GB2508181A - Energy storage capacitor which maintains voltage during discharge - Google Patents

Abstract

An electromechanical battery composed of a parallel plate capacitor having a fixed position plate and a second moveable plate, wherein the moveable plate is constrained by a mechanical spring having a non-linear force-displacement relationship. In another embodiment the spring is replaced by an unrolling/rolling foil plate whose degree of roll is dependent upon the amount of charge held by the capacitor. Furthermore, an electromechanical battery composed of a multi-plate capacitor having a first stack of elastic flexing conducting plates interleaved with a second stack of elastic flexing conducting plates, and a plurality of electrically insulating protrusions disposed between the plates, such that mutual motion as engendered by the application of a voltage between the first and the second electrical connections, is constrained at different positions across the area of the plates by contact with at least some of the protrusions. Each of these arrangements result in a battery which provides and maintains a constant voltage as current is drawn from it during discharge.

Description

ELECTROMECHANICAL BATTERY

FIELD OF THE INVENTION

The present invention relates to the field of energy storage batteries, especially those using mechanical energy as the energy storage medium

BACKGROUND OF THE INVENTION

Autonomous electronic systems which are not connected to the power grid require an electric power source. Most often a chemica' battery serves as the power source in such systems. An ideal batteiy is a device that may store or supply dectric charge while maintaining a constant voltage. A constant level of voltage is frequently crucial for proper operation of dectronic systems. Chemical batteries perform as ideal devices as long as the current they absorb or supply is not excessive, If too much current is extracted from the battery its voltage may drop considerably. Likewise, if too much current is supphed to a battery during charging, it may cause ilTeversible damage due to overheating and unwanted chemical reactions. If excessive amounts of charge are to be stored or extracted in a relative short time, the battery may be replaced by a large capacitor, or may be supplied with a support capacitor to supply the higher current discharges when called for. A capacitor may be charged and discharged rather rapidly, but the voltage on a capacitor is not constant but rather it is proportional to the amount of charge which it carries. If a large capacitor is used.

and only a small part of its stored charge is drawn during the desired current discharge.

then a close to constant voltage can be obtained, but at the cost of the volume and expense of the larger than needed capacitor.

There therefore exists a need for a battery which provides a constant output voltage as current is drawn from it. which does not have the charge and discharge limitations of am electrochemical battery and which does not take up the space of a large capacitative "battery", The disclosures of each of the publications mentioned in this section and in other sections of the specification, are hereby incorporated by reference, each in its entirety.

SUMMARY

The present disdosure describes a new exemplary electromechanical battery that stores and supplies electnc charge at a constant voltage. Instead of transforming electric energy into chemical energy as in a chemical battery, in the dectromechanical battery the electric energy is stored in elastic deformation such as an elastic spring. The electromechanical battery may take the form of a variable capacitor. Seemingly, the simplest ideal variable capacitor is the parallel-plate electromechanical transducer. The parallel-plate transducer is constructed from a movable plate electrode that is suspended on an dastic spring close to a fixed electrode. The movable electrode has a single degree-of-freedom, namely to and from the fixed electrode. The movable electrode is subjected to a voltage and the fixed electrode is electrically grounded. In equilibrium, the attractive electrostatic force between the electrode plates, which is inherenfly non-linear, is balanced by the mechanical restoring force in the elastic spring. If the spring is linearly elastic, then the restoring force is proportional to the displacement of the moveable electrode, and the relationship between the driving voltage between the electrodes and the displacement of the moveable plate is a non-linear function, which becomes unstable, showing a negative stiffness after the point of maximum controlled motion, beyond which the plates pull-in. The pull-in voltage associated with that point is the maximal voltage that can be applied to the linear spring system before it loses stability.

On the other hand, if, for a given capacitor plate geometry, the spring is designed to have a predetermined non-linear force-displacement relation such that the mechanical spring force is proportional to the reciprocal of the square of the residual gap between the plates, i.e. (g-A)2 where 1w is the mechanical restoring force of the elastic spring, g is the initial gap between the electrodes with no voltage applied, and A is the displacement of the moveable electrode, then it can be shown that the voltage on the parallel-plate transducer remains constant independent of plate gap.

