EP3316047B1 - Mechanical watch with isochronous rotary resonator, which is not position-sensitive - Google Patents

Description

Field of the invention

The invention relates to a resonator mechanism for a clockwork movement, comprising an input mobile mounted to pivot about an axis of rotation and subjected to a motor torque, and comprising a central mobile, integral in rotation with said input mobile. around said axis of rotation and arranged to rotate continuously, said resonator mechanism comprising a plurality of N inertial elements, each mobile according to at least one degree of freedom relative to said central mobile, and returned to said axis of rotation by return means elastic, which are arranged to cause a restoring force on the center of mass of said inertial element, said resonator mechanism having a rotation symmetry of order N.

The invention also relates to a timepiece movement comprising at least one such resonator mechanism.

The invention also relates to a timepiece, in particular a watch, comprising such a timepiece movement.

The invention relates to the field of clock resonator mechanisms, constituting time bases.

Invention background

Most current mechanical watches are equipped with a balance-spring and a Swiss anchor escapement mechanism. The balance-spring constitutes the time base of the watch. It is also called resonator.

• entretenir les va-et-vient du résonateur ;
• compter ces va-et-vient.

As for the exhaust, it fulfills two main functions:

• maintain the comings and goings of the resonator;
• count these back and forth.

In addition to these two main functions, the exhaust must be robust, withstand shocks, and avoid jamming the movement (overturning).

The Swiss anchor exhaust mechanism has a low energy efficiency (around 30%). This low efficiency comes from the fact that the movements of the exhaust are jerky, that there are falls or lost paths to accommodate machining errors, and also from the fact that several components transmit their movement via inclined planes that rub against each other.

To constitute a mechanical resonator, an inertial element, a guide and an elastic return element are required. Traditionally, a spiral spring acts as an elastic return element for the inertial element that constitutes a pendulum. This pendulum is guided in rotation by pivots which rotate in smooth ruby bearings. This gives rise to friction, and therefore to energy losses and walking disturbances, which depend on the positions, and which one seeks to suppress. The losses are characterized by the quality factor Q. We seek to maximize this factor Q.

Requirement EP2847547 in the name of Montres BREGUET describes a mechanism for regulating the pivoting speed, around a first pivot axis, of a mobile, in particular a striking ring, comprising a pivoting counterweight around a second pivot axis parallel to the first. The regulator includes means for returning the counterweight to the first axis. When the mobile pivots at a speed lower than a set speed, the counterweight remains confined in a first volume of revolution around the first axis. When this mobile pivots at a speed greater than the set speed, the counterweight engages in a second volume of revolution around the first axis, contiguous and external to the first volume of revolution, and a peripheral portion of the counterweight cooperates in this second volume of revolution with regulation means arranged to cause the mobile to brake and reduce its pivoting speed to the set speed, and to dissipate excess energy. In particular, the mobile is subjected to a braking torque by eddy currents.

Requirement EP14184155 in the name of ETA Manufacture Horlogère Suisse describes a clockwork regulating mechanism comprising, mounted mobile, at least in pivoting relative to a plate, an escapement wheel arranged to receive a driving torque via a gear train, and a first oscillator comprising a first rigid structure connected to the plate by first elastic return means. This regulating mechanism comprises a second oscillator comprising a second rigid structure connected to the first rigid structure by second elastic return means, and which comprises guide means arranged to cooperate with complementary guide means which the escape wheel comprises, synchronizing the first oscillator and the second oscillator with the train.

Requirement EP15153657 on behalf of ETA Manufacture Horlogère Suisse describes a horological oscillator comprising a structure and distinct primary resonators, temporally and geometrically phase-shifted, each comprising a mass biased towards the structure by an elastic return means. This watch oscillator comprises coupling means for the interaction of the primary resonators, comprising motor means for driving a mobile in motion which comprises drive and guide means arranged to drive and guide a control means articulated with means of each articulated transmission, remote from the control means, with a mass of a primary resonator, and the primary resonators and the mobile are arranged in such a way that the axes of the articulations of any two of the primary resonators and the axis of articulation of the control means are never coplanar.

International demand PCT / EP2015 / 065434 on behalf of The Swatch Group Research & Development Ltd describes a timepiece assembly comprising a combined resonator with improved isochronism, with at least two degrees of freedom, which comprises a first linear or rotary oscillator with amplitude reduced in a first direction, with respect to which oscillates a second linear or rotary oscillator of reduced amplitude in a second direction substantially orthogonal to the first direction, this second oscillator comprising a second carrier mass of a slide. This timepiece assembly includes a mobile arranged for the application of a torque to the resonator, this mobile comprising a groove in which the slide slides with minimum clearance. This slide is arranged for at least, either follow the curvature of the groove when it has one, or rub friction in the groove, or else push the interior lateral surfaces that the groove has by magnetized or electrified surfaces that it has the slide.

The document FR630831A in the name of Schieferstein describes a method and a device for the transmission of power between mechanical systems or for the control of mechanical systems, where two oscillating movements of flexible mechanisms, forming a suitable angle between them, act one on the other so that an oscillation takes place which takes place along a closed curve, and which, for the purpose of force transmission or control, is loosely coupled in accordance with a rotary movement. The associated return means are attached to the plate. The connecting elements between the masses are elastic, and therefore do not constitute means of kinematic connections.

The document WO2015 / 104963 and the document WO2015 / 104962 in the name of EPFL describe a mechanical isotropic harmonic oscillator, comprising at least one connection with two degrees of freedom, supporting a mass in orbit relative to a fixed base with springs having isotropic and linear restoring properties. More particularly, a plane spring stage forms a connection with two degrees of freedom causing a purely translational movement of the mass in orbit, so that the mass moves along its orbit while maintaining a fixed orientation. In a variant, each spring stage comprises at least two parallel springs. Again, the springs or other associated return means are attached to the plate.

When a mass, guided in rotation around a fixed axis, and connected to this axis by a linear radial return spring, is driven in its rotation by a grooved wheel, if a pin working in this groove is fixed on the mass , if this mass is punctual, its trajectories are ellipses or circles, and are all isochronous. If the mass has a rotational inertia, then only the circular trajectories are isochronous. Particular conditions, which are rather delicate to develop, can make it possible to stabilize the trajectories on circles, the resonator then remaining isochronous as a function of the drive torque of the wheel.

Summary of the invention

• supprimer les perturbations dues aux frottements des pivots du résonateur pour augmenter son facteur de qualité ;
• supprimer les saccades de l'échappement afin d'augmenter le rendement du mécanisme, et notamment le rendement de la fonction d'entretien et de comptage, habituellement dévolue à un mécanisme d'échappement.

The present invention proposes to achieve two objectives, namely:

• eliminate disturbances due to friction of the pivots of the resonator to increase its quality factor;
• eliminating the jerks of the exhaust in order to increase the efficiency of the mechanism, and in particular the efficiency of the maintenance and counting function, usually assigned to an exhaust mechanism.

