass, which also is a complicated matter, due to the fact there are two types of mass involved: The usual "Gravity mass" and the "Added hydrodynamic mass" of water that has to be displaced, which greatly depends on geometry and directionality. Besides that, we still have the condition that the radius distance, between the centre of mass (2,3,4) and the central articulation (1) axis, cannot change.

So far, our best solution is shown Fig.9, 10. We've used that same variable mass solution in all Figures of this patent of invention, even if not shown Fig.1,2, 5 for clarity.

In terms of directionality, only the spherical shape has geometric characteristics that provide equal added hydrodynamic mass on every direction. The cylindrical shape will work as well, but he spherical shape looks far better and that's the one we'll use for the three large rigid masses (22.23.24), whenever possible.

We've already seen that the large rigid mass (22), that interferes with Ocean waves, works differently relative to the other two large rigid masses (23,24) . The mass (22) has the buoyancy springiness constrain we've already mentioned. This means that the large rigid mass (22) cannot be a sphere, but we can make it a revolution ellipsoid to achieve good directionality independence.

Fig.9, 10 show what could be a good solution for the required variable rigid mass and variable inertia moment problems, which are both simultaneously required for perfect 3 -phase balance. Both depend on added hydrodynamic mass, which in turns depends on geometry and frequency. The frequency is not a problem, since we've already concluded that WECs working frequency must be equal to the waves frequency. Therefore, the frequency will be the frequency known as "buoyancy frequency", which greatly simplifies the problem. Geometry is then the most important matter.

Since we have vertical and horizontal motion (a rotation to be more precise) , the chosen geometry must be such that produces equal added hydrodynamic mass on both said directions. The best geometry is a sphere, but a cylinder will work fine as well. Any other geometry will be much harder, in order to achieve equal values of added mass on both directions, but it can be done using variable flaps for instance.

Fig.9, 10 show what could be either, a sphere or a cylinder, since the dimension orthogonal to the sheet of paper is not defined.

We've already comment that mass and inertia moment must change in order of about four times. The . mass and the added mass, both depend on the volume of the rigid volume, which must be full filled with surrounding seawater. Therefore, in the case of a sphere, the volume depends on the cube of the radius and for the cylinder it will be almost the same. Therefore, if one increases the radius about one-third the volume will double, the gravity mass will double and the added mass will double as well. Hence, if we increase the radius about one third we will get four times total mass.

In order to also achieve four times more inertia moment, all we need to do is to keep the centre of mass (2,3,4) location of each mechanical phase (12,13,14) unchanged.

According to Fig.9, 10, our idea is to use a kind of highly flexible rubber skin (15) around the sphere, the cylinder, or the ellipsoid shape, that could be expanded by means of filling in sea water, like if it was a balloon that one could expand or contract at will, simply by filling in or expelling out surrounding water.

There could be many other solutions, with some advantages and disadvantages. Therefore, we won't claim anything besides the fact that variable mass and equal variable inertia moment is required, for tuning the WEC in a fully balanced 3 -phase architecture . Fig.9 shows the WEC upper buoyant large mass (22). Fig.10 shows both bottom large masses (23,24). In both Fig.9, 10, in order to control the location of the centre of mass (2,3,4) point and keep it unchanged, we've included a kind of several hydraulic jacks (17) that could be easily controlled to ensure that the flexible rubber skin, around the base rigid masses (22,23,24), assumes the required shape and position.

Instead of the said kind of hydraulic jacks (17) , there are many other solutions to control the relative position of the inflated balloon (15) of water.

Finally, we must say that WECs working mechanism is fully based on the relative motion of the three mechanical phases (12,13,14), defined by the angular displacement between two consecutive legs (12,13,14), that should cover some maximum angular value. The WECs entire legs (12,13,14) only perform small angular displacements, where the sine of the angle equals the angle (in radians) . This means that, for instance, a total angular displacement of 15 degrees clockwise plus another 15 degrees displacement counter-clockwise, generate a total stroke of 30 degrees in a circle, which won't cause any error. Nevertheless, the maximum expected amplitude would be below 30 degrees, which means that we won't have any linearity problems if we use conventional linear steel springs and linear oil-hydraulic cylinder dampers.