I'his result means that by using a specifically designed nonlinear spring, it is possible to achieve a constant output voltage from a storage device, and the transducer thus essentially operates as a constant output voltage electromechanical battery.

The mechanical parameters of the spring itself, such as the spring material Young's modulus, cannot he readily changed in static environmental conditions, likewise, the cross sectional dimensions of the spring cannot he readily changed during operation of the battery. According to one method described in this disclosure, such non-linear characteristics can be provided by means of a spring whose length is a function of the flexure applied to it. Such a spring can be provided by use of a beam wrapped over a cam with a predetermined profile, the beam being attached at one end to a point on the cam, and flexed by means of a load applied at the other free end of the beam, remote from the cam.

By this means, as the load on the free end of the beam is changed and the beam flexes, different lengths of the beam become wrapped over the cam and the effective length of the beam changes, thereby changing its force-displacement relation.

A specilic design of a cam-wrapped non-linear spring with a force-displacement law such that it fulfils the conditions given above for constant voltage operation. is shown hereinbelow in the Detailed Description section of this disclosure.

Another exemplary implementation of the electromechanical batteries of the present disclosure using nonlinear spring configurations, can he obtained by use of two juxtaposed capacitor plates, constructed of a flexible conductive material having known elastic properties, with a plurality of insulating protrusions distributed in the capacitor gap, to constrain the movement of the capacitor plates towards each other. A variation of this embodiment uses a three dimensional multiple-plate capacitor, comprised of two interleaved stacks of plates of opposite polarity, with the insulating protrusions disposed in the gaps between the sets of plates in each stack. By this means, a signilicantly higher storage energy density can be achieved.

Yet another exemplary implementation of the electromechanical batteries of the present disclosure differs from those mentioned previously in that a mechanical spring element having a linear elastic characteristic is used. The maintenance of constant output or input voltage is achieved hy means of varying the area of the capacitor as a function of the charge stored therein. As the charge input to the capacitor increases, the area of the capacitor increases accordingly, resulting in a capacitor whose voltage is not affected by the amount of stored charge. this again defining an electro-mechanical battery. The variaHe area capacitor is achieved by use of a rolled-up spring electrode in which the extent of the curled up part is dependent on the charge held in the capacitor.

One advantage of such capacitor-based electromechanical batteries is that they can be charged at a high rate since there is virtually no heating generated as the current flows in to charge the capacitor, and store the elastic energy in the non-linear spring. ibis feature may make them particularly advantageous for use in electrical vehicle applications, since using a high charging current, the charging time can he made very short. Likewise they can he discharged at a high rate.

BRIEF DESCRIPTIoN OF TIlE DRAWINGS

The present invention will he understood and appreciated more fully from the following detailed description, taken in conjunction with the drawings in which: Fig.ia shows schematically a parallel-plate transducer, and Fig. lb shows the equilibrium states of such a transducer; Figs. 2a and 2b illustrate schematically, the response of the transducer of Fig. I with a linear spring. Fig. 2a illustrates the relation between voltage and charge, and Fig. 2b.

the relation between charge and displacement; Figs. 3a and 3h show schematically a spring constructed from two parallel cantilevered beams connected at their free cdgc; Fig. 3a shows the unloaded statc, while Fig. 3b shows the deformed state under a transverse edge loadt; Fig. 4a shows schematically two edge connected cantilever beams of the type shown in Fig. 3a, wrapped over two cams, with Fig. 4b showing the local coordinate system (x,y) of one of the cams; Figs. Sa, 5b and 5c show the response of the electromechanical battery using cam-wrapped beams; Fig Sa shows voltage/displacement curves, Fig. Sb, the voltage charge relation, and Fig. 5c, the resulting eh' *ge/displacement relation; Figs. 6a and 6h illustrate schematically another parallel plate transducer electromechanical battery implementation with a plurality of insulating protrusions distributed in the capacitor gap, to tailor the extent of free movement of the capacitor plates towards each other; Pigs. 6c and 6d show schematically how the devices of Pigs. 6a and 6h can he stacked to produce a three-dimensional electromechanical battery having higher energy density than the planar embodiments of Figs. 6a and 6h; Figs. 7a and 7h illustrate schematically a parallel plate capacitor in which one of the electrodes is rolled up as a scrolled mechanical spring; in Fig. 7a the capacitor is charged at one level, and in Fig. 7b at a higher level, such that the rolled up electrode deploys more; Fig. S shows schematically an external spring app'ying the mechanical force to the rolled up electrode; and Fig. 9 shows schematically the use of gravity to apply the mechanical force to the rolled up electrode.