To achieve these objectives, the invention provides a rotary resonator mechanism according to claim 1.

Historically, watchmakers have not considered rotary resonators as the time base for watches because they are generally not isochronous, and they are sensitive to gravity.

Also a rotary resonator mechanism according to the invention is in particular designed so as to include guides, in which friction of Guidance does not dissipate energy in steady state, thus improving the quality factor.

And, in this particular rotary resonator mechanism, the rotation is maintained by a torque applied directly to a shaft of the resonator, thus avoiding the dynamic losses of a conventional anchor escapement.

• condition d'isochronisme : le mécanisme résonateur rotatif comporte une pluralité d'éléments inertiels mobiles, chacun rappelé vers un axe de rotation principal par des moyens de rappel élastique, dont l'effort élastique de rappel provoque sur le centre de masse de cet élément inertiel une force centrale d'intensité proportionnelle à la distance entre l'axe de rotation et ce centre de masse ;
• condition d'insensibilité aux positions : l'utilisation d'une pluralité d'éléments inertiels mobiles, chacun guidé de façon à pouvoir s'éloigner de l'axe de rotation, en combinaison avec un mécanisme de liaison agencé pour forcer le centre de masse global (de l'ensemble de ces éléments inertiels) à rester sur l'axe de rotation quelle que soit l'amplitude, c'est-à-dire un lien cinématique qui force les centres de masse des différents éléments inertiels à être sur un même rayon, par rapport à l'axe de rotation, à chaque instant ;
• condition d'insensibilité aux chocs et perturbations : frottement radial permettant de ramener les centres de masse des éléments inertiels sur une trajectoire circulaire suite à une perturbation de trajectoire. Ce frottement radial peut être réalisé par frottement de l'air, frottement d'un pivot, d'une glissière, ou similaire.

To obtain a rotary resonator mechanism which can be used as a time base for a time instrument, the invention seeks to comply with the main conditions:

• condition of isochronism: the rotary resonator mechanism comprises a plurality of mobile inertial elements, each biased towards a main axis of rotation by elastic return means, the elastic return force of which causes on the center of mass of this inertial element a central force of intensity proportional to the distance between the axis of rotation and this center of mass;
• condition of insensitivity to positions: the use of a plurality of mobile inertial elements, each guided so as to be able to move away from the axis of rotation, in combination with a connecting mechanism arranged to force the center of mass global (of all these inertial elements) to remain on the axis of rotation whatever the amplitude, that is to say a kinematic link which forces the centers of mass of the different inertial elements to be on a same radius, relative to the axis of rotation, at all times;
• condition of insensitivity to shocks and disturbances: radial friction allowing the centers of mass of the inertial elements to be brought back on a circular trajectory following a trajectory disturbance. This radial friction can be achieved by air friction, friction of a pivot, a slide, or the like.

The invention also relates to a timepiece movement comprising at least one such resonator mechanism.

The invention also relates to a timepiece, in particular a watch, comprising such a timepiece movement.

Brief description of the drawings

• la figure 1 représente, de façon schématisée et en vue en plan, un mouvement mécanique d'horlogerie ne faisant pas partie de l'invention, comportant un barillet entraînant un rouage de finissage, qui entraîne un mobile d'entrée d'un mécanisme régulateur rotatif continu selon l'invention, dans une variante articulée comportant deux éléments inertiels portés par des bras montés pivotants par rapport à une structure commune tournant autour de l'axe de rotation du mobile d'entrée, chaque bras étant rappelé vers cet axe par des moyens de rappel élastique particuliers;
• la figure 2 représente, de façon similaire à la figure 1, un mécanisme dérivé de celui de la figure 1, comportant des moyens pour maintenir à tout instant les centres de masse des éléments inertiels à la même distance de l'axe de rotation de façon à rendre le mécanisme régulateur rotatif continu insensible aux effets du champ de gravité, ces moyens comportant ici un pantographe articulé ;
• la figure 3 est une variante du mécanisme de la figure 2, où les éléments inertiels sont combinés avec des bras adjacents du pantographe ;
• la figure 4 est une variante du mécanisme de la figure 3, où les bras sont tous remplacés par des éléments inertiels articulés sur un mobile central entraîné par le rouage, et un mobile central secondaire constituant ensemble une croix au cœur du pantographe ;
• la figure 5 est un schéma d'un losange formant demi-pantographe à côtés de dimensions quelconques, et la figure 6 est un schéma du même demi-pantographe montrant les coordonnées polaires du centre de masse d'un segment j ;
• la figure 7, similaire à la figure 6, concerne le cas particulier d'un demi-pantographe en losange isocèle régulier, où tous les bras entre articulations sont de longueur égale ;
• la figure 8 représente, de façon schématisée et en perspective, une autre variante, avec une structure voisine de celles des figures 3 et 4, dépourvue d'articulation à pivot, sauf au niveau de l'axe de rotation, et dont les bras constituant les segments du pantographe forment les éléments inertiels, et où les liaisons entre ces bras comportent des guidages flexibles à lames croisées en projection ;
• la figure 8A représente, de façon similaire à la figure 8, une variante avantageuse de réalisation comportant, en superposition, une structure supérieure monobloc, qui comporte toutes les lames supérieures, et une structure inférieure monobloc, qui comporte toutes les lames inférieures ; les figures 8B et 8C sont des vues de côté du mobile central et du mobile central secondaire de ce pantographe ;
• les figures 9 et 10 représentent, de façon schématisée, respectivement en plan et en perspective, une variante ne faisant pas partie de l'invention, présentant une liaison cinématique rigide entre deux éléments inertiels, comportant une roue dentée axiale folle, qui coopère en permanence avec deux secteurs dentés solidaires des éléments inertiels, lesquels sont articulés sur la structure commune par des guidages flexibles à lames croisées en projection ;
• la figure 11 représente, de façon schématisée et en vue en plan, une variante de pantographe, dont le mobile central est fixé au mobile d'entrée par une liaison élastique, et le mobile central secondaire est fixé au mobile d'entrée par une autre liaison élastique ;
• la figure 12 représente, de façon schématisée et en vue en plan, une autre variante ne faisant pas partie de l'invention, présentant une liaison cinématique en guidage linéaire radial, avec une barre de guidage radiale coulissant dans des alésages des éléments inertiels, les moyens de rappel élastique des éléments inertiels étant constitués par des ressorts en vé ;
• la figure 13 représente, de façon schématisée et en vue en plan, une autre variante ne faisant pas partie de l'invention, dans laquelle la liaison cinématique comporte des moyens de guidage curviligne, combinant une rainure courbe du mobile central, et un pion porté par l'élément inertiel concerné, et où les moyens de rappel élastique comportent deux lames élastiques parallèles l'une à l'autre, pour limiter le mouvement de chaque élément inertiel selon un seul degré de liberté ;
• la figure 14 représente, de façon schématisée et en vue en plan, une structure ne faisant pas partie de l'invention, et voisine de celle de la figure 9, comportant une roue dentée axial folle coopérant avec deux roues intermédiaires qui elles-mêmes engrènent avec des roues solidaires des éléments inertiels et des bras, lesquels sont articulés sur la structure commune par des ressorts de traction classiques ;
• la figure 15 représente, de façon schématisée et en vue en plan, une variante ne faisant pas partie de l'invention, où la liaison cinématique est flexible, la structure commune étant une lame flexible qui porte les éléments inertiels, qui portent chacun un bras porteur d'un élément de crémaillère coopérant avec une roue folle axiale ;
• la figure 16 représente, de façon schématisée et en vue en plan, une variante de la figure 15, ne faisant pas non plus partie de l'invention et comportant des moyens de rappel élastique comportant, pour chaque élément inertiel, deux lames élastiques parallèles, pour limiter le mouvement de chaque élément inertiel selon un seul degré de liberté ;
• la figure 17 est un schéma-blocs représentant une montre comportant un mouvement qui comporte lui-même un mécanisme régulateur rotatif continu selon l'invention.