Some Physics of the WEC

Physically, the WEC comprises two cinematically independent systems and, therefore, two de-coupled oscillating systems, both working at resonance with Ocean waves frequency.

We want to describe these two kinematic systems separately and them try to understand how they work together.

The two said cinematic systems are:

1 - The entire WEC, seen as a whole, no matter the shape;

2 - The de-coupled fully balanced 3 -phase mechanic architecture, build-in the WEC, which oscillates in resonance.

The first cinematic system, that models the entire WEC as a whole, is the one that in first place interferes with waves and captures energy from them.

The second cinematic system works like an isolated harmonic oscillator, that stores or delivers energy, accumulated within the motion of masses (22,23,24), by means of increasing or decreasing the entire legs (12,13,14) angular motion amplitude. That angular motion feeds the power-take-off dampers (8,9,10), whose sum of their pressure times flow sinusoids will generate continuous oil-hydraulic power out, to be converted into electricity by means of an hydraulic motor, plus an electrical generator, a transformer, etc., all of the later not shown.

Both said cinematic systems must be in resonance relative to the incident waves frequency. Therefore, both must have exactly the same natural frequency, known to be the square root of system springiness characteristic divided by the system mass characteristic.

Description of the WECs kinematics as a Whole:

The entire WEC, seen as a whole by the incident waves, is a floating body that assumes neutral buoyancy in still waters (26) . In still waters (26) , where no waves exist, such body is acted by a force that push him down due to gravity, plus a buoyancy force up, due to Archimedes Principle, that balances the gravity force down, so that the entire WEC assumes a static equilibrium position as shown Fig.1,3, 4, 6.

Any small wave, or any previous vertical motion of the WEC, causes an unbalance between the vertical gravity force up and the vertical buoyancy force down. Thus, such system becomes an harmonic oscillating system, which only depends on the entire system mass, the entire system buoyancy springiness coefficient and the entire system damping coefficient.

Like any other oscillating system, the entire WEC and waves interact like a forced harmonic system. It is well-known in Physics that only a system in resonance, with the excitation force, maximises the energy conversion.

Why should the entire WEC, seen as a whole, be a large resonant body relative to the incident waves frequency? That ' s required because the experiment and the theory have showed that only a resonant body oscillates in a manner that could generate waves, and thus radiate waves away, able to cancel out the incident waves, instantaneously.

In other words, complex conjugate impedance must exist, between the entire WEC mass (11) and the entire WEC buoyancy springiness, so that the system becomes de-coupled (mω²-k=0) and the WEC damping forces equal the incident wave's force. That's the basic working mechanism we've previously described.

The natural frequency of the WEC, seen as a whole, is:

being K the springiness constant of the large mass buoy (22) and M the total mass of the entire WEC, including the added mass of water that has to be displaced, all of which placed at centre of mass point (11) .

Since the individual masses of each three mechanical phases (12,13,14) are to be equal, and we call them mi, m_2/ πi₃, then:

The mathematical model is shown Fig.7. Notice there are neither springs (5,6,7), nor dampers (8,9,10) shown in Fig.7, because the mathematical model only concerns the calculation of forces that later will be transmitted to the 3 -phase mechanical system.

Based on chosen coordinate system [x,y,t], for displacement and time, along the usual vertical and horizontal directions, plus a second angular coordinate system [S₁₁B₂₁B₃] , as shown Fig.7, the waves exciting forces are shown Fig.7 and one should be able to calculate the respective three resultant tangential forces, that will be seen over time, along the angular coordinate system [0i,02/03. •

Those said three forces, taken along coordinates [øi,02/03. # not shown in Fig.7 but that we know will be there, they will be the three individual forces that will excite each individual phase of the 3 -phase mechanic harmonic system.