DETAILED DESCRIPTIoN

Reference is now made to Fig. Ia, which illustrates schematically a parallel-plate transducer, constructed from a movable plate electrode that is suspended on an elastic spring close to a fixed electrode. The movable electrode has a single degree-of-freedom, A. The area of each of the electrodes is A, and the initial gap between them is g. The movable electrode is subjected to voltage V and the fixed dectrode is electrically grounded.

Ignoring fringing ficlds, the attractive electrostatic force fE between the electrode plates is given by fE, V2 (1) 2-A) where s is the permittivity of free space. In equilibrium, the attractive electrostatic force is balanced by the mechanical restonng force f in the elastic spnng. (2)

2(g-A) lithe spring is linearly elastic, then the restoring Force is = kA (3) where k is the constant stifFness of the spring. In this case equilibrium takes the form 2kA(g-A)2 =0AV2 (4) The equilibrium states of the system arc illustrated in Fig. ib, as a Voltage-displacement plot. In this case, when the parallel-plate transducer is driven by voltage V. the resulting motion of the movahlc platc is clearly a non-linear function of the driving voltage. It is stable up to A = g13 and is unstahle beyond that displacement, that being the point at which pull-in of the system occurs. The pull-in voltage associated with that point is the maximal voltage that can he applied to the linear spring system before it loses stability.

The capacitance of the parallel-plate transducer is given by c = (5) g-A Figs. 2(a) and 2(h) illustrate the response of this parallel-plate transducer with a lincar spring. Fig. 2(a) illustrates the relation between voltage and charge and Fig. 2(h), the relation between charge and displacement, where in both graphs, C0, the value of the capacitance with no voltage applied, is given by: C0 = s0AIg Now, if the spring is designed to have the non-linear force-displacement relation -Bait (6 where VEUT is a constant, then it follows from equilibrium that V2 =V,12 (7) i.e. the voltage on the parallel-plate transducer remains constant independent of plate gap.

This result is important because it means that, by using a specifically designed non-linear spring, it is possible to achieve a constant output voltage from a storage device, and the transducer can thus essentially operate as a constant output vokage electromechanical battery.

The stiffness of the required non-linear spring is given by the first derivative of the force: k = (J) = (8) M dA (g-A)3 from which it is clear that the stiffness needs to be a monotonically increasing function of the displacement A. In order to design the non-linear spring with the correct characteristics, it is clear that the elastic properties of the spring itselF, such as the spring material Youngs rnoduus, cannot he readily changed in static environmental conditions. Likewise, the cross sectional dimensions of the spring cannot he readily changed during operation of the battery.

According to one method described below, such non-linear character sties can be provided by means of a spring whose length is a function of the Ilexure applied to it. Such a spring can be provided by use of a beam wrapped over a cam with a predetermined profile, the beam being attached at one end to a point on the cam, and flexed by means of a load applied at the other free cnd of thc beam, remote from thc cam. By this means, as the load on the free end of the beam is changed and the beam flexes, different lengths of the beam become wrapped over the cam and the effective free ength of the beam changes, thereby changing its force-displacement relation. In the use of such a non-linear spring in the parallel plate transducer devices of the present disclosure, the flexing force at the end of the cam-wrapped beam is the electrostatic force generated between the plates of the transducer.

Using this method, one specific design of a cam-wrapped non-linear spring with a force-displacement aw such that it fulfils the force-displacement conditions given by equation (6) is now shown.

Reference is now made to Pigs. 3a and 3b, which show a spring constructed from two parallel idenlical cantilevered hearns which are connected at their free edge. Fig. 3(a) shows the unloaded state, while Fig. 3(b) shows the deformed state under a transverse edge loadf. Ihis type of suspension is particularly advantageous because its edge does not rotate under flexure, and is therefore well suited for the parallel motion of the parallel-plate transducer.