Other characteristics and advantages of the invention will appear on reading the detailed description which follows, with reference to the appended drawings, where:

• the figure 1 shows, schematically and in plan view, a mechanical clockwork movement not forming part of the invention, comprising a barrel causing a gear train, which drives an input mobile of a continuous rotary regulating mechanism according to the invention, in an articulated variant comprising two inertial elements carried by arms mounted to pivot relative to a common structure rotating around the axis of rotation of the input mobile, each arm being returned to this axis by return means special elastic;
• the figure 2 represents, similarly to the figure 1 , a mechanism derived from that of the figure 1 , comprising means for maintaining at all times the centers of mass of the inertial elements at the same distance from the axis of rotation so as to make the continuous rotary regulating mechanism insensitive to the effects of the gravity field, these means here comprising an articulated pantograph ;
• the figure 3 is a variant of the mechanism of the figure 2 , where the inertial elements are combined with adjacent arms of the pantograph;
• the figure 4 is a variant of the mechanism of the figure 3 , where the arms are all replaced by inertial elements articulated on a central mobile driven by the train, and a secondary central mobile together constituting a cross at the heart of the pantograph;
• the figure 5 is a diagram of a rhombus forming a half pantograph next to any dimensions, and the figure 6 is a diagram of the same half-pantograph showing the polar coordinates of the center of mass of a segment j;
• the figure 7 , similar to the figure 6 , relates to the specific case of a half isograph in regular isosceles rhombus, where all the arms between joints are of equal length;
• the figure 8 represents, schematically and in perspective, another variant, with a structure close to that of figures 3 and 4 , devoid of pivot articulation, except at the level of the axis of rotation, and whose arms constituting the pantograph segments form the inertial elements, and where the connections between these arms comprise flexible guides with crossed blades in projection;
• the figure 8A represents, similarly to the figure 8 , an advantageous alternative embodiment comprising, in superposition, a monobloc upper structure, which comprises all the upper blades, and a monobloc lower structure, which comprises all the lower blades; the Figures 8B and 8C are side views of the central mobile and the secondary central mobile of this pantograph;
• the Figures 9 and 10 show, diagrammatically, respectively in plan and in perspective, a variant not forming part of the invention, having a rigid kinematic connection between two inertial elements, comprising a mad axial gear, which cooperates permanently with two integral toothed sectors inertial elements, which are articulated on the common structure by flexible guides with crossed blades in projection;
• the figure 11 shows, schematically and in plan view, a variant of pantograph, the central mobile of which is fixed to the input mobile by an elastic connection, and the secondary central mobile of which is fixed to the input mobile by another elastic connection;
• the figure 12 shows, diagrammatically and in plan view, another variant not forming part of the invention, having a kinematic connection in radial linear guidance, with a radial guide bar sliding in bores of the inertial elements, the return means elastic inertial elements being constituted by vee springs;
• the figure 13 shows, schematically and in plan view, another variant not forming part of the invention, in which the kinematic connection comprises curvilinear guide means, combining a curved groove of the central mobile, and a pin carried by the inertial element concerned, and where the elastic return means comprise two elastic blades parallel to each other, to limit the movement of each inertial element according to a single degree of freedom;
• the figure 14 shows, schematically and in plan view, a structure not forming part of the invention, and close to that of the figure 9 , comprising a crazy axial toothed wheel cooperating with two intermediate wheels which themselves mesh with wheels integral with inertial elements and arms, which are articulated on the common structure by conventional tension springs;
• the figure 15 shows, schematically and in plan view, a variant not forming part of the invention, where the kinematic connection is flexible, the common structure being a flexible blade which carries the inertial elements, which each carry an arm carrying a rack element cooperating with an axial idler wheel;
• the figure 16 shows, schematically and in plan view, a variant of the figure 15 , not forming part of the invention either and comprising elastic return means comprising, for each inertial element, two parallel elastic blades, to limit the movement of each inertial element according to a single degree of freedom;
• the figure 17 is a block diagram representing a watch comprising a movement which itself comprises a continuous rotary regulating mechanism according to the invention.

Detailed description of preferred embodiments

The invention relates to a resonator mechanism 100 according to claim 1, provided for a clockwork movement 200 intended mainly to be integrated into a watch 300. In fact, the resonator mechanism 100 according to the invention is designed to be isochronous, insensitive to positions in the field of gravity, and, if not insensitive to shocks and disturbances, at least arranged to resume normal walking very quickly.

This resonator mechanism 100 is a rotary resonator. It has the particularity of being devoid of the usual exhaust mechanism, and of operating continuously. The absence of jerks makes it possible to considerably improve the energy efficiency, in comparison with a conventional resonator, of the balance-spring type coupled with an anchor escapement.

This resonator mechanism 100 comprises an input mobile 1, pivotally mounted about an axis of rotation D. This input mobile 1 is subjected to a motor torque. Not being part of the invention, the figure 1 illustrates a conventional configuration of a timepiece movement 200 which comprises means of accumulating and storing energy 210, here comprising in a nonlimiting manner a barrel 211, arranged to conventionally drive a train 220, in particular a train of finishing, the most downstream element of which drives the input mobile 1, thus subjected to the torque of the gear train.

The resonator mechanism 100 comprises a common structure, which is deformable or articulated, and which is rotationally integral with the input mobile 1 around the axis of rotation D. This common structure carries, or comprises, a plurality of elements inertials 2. And this common structure rotates continuously. There is no back-and-forth movement: once subjected to a motor torque, the common structure rotates in a single direction of rotation. This does not prevent that the structure can be reversible, and able to rotate in the other direction if it is subjected to a couple of opposite directions.

Each inertial element 2 is guided, according to at least one degree of freedom with respect to the common structure.

Each inertial element 2 is returned towards the axis of rotation D by elastic return means 4, which are arranged to cause a return force on the center of mass of this inertial element 2.

According to the invention, these elastic return means 4 are embedded in the rotary resonator mechanism 100.