Those forces can be calculated to be:

Fø (t) = 1/3 F₀ cos(α/t+¥) Fø₂(t) = 1/3 F₀ cos(ωt + 2τr/3 + Ψ) Fø₃(t) = 1/3 F₀ Cθs(ωt + 4π/3 + ¥)

Being Ψ a constant phase angle.

Description of the WECs internal 3 -phase architecture:

Fig.8 shows the mathematical model of the 3 -phase mechanic architecture. As usual, in these mathematical models, it was assumed small angular displacements, which means that any angular displacement causes a linear displacement of the springs (5,6,7) and dampers (8,9,10) .

In fact, the WEC spring and damper displacements are linear, but the actual linear extension of each spring, or damper, cannot cover angles larger then 20° or 30° degrees of amplitude, if they are to have a maximum working amplitude of about 10° to 15° degrees, for a maximum stroke of 20° to 30° degrees in total. That's why the intermediate structures (27) in Fig.1,2, 3,4,5, or structures (28,29,30) in Fig.6, are required. Those required intermediate structures (27) , or (28,29,30), are not shown on the mathematical model of Fig.8, because it's just a mathematical model.

The fully balanced 3 -phase mechanic architecture, equivalent to any fully balanced 3 -phase electric architecture, requires that all the three centre of mass (2,3,4), of each respective phase (12,13,14), to be placed exactly at the same radius distance n = r₂ = r₃ from the central articulation (1) axis. Also requires that all the three masses mi, m₂, m₃ of the mathematical model to be equal, meaning that each of the three mechanical phases (12,13,14) have exactly the same inertia moment "I" relative to the central articulation (1) axis. Finally and to be fully balanced, it also requires that all springiness coefficients k_1# k₂, k₃ and all damping coefficients C₁, C₂, C₃ to be equal.

Summarising, a fully balanced 3 -phase mechanic architecture requires that :

Ci = C₂ = C₃ = C

The mathematical model shown Fig.8 greatly simplifies and the equations of motion becomes:

1/3 F₀ cos(ωt + Ψ)

The natural frequency of the harmonic system is

Wo

Being "k" the springiness constant of each of the three springs (5,6,7) and "I" the inertia moment of each entire legs (12,13,14), or mechanical phases (12,13,14), including the added mass of water that has to be displaced during WECs motions.

Such natural frequency is unique, which means that the roots of the determinant of the secular equation, taken for this harmonic system, have a "triple root" around the above value. The above natural frequency happens to be an inflexion point of the secular equation, which means it is a point where the function touches the root's axis, but not crosses it. Therefore, it is not a root of the secular equation in the general sense, where the function crosses the axis, but still it is a zero of the function and thus regarded as a "triple root" of the harmonic system. Basically, this means the solution is unique and there's only one allowed mode for it to have harmonic vibration: The fully balanced 3 -phase mechanic .

The linear displacement of the spring (5,6,7) system, or the power-take-off damper (8,9,10) system, placed at a radius R from the central articulation (1), will be:

R θχ(t) = 1/3 R Fo/ωC sin(ωt + Ψ)

R 0₂ (t) = 1/3 R Fo/α/C sin (α/t + 2π/3 + ¥)

R 0₃ (t) = 1/3 R Fo/α/C sin (ωt + 4ir/3 + Ψ)

In resonance the waves frequency ω and the 3 -phase mechanic natural frequency ω₀ must be equal: ω = ω₀, so that the two previously mentioned de-coupled systems will be:

0

and,

2C -C -C 01 = 1/3 F₀ cos(ωt +Ψ)

-C 2C -C 02 1/3 F₀ cos(ωt + 2τr/3 + Ψ)

-C -C 2C *3 _ 1/3 F₀ cos(ωt + 4?Γ/3 +Ψ)

The first system of the above equations refers to the complex reactive part of the WEC, or else the complex conjugate between the inertia moment and the angular springiness, while the second system of equations refers to the real resistive part of the WEC, or else, the power-take-off (8,9,10).