When the connected edge is subjected to the transverse load f, the Force-displacement relation of the suspension is given by

S

f24EIA (9) 1-lere I. is the length of the beams, P is the Young modulus of the beam material, and I = 1bw is the second moment of the beam cross-section, where b is the beam thickness and w is the beam width.

Now, if this concept is to he used to design a non-linear spring, at least one of the parameters in Eq. (9) must be modified. However, it is impractical to continuously modify the beam dimensions, as expressed in I, or the material parameters, as expressed in P. Reference is therefore now made to Figs. 4a and 4b, which provide a practical schematic illustration of the above mentioned novel method, of how the beam lengths I. of the two edge-connected cantilevered beams may be shortened as a function of the force applied to their free ends, by wrapping the beams over cams. In Fig. 4a, the beams are shown fixed at the initial contact point at the root of the cams, and the force applied to the remote free ends of the coupthd beams. In the parallel plate transducer, this force is the dectrostatic force resulting from the moveable electrode attached to that end. The cams are shown as being identical, to enable parallel operation. Fig. 4h shows the ocal coordinate system (x. y) for one of the beams with the origin at the initial contact point at the root of the cam.

When the beams are wrapped over the cam, the last point of contact is given by Z:, and up to that point the beam is assumed to conform to the cam profile (x). The length of the unwrapped section of the beams is therefore given by (L -xe). At their free ends the beams are subjected to the transverse force F. It can he shown that when a single cantilever beam with a non-rotating edge is wrapped ovcr a cam by application of the transverse force F, the force-displacement relation is given by F(xC)=2(f + (10) AG)= i(x (L-x (L -x (11) 3dx. 6dr x here (x) is the function describing the cain shape, where coordinate system (x, y) is shown in Fig. 4b, and x is the location of the last point of contact between the cam and beam.

As an example of the use of these design equations, a cam with the simple parabolic shape is used in equations (10) and (11): (12) Substituting this cam shape into (II), extracting ç. and substituting it into (10) yields the edge force P. Since the suspension includes two parallel beams, the force is given by: 3 El f=2P= (13) 91] (g-Af Comparing this to equation (6), which is the relationship required to produce a constant voltage characteristic, it follows that 264g3E7 14 Butt -9L3 s0A The curvature of the cam at its origin is given by (15 i] x=O The two beams in the suspension are initially straight and they have a single point of contact with the curved cams at their clamped edge. However, the two beams begin to wrap over the cams only alter the suspension deflection A is sufliciendy large such that the curvature at their clamped edge reaches the value given by equation (15). This occurs when the deflection of the suspension edge reaches the value A = g /3, and up to this deflection (i.e. before the beams begin to wrap over the cams) the suspension responds as a linear spring with constant stiffness k = f/A = 24Ff/I] (see Eq. (9).

It follows that up to the deflection A = g/3 the suspension is linear and the parallel-plate actuator response is given by equation (5). In this region the vohage increases non-lineady from V = 0 to the value given by equation Error! Reference source not found.. Beyond this edge deflection, the vohage remains constant. even though the charge may continue to increase. From the capacitance equation (5), it follows that beyond this deflection, the charge Q is given by Q=CV=! I (16) 31-A/g L L I'he resulting voltage-displacement. voltage-charge, and charge-displacement relations are plotted in Figs. 5(a), 5(b) and 5(c) respectively. In these graphs, the responses of the electromechanical hattery are shown as sohd lines. l'he dashed lines are the response of the linear parallel-plate transducer itself, the dot being the point at which wrapping of the beams begins, and is also the pull-in point of the linear parallel-plate transducer. Fig. 5(a) shows the Vohage-displaeemcnt relation. As is observed, once wrapping begins at displacement g/3, the voltage remains constant as the displacement increases, and the voltage remains at this value so long as the displacement is greater than g/3. Fig. 5(b) shows the Voltage-charge relation, in which it is seen that even as the charge on the parallel plate capacitor increases, the voltage remains constant above g/3. Fig. 5(c) shows the Charge-displacement relation.