This restoring force is directed towards the axis of rotation D, and has an intensity proportional to the distance R _G between the axis of rotation D and the center of mass of the inertial element 2 considered.

In a particular variant, the same elastic return means 4 are common to several inertial elements 2, and may in particular consist of a tension spring joining pins arranged on the inertial masses, or the like.

In another variant, illustrated in particular by the figures 1, 2 , 12, 13 , 14 , where the resonator mechanism 100 is articulated, such elastic return means 4 are arranged between, on the one hand the common structure, and on the other hand an inertial mass 2, or else an arm 31, 32, carrying a inertial mass 2.

In yet another variant, as visible on the figure 15 , the common structure is elastically deformable, and constitutes such elastic return means 4.

The resonator mechanism 100 has rotation symmetry of order N, N being the number of inertial masses 2.

In a variant where the resonator mechanism 100 is articulated, each inertial element 2 is guided, directly or indirectly via arms or secondary articulated systems, relative to the common structure by at least one guide means 5.

The figure 1 thus illustrates an example not forming part of the invention where the common structure comprises a central mobile 30, which carries at its two ends, articulation pivots 51, 52, around axes D31 and D32, and which respectively carry arms 31, 32, which themselves carry inertial elements 2: 21 and 22, which, according to the variant, can be, or else mounted idly on these arms 31, 32, at the axes D1, D2, passing through their center of mass, or mounted fixed relative to these arms.

In this variant of the figure 1 , the elastic return means 4 are in rotation, and separate: 41 and 42, arranged between, on the one hand, the central mobile 30 of the common structure 3 at the level of an internal attachment 410, 420, and on the other hand the arm 31, 32, at an external attachment 411, 421.

It is understood that each inertial element 2 can include a degree of freedom in rotation, as in most of the present figures, or even a degree of freedom in translation as in the figure 12 .

où :

• V_tot est le potentiel élastique, qui représente une énergie élastique,
• ∑_j est la somme sur les j de la quantité entre parenthèses,
• ω₀ est la vitesse de rotation qu'on veut imposer,
• Rj(βi) est la position du centre de masse de l'élément inertiel j, en fonction de la valeur du degré de liberté βi,
• M_j est la masse de l'élément inertiel j.

In the variant where each inertial element 2 has a degree of freedom in rotation, more particularly, the elastic return means 4 cause an elastic potential, comparable to a total elastic potential energy, characterized by the following relation: $${\mathrm{V}}_{\mathrm{early}}=\mathrm{½}.{{\mathrm{\omega }}_0}^2.{\displaystyle {\sum }_{\mathrm{j}}\left({\mathrm{M}}_{\mathrm{j}.\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">R</figure-callout>}2\mathrm{j}}\left(\mathrm{\beta i}\right)\right)},$$

or :

• V _tot is the elastic potential, which represents an elastic energy,
• ∑ _j is the sum over j of the quantity in parentheses,
• ω ₀ is the rotational speed that we want to impose,
• Rj (βi) is the position of the center of mass of the inertial element j, as a function of the value of the degree of freedom βi,
• M _j is the mass of the inertial element j.

We understand that, in the articulated example of the figure 1 , comprising two inertial elements 21 and 22, the resonator mechanism 100 according to the invention must control, at all times, three angles: that made by the common structure 3 with a plate of the clockwork movement, or the like, and those, β1 and β2, what do the centers of mass of the inertial elements 21 and 22 with respect to the common structure 3, with reference to the axes D31 and D32 of the respective guides 51 and 52. Of course, in the case of N inertial elements, it is a question of controlling N + 1 angles.

The system is self-regulated: under the effect of the torque imparted by the movement's driving means, each inertial element tends to move away from the axis of rotation D, to a radial position where the friction of the air print a resistant torque which balances, in a tangential direction, the effect of the torque applied to the input mobile 1, relative to the center of mass of the inertial element. In the radial direction, it is the centrifugal force which balances the radial component of the restoring force impressed by the elastic restoring means 4. This double balance, tangential and radial, determines the radial position of the center of mass at all times , as a function of the instantaneous value of the torque emitted by the motor means. The angular speed of rotation is equal to the square root of the quotient of the stiffness of the elastic return means by the mass of the inertial element, while the instantaneous radius of the center of mass with respect to the axis of rotation D is equal at the square root of the quotient between the engine torque and the product of the angular speed and the coefficient of friction between the ambient medium and the inertial element.

The centers of mass of the inertial elements tend to reach the axis of rotation D, when the drive means are stopped, this position corresponding to the exercise of zero tensile force on the part of the elastic return means 4 It may be easier to produce a resonator mechanism 100 where the inertial masses 2 approach the axis of rotation, especially if these inertial masses 2 are in the same plane, and for example come into contact with one another. 'other in a rest position, the elastic return means 4 then being assembled with a prestress.

The disturbance due to the gravity field tends, in certain positions of the watch 300, to differentiate the behavior of the inertial elements. For example, the figure 1 has a reference Z, in the plane of the sheet and directed towards the bottom of the sheet, which indicates the vertical of the place and the field of gravity, the inertial element 22 tends to deviate from the common structure 3, while the inertial element 21 tends to approach it. If the inertial elements 2 are completely free radially, it may thus be that they are located on different radii with respect to the axis of rotation D.

It is therefore advantageous, to overcome this effect of the gravity field, to carry out a transfer of movement reducing the number of degrees of freedom of each inertial element 2, and to establish a mechanical coupling which forces the radial position, with respect to the axis of rotation D, of each inertial element 2 with respect to the others. Thus the overall center of mass of the entire resonator mechanism can remain on the axis of rotation D. Preferably, a symmetry is established with respect to the axis of rotation D.

To this end, the rotary resonator mechanism 100 advantageously comprises a kinematic connection, and more particularly a rigid kinematic connection, between at least two inertial elements 2, and preferably between all the inertial elements 2. This connection forces the inertial elements 2 to find at the same distance of the axis of rotation D, permanently. In other words, the inertial elements 2 have only one degree of freedom with respect to the common structure 3.

This kinematic link is useful at low frequencies, 2 to 5 Hz in particular. On the other hand, if the speed of rotation of the common structure 3 is high, in particular corresponding to a period greater than or equal to 20 Hz, for example of the order of 50 Hz, the effect of the gravity field is negligible compared to the effects of inertia, and such a kinematic link is not essential. Such a very simple embodiment may be suitable for single-use applications, such as fireworks or the like. Kinematic connection becomes necessary, however, as soon as one seeks to achieve good chronometric performance, in particular for use in a watch.

Different examples of such kinematic connections are illustrated on the figures 2 , 3 , 4 , 8 , 9, 10 , 12, 13 , 14, 15 and 16 , and will be discussed later. Most are rigid articulated kinematic connections, some illustrating flexible kinematic connections.