This ends the description of the 3 -phase mechanic architecture. Now we are to describe how this 3 -phase mechanic system must interact with the previous description. The previous description was relative to the kinematics of the entire WEC, seen as a whole, which also carries vertical linear springiness and has its natural frequency too.

In order to understand how the two said Physical systems interact, one must understand the behaviour of a free massive floating body inside water. It can be shown that only a floating body in resonance with the incident waves radiates away waves that are in counter-phase and, thus, can cancel the incident waves and extract power from them.

Hence, the obvious conclusion is that: Both said Physical systems must have exactly the same natural frequency ω₀, which in turns has to be equal to waves frequency ω for resonance . Therefore :

which also can be written as :

being: m the mass of each individual phase (12,13,14), K the buoyancy springiness coefficient of the large mass buoy (22) , k the angular springiness coefficient of each of the three mechanical springs (5,6,7), R the radius distance between any application point of any spring (5,6,7) and the central articulation (1) axis, and r the radius distance between the centre of mass (2,3,4) of each mechanical phase (12,13,14) and the central articulation (1) axis.

Any value of buoyancy springiness coefficient K will work, for any given total mass M. But if the entire WEC is tuned in resonance, then motion will be amplified and we can capture a wave front width much larger then the actual width of the large mass (22) , up to a maximum of the wavelength divided by 27τ, according to the point absorber theory.

Fig.11 shows how the entire WEC motion will look like. Fig.11 is a highly simplified and schematic view of the WEC, which only shows the large masses (22,23,24), the legs structures (19,20,21), the central articulation (1) and, the most important: The centre of mass (11) point of the entire WEC.

According to Fig.11, the wave shown travels from right to left. The wave size and WEC motion are both highly- exaggerated in order to explicit the relevant details. Also notice that in Fig.11, instead of a moving wave and a fixed WEC, we show a fixed wave and we assume the WEC is moving from left to right. Otherwise we'll need to use tens of Figures, instead of only one, and we'll loose clarity.

A close analysis of Fig.11 reveals that the centre of mass (11) of the entire WEC won't move vertically and only moves horizontally. In fact, the motion of the centre of mass (11) is a minimum, in agreement with the "Principle of the Stationary Action", from which the Lagrangian analysis and Quantum Mechanics follows. Physically, the entire WEC mass, placed at the centre of mass (11) , wants to move the less as possible, as it should be expected.

The spherical 3 -Phase Mechanic

One final problem remains. The previously described WEC is dependent on the wave's directionality. It requires some means to keep the WEC perfectly oriented with the incident waves, either by means of a special mooring system, aimed for directionality, or by means of an external propulsion and guidance system to keep the WEC always facing the waves.

Therefore, it would be great if we could arrange, the already described 3 -phase architecture, in a manner that it could work independent of waves direction.

Once skilled on the 3 -phase architecture and trained on the geometric properties of three equal sinusoids de-phased 120° degrees, it is straightforward the invention of the new required geometry, which is the geometric tetrapod, also known as the breakwater shape.

A tetrapod is a four leg object having four projections radiating from one central node (1) , with each forming an angle of 120° degrees with any other, so that no matter how the object is placed on a relatively flat surface, three of the projections will form a supporting tripod and the fourth will point directly upward, as shown Fig.12, 13.

The working mechanism of the new geometry is exactly the same as previously described, only that now we have one more deeply submerged entire leg. Everything else remains the same . The additional required springs (40,41,42), three more, and the additional required power-take-off systems, also three more, placed exactly like the springs (40,41,42) , they are in fact redundant and they won't produce more power just because they exist. Most of them only will work partially and sometimes don't work at all, depending on waves direction relative to the WEC.