Reference is now made to Figs. 6a and 6b, which illustrate another exemplary implementation of the electromechanical batteries of the present disclosure using nonlinear spting configurations, involving a particularly simple method of construction. This implementation comprises two juxtaposed capacitor plates (electrodes), 60, 61, at least one of which being a flexible conductive material 60 having known elastic properties, and a plurality of insulating protrusions 62, 63, 64 distributed in the capacitor gap. to constrain the free movement of the capacitor plates towards each other. This can he practically achieved by fixing the protrusions to one plate. which is generally, for ease of construction, the fixed plate, and allowing the opposing plate to move towards that fixed plate. Alternatively, both capacitor plates can be movable and flexible, and the protrusions can be attached to a third insulating sheet disposed between the two movable conducting plates (this embodiment not shown). The protrusions should have predetermined different heights, and are distributed in a predetermined pattern over the surface of the capacitor plates. In the example shown in Figs. 6a, 6h. the protrusions 62 have the greatest height.

those designated 63 have a lower height, and those 64 the lowest height. Alternatively, a random pattern can he generated hy spraying the protrusions in the form of particles of differing sizes onto the surface.

As the capacitor is charged to a charge level Q hy the application oF an external voltage between the plates. the plates are electrostatically attracted towards each other, the displacement being determined by the elastic properties of the moving capacitor plate 60 (or patcs in the case of the douNe sided implementation). So long as the charge Q is sufficiently small that the movable plate 60 (or plates) is moving in free space and does not come into contact with any of the protrusions, as is shown in Fig. 6a, the plate has a known elastic characteristic for these small displacements. however, as is shown in Fig. 6b the moment that the charge on the movable plate 60 has increased to a level Q + AQ, such that the p'ate 60 touches the second highest protrusion or protrusions 63, the patc's movement at that point is brought to a stop, and its displacement at those positions remains fixed, though its angular orientation and curvature can change and amend the stored elastic energy, even for the section of the plate between the highest protrusion or protrusions 62 and the second highest protrusion or protrusions 63. This "semi-static" section thus also contributes to the stored elastic energy and affects the elastic characteristic of the whole plate. For the purposes of defining the dastic characteristics of the entire p'ate, the remaining sections 66 of the flexing plate now have smaller lateral dimensions, and hence stiffer spring properties, and consequently a different force-displacement characteristic.

This process continues as the remaining free scctions 66 of thc flexible plate contact lower and lower protrusions, and acquire stiFfer and stiller spring properties. Ihus, the overall stiffness characteristic of the flexible plate 60 is synthesized from the stiffnesscs of a number of secondary plates. having different stiffness characteristics, starting with that of the whole plate freely suspended only at its outer edges when no voltage is applied, and finishing, when the rated voltage is applied, with a plate that is held under dectrostatic force against all of the various protrusions, and with the different sections having different Force-displacement laws operating on them. By correct selection oF ihe heights and distribution of the protrusions, it is possible to design and construct a parallel plate capacitor, in which the stiffness of the plates can be tailored to have the desired force-displacement characteristic to fulfill the conditions of equation (6), and hence to provide a constant voltage charactcristic, this defining the electromechanical hattery.

One of the disadvantages of the implementations of the electromechanical hattery shown in Figs. 6a and 6h is that the energy storage density is limited because of the planar nature of the device. Reference is now made to Figs. 6c and 6d, which show a further development of the "protrusioned plate" embodiments of Figs. 6a and 6h, in which the planar plate geometry is multiplied by means of stacking of the capacitor plates one on top of the other.

By this means, it becomes possible to construct a three dirnensiona parallel plate capacitor, operative as a mechanical battery. and having a much higher energy storage density than the configurations of Figs. 6a and 6b. Fig. 6c shows the construction of the 3-D multiple plate capacitor in its uncharged condition. l'he plates are staclced with alternate plates being connected electrically, such that a multi-layer plate capacitor is formed. The insulating protrusions are shown as the blaclc bloclcs, and their heights and positions are calcu'ated to give the desired elastic characteristic for the plates such that the constant voltage property is achieved for the capacitor stack. Fig. 6d shows the effect of applying a charging voltage to the capacitor stack. The capacitor plates are attracted to each other by the electrostatic forces, storing dastic energy because of the elastic deformation the plates undergo as they move into contact with the protrusions, until they are completely compacted against all of the protrusions. As is observed in Fig. 6d, the motion of the plates towards each other has also caused a compacting down of the stack as the protrusion spaces are filled by the plate distortion motion. In this situation, the distorted plates have the maximum rated stored elastic energy, though if the charge is increased, the plates may continue to bend more while constrained against the protrusions, but the force-displacement relation at that stage may become considerably more complex.