The figure 2 illustrates, in a deployed position, an advantageous embodiment according to the invention, where the kinematic connection is achieved thanks to a pantograph structure: the resonator mechanism 100 comprises a structure articulated in pantograph in symmetry about the axis of rotation D, comprising at least all the inertial elements 2, articulated directly, or articulated indirectly by means of arms which are designated, depending on the variants, by the references 31, 32, 131, 132, 121, 122, 123.124, around the central mobile 30 and a secondary central mobile 130 which is arranged to pivot about the axis of rotation D, and which constitutes with the central mobile 30 a crossed structure. By “arm” here is meant a component comprising two articulations.

The term “pantograph” is used to designate a double articulated structure around a central axis, the double diamond shape is more particularly illustrated in the figures; the part of the structure located on one side of the central axis is called a "half pantograph". The pantograph has two half pantographs, with common elements, forming a crossed structure.

More particularly, this cross structure constituted by the central mobile 30 and the secondary central mobile 130 has its center of mass on the axis of rotation D.

So on the figure 2 , the kinematic connection and the guides are made by combining, on the basis of the example of the figure 1 , a central mobile 30, a secondary central mobile 130 pivoting around the axis of rotation D at an axial pivot, the two arms 31 and 32 pivoted on the central mobile 30, two other secondary arms 131 and 132 pivoted mad , both on the secondary central mobile 130 around axes D131 and D132, at the level of non-detailed pivots, and on the inertial elements 21 and 22 at the level of axes D1 and D2, and the seven articulations necessary for its operation, so as to form a pantograph having a rotation symmetry of order 2.

In a particular variant, the secondary central mobile 130 pivots madly about the axis of rotation D.

The elastic return means 41 and 42 are the same as on the figure 1 , since the linkage formed by the two arms 131 and 132 around the secondary central mobile 130 is passive, its only function being to maintain the centers of mass of the inertial elements 21 and 22 in symmetry with respect to the axis of rotation D.

Naturally, as visible on the variants illustrated in figures 3 and 4 , certain arms can constitute inertial elements. The variant of the figure 3 , very close to that of the figure 2 , illustrated in a folded position, combines the inertial element 21 and the secondary arm 131 to constitute an inertial element 121, and combines the inertial element 22 and the secondary arm 132 to constitute an inertial element 123, the arm 31 constituting an element inertial 122, and the arm 32 constituting an inertial element 124.

More particularly, all the inertial elements 2 are articulated directly on the central mobile 30 and the secondary central mobile 130. Thus, the variant of the figure 4 , very compact, comprises four inertial elements which also constitute arms 31, 32, 131, 132, articulated in pantograph around the central mobile 30 and the secondary central mobile 130.

The Figures 5 and 6 are diagrams of the half pantograph, with in figure 6 the polar coordinates of the center of mass of a segment j. Here we call "segment" the geometric definition of one side of the rhombus of the half pantograph, and we designate by "arm" the physical component incorporated into the mechanism.

avec les centres de masse G3 et G4 des segments 73 et 74 qui sont situés sur la droite qui lie les rotules de part et d'autre du segment concerné, respectivement A13 à A34, et A24 à A34.The figure 7 illustrates the particular case of an isosceles and regular diamond half pantograph, where: $${\mathrm{<figure-callout\; id="1"\; label="\beta "\; filenames="imgf0004.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_1={\mathrm{<figure-callout\; id="2"\; label="\beta "\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_2={\mathrm{<figure-callout\; id="3"\; label="\beta "\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_3={\mathrm{<figure-callout\; id="4"\; label="\beta "\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_4,$$

with the centers of mass G3 and G4 of the segments 73 and 74 which are located on the right which links the ball joints on either side of the segment concerned, A13 to A34, and A24 to A34 respectively.

(cette condition permet de garantir l'isochronisme d'un pantographe quelconque), où :

• V(β₁) est le potentiel en fonction de l'angle β₁,
• β₁ est l'angle d'ouverture du pantographe, c'est-à-dire l'angle entre d'une part la droite qui joint la pointe du pantographe opposée à l'axe de pivotement à l'axe de pivotement, et d'autre part le segment considéré,
• ω₀ est la vitesse de rotation du mécanisme résonateur rotatif 100,
• ∑j est la somme sur les j de la quantité entre parenthèses,
• M_j est la masse de l'élément inertiel 2 de rang j
• R_j(β₁) est la distance de l'axe de rotation au centre de masse Gj de l'élément inertiel 2 de rang j,
• R'_j(β₁) est la dérivée de la distance entre l'axe de pivotement et le centre de masse de l'élément inertiel 2 de rang j par rapport à β₁.

In the case of any half-pantograph, as visible on the Figures 5 and 6 , each member, in the form of a quadrilateral, of the pantograph comprises four segments 71, 72, 73, 74, articulated between them and with respect to a pivot axis constituted by a main ball joint 70 or the axis of rotation D. The central mobile 30 consists of two first segments 71 in the extension of one another relative to the main ball 70, and the secondary central mobile 130 consists of two second segments 72 in the extension of one another by relative to the main ball joint 70. And the elastic return means 4 generate a potential energy V which is a function of the angle of deformation β ₁ of the pantograph member, satisfying the relation: $$\partial \mathrm{<figure-callout\; id="1"\; label="V\; \beta "\; filenames="imgf0004.png"\; state="\{\{state\}\}">V\; </figure-callout>}\left({\mathrm{\beta }}_{}\right)\left({\mathrm{}}_1\right)/\partial {\mathrm{<figure-callout\; id="1"\; label="\beta "\; filenames="imgf0004.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_1=\mathrm{½}.{{\mathrm{\omega }}_0}^2.{\displaystyle \sum \mathrm{j}\left({\mathrm{M}}_{\mathrm{j}}.{\mathrm{<figure-callout\; id="1"\; label="R\; j\; \beta "\; filenames="imgf0004.png"\; state="\{\{state\}\}">R\; </figure-callout>}}_{\mathrm{j}}\left({\mathrm{\beta }}_{}\right)\left({\mathrm{}}_1\right).\mathrm{R}{\prime }_{\mathrm{<figure-callout\; id="1"\; label="j\; \beta "\; filenames="imgf0004.png"\; state="\{\{state\}\}">j\; </figure-callout>}}\left({\mathrm{\beta }}_{}\right)\left({\mathrm{}}_1\right)\right)},$$

(this condition guarantees the isochronism of any pantograph), where:

• V (β ₁ ) is the potential as a function of the angle β ₁ ,
• β ₁ is the opening angle of the pantograph, that is to say the angle between on the one hand the straight line which joins the point of the pantograph opposite the pivot axis to the pivot axis, and on the other hand the segment considered,
• ω ₀ is the speed of rotation of the rotary resonator mechanism 100,
• ∑j is the sum over j of the quantity in parentheses,
• M _j is the mass of the inertial element 2 of rank j
• R _j (β ₁ ) is the distance from the axis of rotation to the center of mass Gj of the inertial element 2 of rank j,
• R ' _j (β ₁ ) is the derivative of the distance between the pivot axis and the center of mass of the inertial element 2 of rank j with respect to β ₁ .