The geometric properties of three equal sinusoids de-phased 120° degrees (the 3 -phase architecture) is that the sum of any two sinusoids is equal to the symmetric of the third sinusoid, so that the sum of all three sinusoids equals to zero. This property is well-known and often used in many structures which are regular tripods .

The above property means that for every plane, passing through the central spherical articulation (1) , the sum of the displacements, velocities or accelerations one side of that plane will be equal to the sum of the displacements, velocities or accelerations the other side of that plane.

Therefore, based on the above property, we can always arrange the power-take-off system so that, no matter what the wave direction is, the plane orthogonal to the wave's direction, passing through the central spherical articulation (1) , will have the sum of forces one side of that plane equal to the sum of forces the other side of that same plane.

The above holds true if all six springs (5,6,7,40,41,42) are equal and if the damping coefficient of all the "parallel" power-take-off systems are equal as well. Therefore, the only condition are equal springiness and equal damping coefficients, which is very easy to achieve and doesn't require any kind of control, other then an equal opening of all the power-take-off control valves and the use equal springs .

As usual, in a way which is equivalent to every electrical 3- phase system, we can arrange the geometry of the springs and the power-take-off damping systems in delta or star arrangement .

Fig .12 shows the spherical 3 -phase mechanical system in a delta arrangement, while Fig.13 shows the same spherical 3- phase mechanical system in a star arrangement .

According to Fig.12, 13 the spherical 3 -phase mechanical system comprises a spherical central articulation (1) , where all the individual legs connect, four large rigid masses (22,23,24,38), four leg structures (19,20,21, 39), six equal springs (5,6,7,40,41,42), six equal power-take-off damping systems (not shown) that must be parallel to the said spring systems and will connect exactly like the spring system (5,6,7,40,41,42) does.

Similarly to the previous "Detailed Description of the Invention", according to Fig.12 each spring/damper connects to two different legs and now any leg is connected by three different springs/dampers.

According to Fig.13 each spring/damper again connects to two different legs, but now the vertical leg, which carries the mass (22) that interferes with Ocean waves, is connected by three different springs/dampers, while the three bottom legs are only connected by two different springs/dampers, since there ' s a bottom star arrangement of three springs/dampers at 120° degrees angle to each other.

The most important of all is that any of the four legs forms an angle of 120° degrees with any other leg.

The power-take-off systems, are not shown in Fig.12, 13 for the sake of simplicity. Instead of the springs (5,6,7,40,41,42) symbol we could have shown the dashpots symbol to represent the power-take-off system, or else one could just consider that inside every spring (5,6,7,40,41,42) there is an oil- hydraulic cylinder working as power-take-off damper (like in almost all automobile front suspension there ' s a damper inside an helical spring) .

In order to have a fully balanced spherical 3 -phase mechanic architecture, the inertia moment of every entire leg must be equal. This means that the entire leg mass, placed at the centre of mass (2,3,4,43), times the square of the radius distance between that centre of mass (2,3,4,43) and the central articulation (1) must be equal for any of the four legs that compose the spherical 3-phase mechanic.

Finally, all we need to describe is how we separate each of the three individual mechanical phases.

As in our previous "Detailed Description of the Invention" each individual mechanical phase is defined by the relative motion between consecutive legs, either in terms of relative displacement, relative velocity or relative acceleration, since displacement, velocity and acceleration are all mathematically related to each other. The only difference is that now individual phases could be composed of the sum of one, two or three legs relative displacement, depending on waves direction. The relevant points are the vertical plane, orthogonal to the waves direction, and the horizontal plane, parallel to the waves direction, both of which passing through the central spherical articulation (1) and both orthogonal to each other.