Such a multi-plate capacitor can have its energy storage density increased if a high dielectric constant material is positioned between the plates, such as by immersing the capacitor in a high dielectric constant oil bath. This also enables higher voltages to be used before breakdown, again leading to higher energy density. A particularly advantageous aspect of these 3-D multi-plate capacitors is that they can be constructed by planar fabrication techniques, using thin films having deformable properties, and can thus he readily used as mechanical batteries in MEMS or microelectronic circuits. Furthermore, in order to achieve even larger energy densities, it is possible to fabricate a number of such multi-plate capacitors over a larger area of the substrate on which they are fabricated, in accordance with the battery capacity required.

Reference is now made to Figs. 7a and 7h, which illustrate yet another exemplary implementation of the electromechanical batteries of the present disdosure. l'his implementation differs however from those described previously in that a mechanical spring element having a linear elastic characteristic is used. The maintenance of constant output or input voltage is achieved by means of varying the area of the capacitor as a function of the charge stored therein. As the charge input to the capacitor increases, the area of the capacitor increases accordingly, resulting in a capacitor whose voltage is not affected by the amount of stored charge, this again defining an electro-mechanical battery.

Such a capacitor configuration can be achieved by use of a charged electrode positioned above a fixed ground electrode, with a thin dielectric sheet between the two electrodes. (It should be noted that the positional relationship "above" is being used only in order to relate to the drawings of Figs. 7) The charged upper electrode may he constructed of a thin metallic sheet, or of another stiff conductive material, scrolled up in the form of a rolled mechanical spring, having an at least partly rolled equilibrium position with no stored charge, as shown in Fig. 7a. As the voltage applied to the capacitor is increased and the stored charge consequently also increases, the dectrostatic Rrces between the charge electrode and the ground plate cause unrolling of the scrolled up electrode, as shown in Fig. 7h. thus increasing the area of the capacitor and its capacitance, and hence reducing the voltage relating to the stored charge. Conversely withdrawal of charge from the capacitor causes a reduction in the electrostatic forces between the electrodes, therefore allowing the upper electrode to curl up more towards its elastic equilibrium position, reducing the area of the capacitor, it nevertheless maintaining the same voltage between the electrodes.

Correct selection of the elastic properties and dimensions of the rolled electrode mechanical spring is necessary in order to produce a fixed voltage characteristic of the capacitor. The equilibnum between the electrostatic forces generated between the charged plates and the mechanical forces operating on the rolled-up section of the electrode is thus responsible for maintaining a constant voltage across the capacitor.

In the above described operating scenario, the mechanical forces have been supplied by the elasticity of the rofled up foil, acting as a mechanical spring. This would appear to he the simplest way of implementing this particular configuration. However alternative methods of providing the mechanical force can also he used, in which case, the foil need not have any spring properties at all, but could he a completely tension-free foil having essentially zero dastic properties and no preloaded stress whatsoever.

In one such example. shown in Fig. 8. an external linear spring could be attached from an anchor point to the axle onto which the foil is rolled up, thereby providing the mechanical force tending to keep the foil in its roBed up state, as a counter to the electrostatic forces tending to unroll the foil from its rolled up slate.

hi another such example, shown in Fig. 9, use is made of gravity in order to provide the mechanical force to counter the dectrostatic Force. Ibis is achieved in Fig. 9 by Forcing the unraveling foil to roll uphill against gravity as the charge in the capacitor is increased, and vice versa as it is decreased. Since the gravitational force on the thin foil may he very small, it may he necessary to add a weight to the foil to generate sufficient reactive force to the electrostatic force.