More particularly, the center of mass of each arm (31; 32; 131; 132; 121; 122; 123; 124) which is between two joints, is located on a straight line joining the two joints on either side of the arm considered.

More particularly, and in particular in the variant of figures 4 and 7 , each member of the half-pantograph has four segments of equal length L, together constituting a regular diamond. And the center of mass of the central mobile 30 and that of the secondary central mobile 130 are on the axis of rotation D of the resonator mechanism 100, and the centers of mass of each of the inertial arms are on a line defined by the two articulations of the corresponding arm.

où :

• β₁ est l'angle d'ouverture du pantographe,
• L est la longueur de chaque segment entre les articulations,
• M₃ est la masse d'un troisième segment 73 formant un des deux éléments inertiels opposés à l'axe de pivotement constitué par une rotule principale 70 ou par l'axe de rotation D, et compris entre une première rotule latérale A13 et une rotule de sommet A34 opposée à une rotule d'axe A12 constituant la rotule principale 70,
• M₄ est la masse d'un quatrième segment 74 formant l'autre des deux éléments inertiels opposés audit axe de pivotement, et compris entre une deuxième rotule latérale A24 et la rotule de sommet A34,
• R₃ est la distance de la première rotule latérale A13 au centre de masse G3 du troisième segment 73,
• R₄ est la distance de deuxième rotule latérale A24 au centre de masse G4 du quatrième segment 74,
• ω₀ est la vitesse de rotation du résonateur rotatif.

More specifically, with reference to the notations of the figure 7 , the potential energy V _tot of the elastic return means is related to their deformation angle by the relation: $${\mathrm{V}}_{\mathrm{<figure-callout\; id="1"\; label="early\; \beta "\; filenames="imgf0004.png"\; state="\{\{state\}\}">early\; </figure-callout>}}\left(\mathrm{\beta }\right)\left(\mathrm{}1\right)=\mathrm{<figure-callout\; id="3"\; label="L\; M"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">L\; </figure-callout>}\left({\mathrm{M}}_{}\right)\left({\mathrm{}}_3.{\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">R</figure-callout>}}_3+{\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">M</figure-callout>}}_4.{\mathrm{<figure-callout\; id="4"\; label="R"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">R</figure-callout>}}_4\right).{{\mathrm{\omega }}_0}^2.\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{<figure-callout\; id="1"\; label="\beta "\; filenames="imgf0004.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_1$$

or :

• β ₁ is the opening angle of the pantograph,
• L is the length of each segment between the joints,
• M ₃ is the mass of a third segment 73 forming one of the two inertial elements opposite the pivot axis constituted by a main ball 70 or by the axis of rotation D, and comprised between a first lateral ball A13 and a ball vertex A34 opposite a ball joint with axis A12 constituting the main ball joint 70,
• M ₄ is the mass of a fourth segment 74 forming the other of the two inertial elements opposite to said pivot axis, and lying between a second lateral ball joint A24 and the crown ball A34,
• R ₃ is the distance from the first lateral ball joint A13 to the center of mass G3 of the third segment 73,
• R ₄ is the distance from the second lateral ball joint A24 to the center of mass G4 of the fourth segment 74,
• ω ₀ is the rotational speed of the rotary resonator.

Such a pantograph type structure, combined with adequate elastic return means, thus constitutes a mechanism which, theoretically, makes it possible to guarantee the constancy of the period of rotation of the input mobile 1, and to ensure the insensitivity to changes in position in the gravity field.

The practical realization nevertheless requires execution precautions, because of the large number of articulation guides, synonymous with friction and loss of performance.

Other types of kinematic connection will be presented later.

To overcome the cost of an articulated system, linked to the machining precision and the parallelism of the axes, and the deterioration of the yield by friction with the pivots, a particular embodiment of the invention relates to a mechanism whose at least one of the guide elements and at least one of the elastic return means 4 are produced jointly by a flexible guide. That is to say that the distinct functions of guidance and elasticity are carried out by a single flexible guidance. More particularly, with the exception of the guides at the level of the axis of rotation, all of the guides in rotation and of the elastic return means are produced by flexible guides.

More particularly, at least one such flexible guide comprises at least two blades included in planes, and which define with each other the virtual axis of rotation of a flexible rotary guide.

More particularly, in a pantograph type structure as described above, at least four of its joints are produced by flexible rotary guides.

The figure 8 thus illustrates a structure close to that of figures 3 and 4 , devoid of pivot articulation, except at the level of the axis of rotation D, and the arms 31, 131, 32, 132 of which constitute the pantograph segments form the inertial elements. In this nonlimiting variant, the flexible guides each comprise two blades, arranged in parallel and distinct levels, and which, in projection on a parallel plane, intersect at the level of the axes of articulation D31, D1, D131, D132, D2 , and D32.

A simple realization is illustrated in Figures 8A, 8B and 8C , and consists of the superposition of a one-piece upper structure 101, which includes all of the upper blades 103, and of a one-piece lower structure 102, which includes all of the lower blades 102. These upper structure 101 and lower structure 102 can be very easily assembled to each other, by gluing, riveting, or the like, and the radial positions of the various articulations, as well as the symmetry of the inertial elements, with respect to the axis of rotation D, are perfectly guaranteed.

More particularly, these flexible rotary guides between two components are of the type with crossed blades in projection, as explained above, whose opening angle θ, read on the projection plane between the crossing axis C and the points of embedding of the blades on one of the components, has a value of 40 ° +/- 4 °, and the blades crossing at a length proportion of 0.15 +/- 0.015. This crossing can be carried out both near the most mobile component, that is to say whose stroke is the greatest, as well as the least mobile component, and it is in general determined by the dimensioning of the components to ensure the required distance between the installation points of the boards.

More particularly, the flexible guides are made of oxidized silicon to compensate for the thermal effects.

The Figures 9 to 16 , where only the variant of figure 11 is part of the invention, illustrate several variants making it possible to guarantee the radial symmetry of movement of the centers of mass of the inertial elements, as the case may be, on the basis of articulated rigid kinematic connections, or else of flexible kinematic connections.

The realization of Figures 9 and 10 , not forming part of the invention, comprises, to establish the rigid kinematic connection between the inertial elements 2 (21 and 22), a toothed wheel 60 mounted idly concentrically with the axis of rotation D, and which cooperates permanently with two toothed sectors 61 and 62 integral with the inertial elements 21 and 22. The latter are shown here articulated on the common structure 3 by such flexible guides with crossed blades in projection 41 and 42.

In a particular variant of the pantograph type structure, comprising a central mobile 30 and a secondary central mobile 130, the central mobile 30 is fixed to the input mobile 1 by an elastic connection 80, and the secondary central mobile 130 pivots around the axis of rotation D, but this pivoting is limited by an elastic connection 80 connecting it to the input mobile 1. In this particular variant illustrated by the figure 11 , the central mobile 30 and the secondary central mobile 130 are each subjected to a drive torque equivalent to half the equivalent exhaust torque in a conventional exhaust mechanism.