The first individual mechanical phase will be the sum of legs relative displacements computed one side of the above-said vertical plane. The second individual mechanical phase will be the sum of legs relative displacements computed the other side of the same above-said vertical plane. Finally, the third individual mechanical phase will be the sum of three legs relative displacements below the above-said horizontal plane .

In practice we don't have to worry with the above said two orthogonal planes, once we have set all springs (5,6,7,40, 41,42) equal and we have all power-take-off dampers equal. The total oil -hydraulic power, composed by the sum of all six oil -hydraulic power-take-off dampers will be a constant value that will fed an hydraulic motor to drive an electrical generator. All we need to do is to equally open the oil control valve of every power-take-off damper to ensure equal damping coefficient of all six dampers.

Imperfect Modes of carrying out the Invention

According to our previous description, any unbalance will produce losses and, therefore, will produce an imperfect mode of carrying out the invention. Hence, there are plenty imperfect mode of carrying out the invention and it will be difficult to comment them all .

Assuming a WEC which always has three legs/phases (12,13,14) connected to a central articulation (1), three masses (22,23, 24), three springs (5,6,7) and three power-take-off dampers (8,9,10), some of the most obvious imperfect modes are those whose legs inertia moment, springiness coefficients, or damping coefficients are not equal.

Other imperfect modes are those whose angle between legs is not exactly 120° degrees, but any angle. All of them will work as well, but they won't be able to produce constant power output and a control strategy will be hard to achieve.

Nevertheless, there are some imperfect modes, which only concern the WEC spatial orientation, that we want to comment and are shown in Fig.14, 15, 16.

Fig.14 shows a WEC, according to this patent of invention, which has two rigid masses (22,23) that directly interfere with Ocean waves. After many failed attempts to build a 3- phase mechanic without mooring, the WEC shown Fig.14 was our starting point for the study and development of this patent. Assuming an equal distribution of wave energy between the two capturing buoys (22,23) we've concluded that the required distance, between the two buoys (22,23), must be equal to the wavelength. Otherwise the total power generated over a period will be a sinusoid, not a constant value, with more or less amplitude, whose minimum value could be more or less close to zero, but it works.

Fig.15, 16 show two similar situations, which are symmetric of each other, and whose performance will only depend on which direction the waves travel.

Assuming that waves travel from the right to the left and assuming that we could capture all the wave energy content with a single floating buoy (22), then the WEC shown Fig.15 will be as good as the previously described "Best Mode of Carrying Out the Invention" , since no wave exists at the position of the rigid mass (24) .

The main problem with the WEC of Fig.15 is that 100% wave energy capture is only theoretical and most certainly can't be achieved in practice. Only perhaps 70% or 80% can be captured. Then the wave that could pass the WEC, without being captured, will have a much smaller amplitude, but we are not sure about what would be its wavelength. If the wavelength remains the same (according to the theory) then most certainly the rigid mass (24) will capture part of that energy and will produce an imperfect 3-phase mechanic. But if the wavelength is reduced, then there are good changes that no significant energy exists at the rigid mass (24) depth and the WEC shown Fig.15 will be as good as the previously described "Best Mode of Carrying Out the Invention" .

Again assuming that waves travel from the right to the left, the WEC shown Fig.16 will be an imperfect mode of carrying out the invention, quite similar to that shown Fig.14, if the rigid mass (23) is positioned at a depth where some wave energy still exists. To avoid that we'll need a WEC with much longer legs (12,13,14), which will have higher unnecessary costs .

In practice and for the described "Best Mode of Carrying Out the Invention", it will be difficult to guarantee a perfect vertical position, as shown Fig.1,2, 3 ,4, 5,6. A perfect vertical position can only be achieved if we are able to capture the exact amount of wave energy, after the unavoidable viscous and drag losses. Any failure to do so causes the entire WEC to rotate as a whole, which is allowed but not desired. We must adjust the power-take-off to capture the exact wave height amplitude (the actual wave energy content) , to avoid WEC rotation as a whole, clockwise or counter-clockwise, depending on which side the unbalance is: To much wave induced force, or to much WEC reactive force.