It is appreciated hy persons skilled in the art that the present invention is not limited by what has been particularly shown and described hereinabove. Rather the scope of the present invention includes both combinations and subcombinations of various features descnbed hereinabove as well as vanations and modifications thereto which would occur to a person of skill in the art upon reading the above description and which are not in the

prior art.

Claims (14)

1. CLAIMS1. An electromechanical battery, comprising: a parallel plate capacitor, comprising; a fIrst plate, having a fixed position; and a second moveable plate, disposed with its surface in proximity to said first p'ate, the motion of said second plate towards said first plate being constrained by a mechanical spring having an non-linear characteristic; wherein said non-linear characteristic is a non-linear force-displacement relationship, said relationship being such that the voltage across said capacitor remains constant with changes in the charge held by said capacitor.
2. 2. An electromechanica' battery according to claim 1, wherein the charge held by said parallel plate capacitor generatcs an attractivc electrostatic force between said plates which is in equilibrium with the mechanical force exerted on said moveable plate by said mechanical spring.
3. 3. An electromechanical battery according to either of the prcvious claims, wherein said mechanical spring having a non-linear characteristic is a beam with one end section of its length wrapped on a cam, such that when that end of the beam remote from said cam is displaced in a direction perpendicular to the length of said beam, the free length of said beam changes.
4. 4. An electromechanical battery according to claim 3. wherein said end of said beam remote from said cam is attached to said second moveable plate.
5. 5. An electromechanical battery according to either of claims 3 and 4, wherein the profile of said cam is a parabola.
6. 6. An electromechanical battery according to either of claims I and 2, wherein said mechanical spnng having a non-linear characteristic is the elastic flexing of said second plate.
7. 7. An electromechanical battery according to claim 6, further comprising a p'urality of electrically insulating protrusions disposed between said plates, such that said motion of said second plate towards said first plate is constrained at different positions across the area of said plate by contact with at thast some of said protrusions.
8. 8. An electromechanical battery according to claim 7, wherein at least one of the height and position of said protrusions is such that the elastic flexing of said second plate has the non-linear characteristic necessary to the ensure that said voltage across said capacitor remains constant with changes in the charge held by said capacitor.
9. 9. A three dimensional electromechanical battery, comprising: a multi-plate capacitor comprising: a first stack of conducting plates having elastic flexing properties; a second stack of conducting plates having elastic flexing properties.the plates of said second stack being interleaved with said plates of said first stack, a first electrical connection connecting the plates of said first stack together, and a second electrica' connection connecting the plates of said second stack together, and a plurality of electrically insulating protrusions disposed between said p'ates, such that mutual motion of said plates of said first stack relative to said plates of said second stack, as engendered by the application of a voltage between said first and second electrica' connections, is constrained at different positions across the area of said plates by contact with at least some of said protrusions.
10. 10. A thrcc dimensional electromechanical battery according to claim 9, wherein the heights and positions of said protrusions is such that the elastic flexing of said plates of said first stack and that of said plates of said second stack have the non-linear characteristic necessary to the ensure that said voltage across said capacitor remains constant with changes in the charge held by said multi-plate capacitor.
11. 11. An electromechanical battery, comprising: a parallel plate capacitor, comprising; a first foil, having a fixed position; and a second Foil, disposed with its surFace in proximity to said First Ru.said second foil being in a rolled up state when no voltage is applied across said capacitor.the unrolling of said second foil being constrained by a mechanical spring having a linear force-displacement characteristic; wherein unrolling of said second foil as a result of increased electrostatic attraction to said first foil because of an increase in the charge held by said capacitor, results in an increase in the capacity oF said parallel plate capacitor, such that the voltage across said capacitor remains constant in spite of the change in the charge held by said capacitor.
12. 12. An electromechanical battery according to claim II, wherein said Unear spring is generated by the flexing tension within said rolled up foil.
13. 13. An electromechanical battery according to claim ii, wherein said linear spring is an external spring attached to an axis around which said rolled up IoU is curled.
14. 14. An electromechanical battery according to claim ii, wherein said linear spring is generated by alignment of said parallel plate capacitor out of the horizontal plane such that said rolled up section of said second foil must operate against gravity as it unrolls.