More particularly, this elastic connection 80 is a flexible rotary guide, in particular comprising two elastic blades.

The figure 12 illustrates another variant, not forming part of the invention in which the kinematic connection comprises radial linear guide means 90, with a radial guide bar 91 sliding in bores 911 and 912 of the inertial elements 21 and 22. The means elastic return 4 are here constituted each time by a vee spring 41, 42.

The figure 13 illustrates yet another variant, not forming part of the invention and in which the kinematic connection comprises curvilinear guide means 95, combining a curved groove 35 of the central mobile 30, and a pin 25 carried by the inertial element 21, 22, concerned. In this variant, the elastic return means 4 comprise, for the suspension and the return of each inertial element 21, 22, two elastic blades 45 and 46 substantially parallel to one another, so as to limit the movement of each inertial element 21, 22, according to a single degree of freedom.

The figure 14 represents a structure close to that of the figure 9 , not part of the invention and comprises a toothed wheel 60 mounted idly concentrically with the axis of rotation D, and which cooperates permanently with two intermediate wheels 610 and 620, which themselves mesh with wheels or sectors toothed 61 and 62 integral with the inertial elements 21 and 22 and the arms 31 and 32. The latter are shown here articulated on the common structure 3 by conventional tension springs.

The figure 15 illustrates a variant not part of the invention and where the kinematic connection is not rigid, but flexible, the common structure 30 being a flexible blade which carries the inertial elements 21 and 22, which each carry an arm carrying a rack element 161, 162, which cooperates with an axial idler wheel 60. In this very simple mechanism, the inertial elements 21 and 22 can however move according to two degrees of freedom.

The embodiment not forming part of the invention and illustrated in figure 16 solves this problem, through employment, as in carrying out the figure 13 , elastic return means 4 which comprise, for the suspension and the return of each inertial element 21, 22, two elastic blades 45 and 46 substantially parallel to each other, so as to limit the movement of each inertial element 21, 22, according to a single degree of freedom.

In a particular embodiment, the complete resonator mechanism 100 (guide, inertial element, elastic return means, arm, mobile) is in one piece. The entire rotary resonator can be made of silicon machined by multi-level DRIE, for example. When this execution is awkward, in particular when using blades crossed in different levels, it is advantageously possible, as in the case of the figure 8A , superimpose an upper structure 101 in one piece and a lower structure 102 in one piece, each simple to manufacture, and which can be very easily assembled together, by gluing, riveting, screwing or the like. More particularly, the one-piece upper structure 101 and the one-piece lower structure 102 are assembled to each other irreversibly to create a non-removable one-piece component.

In a particular variant, the frequency of rotation of the rotary resonator mechanism 100 is greater than 20 Hz, and in particular greater than 50 Hz. This relatively high frequency makes it possible to limit the sensitivity to positions in the gravity field, in the case which is not part of the invention where there is no kinematic link.

It is understood that the invention, designed for counting time, can also be used for other mechanisms, such as a ringing regulator, or the like. The elastic return means of the invention are embedded in the rotary resonator, which simplifies its construction.

In addition, the kinematic connection means of the invention reduce the number of degrees of freedom of the system by completely linking the displacement of the masses, whereas in the prior art, the link is flexible and cannot reduce the number of degrees of freedom.

The invention also relates to a timepiece movement 200, comprising a plate carrying means of energy accumulation and storage 210, in particular at least one barrel 211, arranged to conventionally drive a gear train 220, in particular a gear train , the most downstream element of which is arranged to drive the input mobile 1 of such a rotary resonator mechanism 100, which comprises this movement 200.

The invention also relates to a timepiece, in particular a watch 300, comprising at least one timepiece movement 200, and / or such a rotary resonator mechanism 100.

• suppression du mécanisme d'échappement traditionnel, permettant une simplification du mécanisme;
• suppression du travail du frottement des pivots d'un balancier-spiral, permettant d'augmenter le facteur de qualité du mécanisme résonateur ;
• suppression des saccades de l'échappement, permettant d'augmenter le rendement ;
• augmentation de la réserve de marche et/ou de la précision des montres mécaniques actuelles.

This invention has various advantages, and in particular:

• elimination of the traditional exhaust mechanism, allowing a simplification of the mechanism;
• elimination of the friction work of the pivots of a balance-spring, making it possible to increase the quality factor of the resonator mechanism;
• elimination of exhaust jerks, making it possible to increase efficiency;
• increase in the power reserve and / or the precision of current mechanical watches.

For a given movement size, it is possible to quintuple the autonomy of the watch, and to double the regulating power of the watch. This amounts to saying that the invention allows a gain of a factor of 10 on the performance of the movement.

Claims (23)

1. Resonator mechanism (100) for a timepiece movement having an input wheel train (1) mounted to pivot around an axis of rotation (D) and subjected to a driving torque, and having a central wheel train (30) fixed in rotation to said input wheel train (1) around said axis of rotation (D) and arranged to turn continuously, wherein said resonator mechanism (100) has a plurality of N inertial elements (2), each being movable in relation to said central wheel train (30), and restored to said axis of rotation (D) by elastic restoring means (4) belonging to said resonator mechanism (100), which are arranged to cause a restoring effort on the centre of mass of said inertial element (2), wherein said resonator mechanism (100) has a rotational symmetry of order N, where said resonator mechanism (100) has kinematic linkage means between all said inertial elements (2) and that are arranged to maintain at any time all of the centres of mass of said inertial elements (2) at the same distance, R, from said axis of rotation (D), and where said elastic restoring means (4), which are rotational and borne by said resonator mechanism (100), cause an elastic potential characterised by the following equation: $$\mathrm{V}=1/2.{{\mathrm{\omega }}_0}^2.{\displaystyle {\sum }_{\mathrm{j}}{\mathrm{M}}_{\mathrm{j}}{\mathrm{R}}^2}$$

   

   where:

   - V is the elastic potential,

   - ω₀ is the speed of rotation to be imposed,

   - R_j=R is the distance of the axis of rotation from the centre of mass G_j of the inertial element j,