Therefore, some rotation in any direction is expected, but not very large rotations that could position the WEC in a situation like those shown Fig.15 or Fig.16.

Claims

1. A Wave Energy Converter (WEC) almost fully neutral buoyant and, thus, almost fully submerged, comprising a central articulation (1), three rigid legs (12,13,14), three spring

(5,6,7) systems and three power-take-off damping (8,9,10) systems. Each of those said rigid legs (12,13,14) have one extremity firmly connected (by means of a bearing) to the central articulation (1) , while the other leg structure

(19,20,2) extremity is firmly connected to one of three large rigid masses (22,23,24) that could, or not, interfere with Ocean incident waves, depending on that mass (22,23,24) location according to its water depth position. At least one of the three large rigid masses (22,23,24) must severely interfere with the Ocean waves, in order to capture energy from waves. Such system above doesn't hold in any particular position, nor assumes any configuration in space, nor has any specific shape. Therefore we claim that the WEC is characterised in that the system acquires some rigidity, and thereby a shape over time, by means of the said three mechanical springs (5,6,7). Each of those springs is articulate connected on two of the previous said legs

(12,13,14) and each leg (12,13,14) is connected by two different springs (5,6,7). This is equivalent to say that the entire spring system (5,6,7) assumes a triangular shape, with a leg (12,13,14) connected on every corner (a delta configuration) . Likewise, each of the three power-take-off damping (8,9,10) systems is to be articulate connected on two consecutive legs (12,13,14), exactly like the three springs

(5,6,7) connect. Therefore, the spring (5,6,7) and the power- take-off (8,9,10) systems work in-phase and work in parallel, but they are not necessarily parallel. Only the spring

(5,6,7) system provides some rigidity for the entire WEC. The said three springs (5,6,7) are to be pre-tensioned, either all of them loaded at traction or compression, it doesn't matter as long they are all pre-tensioned the same way.

2. A Wave Energy Converter, according to claim 1, that in order to achieve some rigidity between the three legs (12,13,14) and thereby to assume a particular shape, is characterised in that each one of the three springs (5,6,7) has one extremity connected to a point articulation (31,32,33), that receives motion from the relative motion of two consecutive legs (12,13,14), and the other extremity connected to the central articulation (1) . Relative motion from two consecutive legs (12,13,14) must be obtained by means of fully symmetric articulated rods (28,29,30), via fully symmetric articulations (34,35,36) on each leg (12,13,14). Likewise, the power-take-off damping (8,9,10) system could connect exactly the same. This is equivalent to say that the spring (5,6,7) system, or the damping (8,9,10) system, each could assume a star like shape, instead of the previous delta-triangular shape described claim 1.

3. A Wave Energy Converter, according to claim 1 and 2, characterised in that all of the three large rigid masses (22,23,24) can change the actual mass value, by means of filling in or expelling out some of the surrounding sea water, at variable volume.

4. A Wave Energy Converter, according to claim 1 and 2, characterised in that all the three entire legs (12,13,14) have exactly the same inertia moment relative to the central articulation (1) . The inertia moment is the total mass of the entire leg (12,13,14), placed at the centre of mass (2,3,4), times the square of the distance between the central articulation (1) axis and the respective leg (12,13,14) centre of mass (2,3,4) . The total mass of each entire leg (12,13,14), or each mechanical phase (12,13,14), is the mass of the respective leg structure (19,20,21) , plus the respective large rigid mass (22,23,24), which is connected to that leg structure (19,20,21), plus the mass of one-third of the entire spring (5,6,7) system mass, plus one-third of the power-take-off (8,9,10) systems mass, plus the so-called "water added mass" that is the mass of surrounding water that has to be moved (or accelerated when a rigid volume moves) , plus one-third of the central articulation (1) mass too, which also includes one-third of the central intermediate structure (27), or (28,29,30), depending on claim 1 or 2, for a delta or star configuration.

