EP3907563B1 - Timepiece mechanism comprising a pivot member - Google Patents

Description

The present invention relates to a timepiece mechanism comprising a pivoting member mounted on a pivoting axis and subjected to the action of at least one spring arranged to work within a predetermined range of winding angles, said spring comprising at least one arm elastic having at one of its ends a first rotary element integral at least in rotation with the pivot axis of the pivoting member, said spring having zero or negative stiffness in at least part of the predetermined range.

Such a pivoting member is for example a finger acting on a rocker having a feeler cooperating with a snail cam of an instantaneous minute counter mechanism of a chronograph, as described in the publication WO 2020/016818 . The first rotatable element of the spring is mounted on the pivot axis of the finger so that the first end of the spring is pivoted. The rocker is held against the periphery of the snail cam by said spring acting on the pivot axis of the finger, this finger itself acting on the rocker. With each revolution of the cam, the rocker rises along the cam, which progressively arms the spring. The pivoting member can also be the rocker itself, the first rotating element of the spring then being mounted on the axis of the rocker. At its second end, the spring has a base fixed to the frame of the timepiece mechanism by two pins, so that this second end of the spring is recessed.

This assembly makes it possible to obtain a spring having substantially zero or slightly negative stiffness in the predetermined range of angular positions that the first rotary element can assume during operation of the mechanism. This makes it possible to reduce the intensity of the force applied to the snail cam by the spring compared to a traditional spring, thus reducing the energy required to rotate the snail cam.

The slightly negative stiffness of the spring also allows the finger to press on the rocker with a slightly decreasing force making it possible to partially compensate for the variation of the lever arm of the force applied to the cam by the rocker on one rotation revolution of this cam. . This makes it possible to have a lower variation in the torque required to rotate said cam.

However, in order to be able to completely compensate for the variation of the lever arm, it is necessary to use a spring having an elastic arm of variable section. The section of the spring's elastic arm, one end of which is pivoted and the other end is embedded, must therefore vary between these two ends to obtain a constant torque applied to the cam, making it possible to reduce energy consumption and limit the jerks.

A disadvantage of this spring at one end pivoted and the other end embedded is therefore that it can be complex to manufacture due to the variable section or thickness of its elastic arm.

Another drawback of this spring with one end pivoted and the other end embedded is the difficulty encountered by the watchmaker in fitting the base of the spring provided for this purpose onto the frame, said base having to be housed between two pins.

The present invention aims to remedy these drawbacks by proposing a watch mechanism comprising a pivoting member subjected to the action of a spring having zero or negative stiffness, said spring being simple to mount.

The present invention also proposes a timepiece mechanism comprising a pivoting member subjected to the action of a spring having a negative stiffness, said spring also being simple to manufacture.

To this end, the present invention relates to a watch mechanism comprising a pivoting member mounted on a pivot axis and subjected to the action of at least one spring arranged to work within a predetermined range of winding angles, said spring comprising at least one elastic arm having at one of its ends a first integral rotary element at least in rotation of the pivot axis of the pivoting member, said spring having zero or negative stiffness in at least part of the predetermined range.

According to the invention, the elastic arm has at the other of its ends a second rotary element also pivotally mounted.

Thus, the spring can be easily put in place by the watchmaker. In addition, the two pivoted ends of the spring make it possible to reduce the torque applied by the spring as well as the stress in the elastic arm with respect to a spring at one pivoted end and at the other recessed end.

Preferably, the or each elastic arm is sinuous in shape.

According to a preferred embodiment, the geometric shape of the or each elastic arm is a Bézier curve or a succession of Bézier curves.

Advantageously, the center distance between the first and second rotary elements can be chosen so that the spring has a negative or zero stiffness in said at least part of the predetermined range, preferably in substantially the entire predetermined range.

According to one embodiment, the or each elastic arm of the spring has a constant section, the stiffness of the spring being negative or zero in said at least part of the predetermined range, preferably in substantially the entire predetermined range.

Thus, the invention makes it possible in particular to obtain a spring with negative stiffness without having to change the section of the elastic arm, so that said spring is simple to manufacture.

According to another embodiment, the or each elastic arm of the spring has a variable section, the variation of which is chosen to make the stiffness of the spring less negative, or even zero, in said at least part of the predetermined range, preferably in substantially the whole beach predetermined, with respect to an elastic arm of the same shape but of constant section.

Thus, the invention makes it possible to obtain a spring whose stiffness is chosen to be zero or negative depending on the intended application for the pivoting member.

The invention further proposes a timepiece, such as a wristwatch or a pocket watch, comprising this timepiece mechanism.