   - M_j is the mass of the inertial element j,

   said resonator mechanism (100) being characterised in that said resonator mechanism (100) has a pantograph structure articulated around said axis of rotation (D) having at least all said inertial elements (2) either directly articulated or indirectly articulated by means of arms (31; 32; 131; 132; 121; 122; 123; 124), around said central wheel train (30) and a secondary central wheel train (130), which is arranged to pivot around said axis of rotation (D) and which together with the central wheel train (30) constitutes a crossed structure.
2. Resonator mechanism (100) according to claim 1, characterised in that said crossed structure formed by said central wheel train (30) and said secondary central wheel train (130) has its centre of mass on said axis of rotation (D).
3. Resonator mechanism (100) according to claim 1 or 2, characterised in that each member of said pantograph comprises four segments (71, 72, 73, 74) articulated to one another and in relation to a pivot axis formed by a main joint (70) or to said axis of rotation (D), wherein said central wheel train (30) is formed from two first segments (71) in the extension of one another in relation to said main joint (70), and said secondary central wheel train (130) is formed from two second segments (72) in the extension of one another in relation to said main joint (70), and in that said elastic restoring means 4 generate a potential energy V, which is dependent on the angle of deformation β₁ of said pantograph member in accordance with equation: $$\partial \mathrm{V}\left({\mathrm{\beta }}_1\right)/\partial {\mathrm{\beta }}_1={{\mathrm{\omega }}_0}^2.{\displaystyle {\sum }_{\mathrm{j}}\left({\mathrm{M}}_{\mathrm{j}}.{\mathrm{R}}_{\mathrm{j}}\left({\mathrm{\beta }}_1\right).\mathrm{R}{\prime }_{\mathrm{j}}\left({\mathrm{\beta }}_1\right)\right)},$$

   

   where:

   - V(β₁) is the potential as a function of angle β₁,

   - β₁ is the opening angle of the pantograph, i.e. the angle between, on the one hand, the straight line that joins the point of the pantograph opposite the pivot axis to the pivot axis and, on the other hand, the segment (71) originating from the pivot axis,

   - ω₀ is the speed of rotation of said rotary resonator mechanism (100),

   - ∑j is the sum over the js of the quantity between parentheses,

   - M_j is the mass of the inertial element j

   - R_j(β₁) is the distance of the axis of rotation to the centre of mass G_j of the inertial element j,

   - R'_j(β₁) is the derivative of the distance between the pivot axis and the centre of mass of the inertial element j in relation to β₁.
4. Resonator mechanism (100) according to one of claims 1 to 3, characterised in that said articulated structure forms a pantograph having a symmetry around said axis of rotation (D) or having a symmetry of rotation of order 2 around said axis of rotation (D).
5. Resonator mechanism (100) according to one of claims 1 to 4, characterised in that all said inertial elements (2) are articulated directly to said central wheel train (30) and said secondary central wheel train (130).
6. Resonator mechanism (100) according to one of claims 1 to 5, characterised in that the centre of mass of each of said arms (31; 32; 131; 132; 121; 122; 123; 124), which is contained between two articulations, is located on a straight line joining the two articulations on either side of said arm in question.
7. Resonator mechanism (100) according to one of claims 1 to 6, characterised in that each member of said pantograph comprises four segments of equal length and together form a regular rhombus.
8. Resonator mechanism (100) according to claims 6 and 7, characterised in that the potential energy V_tot of said elastic restoring means (4) is linked to their angle of deformation by the equation: $${\mathrm{V}}_{\mathrm{tot}}\left(\mathrm{\beta }1\right)=\mathrm{L}\left({\mathrm{M}}_3.{\mathrm{R}}_3+{\mathrm{M}}_4.{\mathrm{R}}_4\right).{{\mathrm{\omega }}_0}^2.\cos 2{\mathrm{\beta }}_1,$$

   

   where:

   - β₁ is the opening angle of the pantograph, which is the angle between the straight line that joins the point of the pantograph opposite the pivot axis to the pivot axis, on the one hand, and the segment originating from the pivot axis, on the other hand,

   - L is the length of each segment between the articulations,

   - M₃ is the mass of a third segment (73) forming one of the two inertial elements opposite the pivot axis formed by a main joint (70) or by said axis of rotation (D) and contained between a first lateral joint (A13) and an apex joint (A34) opposite an axis joint (A12) forming said main joint (70),

   - M₄ is the mass of a fourth segment (74) forming the other of the two inertial elements opposite said pivot axis and contained between a second lateral joint (A24) and said apex joint (A34),

   - R₃ is the distance of the first lateral joint (A13) from the centre of mass G3 of said third segment (73),

   - R₄ is the distance of the second lateral joint (A24) from the centre of mass G4 of said fourth segment (74),

   - ω₀ is the speed of rotation of the rotary resonator.
9. Resonator mechanism (100) according to one of claims 1 to 8, characterised in that said central wheel train (30) and said secondary central wheel train (130) are each fixed to said input wheel train (1) by an elastic connection (80).
10. Resonator mechanism (100) according to claim 9, characterised in that said elastic connection (80) is a flexible rotary guide arrangement having two elastic blades.
11. Resonator mechanism (100) according to one of claims 1 to 10, characterised in that each said inertial element (2) is guided directly or indirectly by means of arms or secondary articulated systems in relation to the common structure by at least one guide means (5), and in that at least one of the guide elements (5) and at least one of said elastic restoring means (4) are jointly made by a flexible guide means.
12. Resonator mechanism (100) according to claim 11, characterised in that except for guide arrangements at the level of said axis of rotation (D), all the guide arrangements in rotation and elastic restoring means (4) belonging to said resonator mechanism (100) are formed by flexible guide means.
13. Resonator mechanism (100) according to claim 11 or 12, characterised in that at least one said flexible guide means has at least two elastic blades contained in planes and together define the virtual axis of rotation of a flexible rotary guide arrangement.
14. Resonator mechanism (100) according to one of claims 1 to 10, characterised in that in said pantograph type structure at least four of its articulations are formed by flexible rotary guide arrangements according to claim 13.
15. Resonator mechanism (100) according to claim 13 or 14, characterised in that at least one said flexible rotary guide arrangement between two components is a guide arrangement with crossed blades projecting on a projection plane.
16. Resonator mechanism (100) according to one of claims 11 to 14, characterised in that said flexible guide means are made from oxidised silicon to compensate thermal effects.
17. Resonator mechanism (100) according to claim 1, characterised in that said kinematic linkage means between all said inertial elements (2) have at least one idle wheel (60) mounted loosely concentrically to said axis of rotation (D) and which cooperates continuously with a toothed sector or a rack (61, 62) belonging to each said inertial element.
18. Resonator mechanism (100) according to claim 1, characterised in that said kinematic linkage means have radial linear guide means (90) with a radial guide bar (91) sliding into bores (911, 912) belonging to said inertial elements (2).
19. Resonator mechanism (100) according to claim 1, characterised in that said complete resonator mechanism (100) is made of a single piece.
20. Resonator mechanism (100) according to claim 1, characterised in that said resonator mechanism (100) has flexible guide means with crossed blades in different levels and has, in superposed arrangement and fitted together, a single-piece upper structure (101), which comprises all the upper blades (103), and a single-piece lower structure (102), which comprises all the lower blades (102).
21. Resonator mechanism (100) according to one of claims 1 to 20, characterised in that the rotation frequency of said rotary resonator mechanism (100) is higher than 20 Hz.
22. Timepiece movement (200) having a rotary resonator mechanism (100) according to one of claims 1 to 21, and having a support plate of means for accumulating and storing energy (210) or at least one barrel (211) arranged to drive a wheel train (220) arranged to drive the input wheel train (1) of said rotary resonator mechanism (100).
23. Watch (300) having at least one timepiece movement (200) according to claim 22.

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