5. A Wave Energy Converter, according to claim 1 and 2, characterised in that all the three large mechanical springs (5,6,7) have exactly the same springiness coefficient. The springiness coefficient is the value of force the spring generates divided by the elongation of the spring.

6. A Wave Energy Converter, according to claim 1 and 2, characterised in that all the three power-take-off damper (8,9,10) systems have exactly the same damping coefficient. The damping coefficient is the value of the force the power- take-off damper generates divided by the power-take-off internal velocity, that results from the relative motion of the entire legs (12,13,14) connected to the extremity of each power-take-off damper (8,9,10).

7. A Wave Energy Converter, according to claim 1, 2 and 4, characterised in that the angle between each of two consecutive entire legs (12,13,14) is exactly 120 degrees at the WEC equilibrium position. 120 Degrees is equal to 2pi/3 radians = 2.0943951023932 radian. The said equilibrium position is the configuration assumed by the WEC, or the shape of the legs/phase (12,13,14) system, when there are no external forces applied to the WEC, nor any previous motion of the legs (12,13,14) exists. To be more precise, we claim that the angular distance between the centre of mass (2,3,4) of each entire leg (12,13,14) is exactly 120 degrees on a 360 degrees circle.

8. A Wave Energy Converter, according to claim 1 and 2, characterised in that only one of the three (12,13,14) entire legs (12) , and specially the rigid mass connected to that leg (22) , interferes with the Ocean waves and captures wave energy. Therefore, the other two entire legs (13,14) and their rigid masses (23,24) must be in a position so deep underwater that no significant energy of the waves could be transferred to them.

9. A Wave Energy Converter, according to claim 1 and 2, characterised in that the single large rigid mass (22) that interferes with Ocean waves is positioned partially above the sea level (the still water surface) and mostly submerged (underwater) . Therefore, such large mass (22) works as a buoy (22) that carries some springiness in the vertical direction, whenever a change of its vertical position occurs.

10. A Wave Energy Converter, according to claim 1, 2 and 9, characterised in that the entire WEC mass and the springiness coefficient of the single large rigid mass (22) , that interferes with Ocean waves, is in resonance with waves frequency.

11. A Wave Energy Converter, according to claim 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, characterised in that it works as a fully balanced 3 -phase mechanic that produces continuous power, with a constant output value when working with monochromatic waves, without the requirement of any energy storage system placed after the power-take-off damping (8,9,10) system. In the case of polychromatic waves (the real sea state) the WEC is characterised in that it produces continuous power, but only during a time interval equal to the wave period, since real sea states are composed of individual waves of different energy content (the wave amplitude) each.

12. A Wave Energy Converter according to claim 11, characterised in that the 3 -phase mechanic is in resonance with Ocean waves frequency.

13. A Wave Energy Converter according to claim 11 and 12 aimed to be independent of waves directionality, which we called a spherical 3 -phase mechanic and whose geometry is that of a regular tetrapod (four legs) , comprising a spherical central articulation (1) , where all the individual four legs connect, four large rigid masses (22,23,24,38), four leg structures (19,20,21,39), six equal springs (5,6,7,40,41,42), six equal power-take-off damping systems that must be parallel to the said spring systems and will connect exactly like the spring system (5,6,7,40,41,42) does. Each spring/damper connects two different legs and any leg is connected by three different springs/dampers. Any of the four legs forms an angle of 120° degrees with any other leg.

14. A Wave Energy Converter according to claim 13, characterised in that each spring/damper again connects to two different legs, but now the vertical leg, which carries the mass (22) that interferes with Ocean waves, is connected by three different springs/dampers , while the three bottom legs are only connected by two different springs/dampers, because there ' s a bottom star arrangement of three springs/dampers at 120° degrees angle to each other.