• la figure 1 est une vue plane de dessus d'un ressort utilisé dans le mécanisme horloger selon l'invention;
• la figure 2 est une vue plane de dessus d'une variante de ressort utilisé dans le mécanisme horloger selon l'invention, le ressort apparaissant en clair étant en position de repos et le ressort apparaissant en sombre ayant ses éléments rotatifs pivotés pour occuper une position angulaire θ par rapport à la position de repos;
• la figure 3 est une représentation graphique du moment normalisé exercé dans un ressort à extrémités pivotée et encastrée (courbe C1) et dans le ressort de la figure 1 (courbe C2), par un bras élastique de section constante, pour un entraxe de 3 mm;
• la figure 4 est une représentation graphique de la contrainte normalisée sur un ressort à extrémités pivotée et encastrée (courbe Ct1) et sur le ressort de la figure 1 (courbe Ct2), le bras élastique étant de section constante, pour un entraxe de 3 mm ;
• la figure 5 est une représentation graphique du moment normalisé exercé dans un ressort à extrémités pivotée et encastrée par un bras élastique de section constante (courbe C1) et dans le ressort de la figure 1, par un bras élastique de section constante (courbe C2) et par des bras de différentes sections variables (autres courbes) pour un entraxe de 3 mm ;
• la figure 6 est une représentation graphique du moment normalisé exercé dans un ressort à extrémités pivotée et encastrée (courbe C1) et dans le ressort de la figure 1 (courbe C2'), par un bras élastique de section constante, pour un entraxe de 5 mm ;
• la figure 7 est une représentation graphique de la contrainte normalisée sur un ressort à extrémités pivotée et encastrée (courbe Ct1) et sur le ressort de la figure 1 (courbe Ct2'), le bras élastique étant de section constante, pour un entraxe de 5 mm ;
• la figure 8 est une vue plane de dessous d'un mécanisme horloger comprenant un organe pivotant selon un exemple de réalisation de l'invention ; et
• la figure 9 est une vue isométrique d'un organe pivotant selon un autre exemple de réalisation de l'invention.

Other characteristics and advantages of the present invention will appear on reading the following detailed description of various embodiments of the invention, given by way of non-limiting examples, and made with reference to the appended drawings in which:

• the figure 1 is a top plan view of a spring used in the timepiece mechanism according to the invention;
• the picture 2 is a plan view from above of a variant of the spring used in the timepiece mechanism according to the invention, the spring appearing in light being in the rest position and the spring appearing in dark having its rotating elements pivoted to occupy an angular position θ by relative to the rest position;
• the picture 3 is a graphic representation of the normalized moment exerted in a spring with pivoted and embedded ends (curve C1) and in the spring of the figure 1 (curve C2), by an elastic arm of constant section, for a center distance of 3 mm;
• the figure 4 is a graphic representation of the normalized stress on a spring with pivoted and embedded ends (curve Ct1) and on the spring of the figure 1 (curve Ct2), the elastic arm being of constant section, for a center distance of 3 mm;
• the figure 5 is a graphic representation of the normalized moment exerted in a spring with pivoted ends and embedded by an elastic arm of constant section (curve C1) and in the spring of the figure 1 , by an elastic arm of constant section (curve C2) and by arms of different variable sections (other curves) for a center distance of 3 mm;
• the figure 6 is a graphic representation of the normalized moment exerted in a spring with pivoted and embedded ends (curve C1) and in the spring of the figure 1 (curve C2'), by an elastic arm of constant section, for a distance between centers of 5 mm;
• the figure 7 is a graphic representation of the normalized stress on a spring with pivoted and embedded ends (curve Ct1) and on the spring of the figure 1 (curve Ct2′), the elastic arm being of constant section, for a center distance of 5 mm;
• the figure 8 is a plan view from below of a timepiece mechanism comprising a pivoting member according to an exemplary embodiment of the invention; and
• the figure 9 is an isometric view of a pivoting member according to another exemplary embodiment of the invention.

In the context of the present invention, the term “stiffness” means tangential stiffness.

With reference to figure 1 and 2 , the present invention relates to a timepiece mechanism comprising a pivoting member mounted on a pivot axis and subjected to the action of at least one spring 100 arranged to work within a predetermined range of winding angles. Said spring 100 is specially shaped to have zero or negative stiffness in at least part of the predetermined range. Such a spring 100 makes it possible at least to improve, or even guarantee, the constancy of the torque or moment of force that it exerts on the pivoting member and thus at least reduce the energy consumption.

The spring 100 comprises at least one elastic arm 102 in the form of a blade having at one of its ends a first rotary element 104 secured at least in rotation to the pivot axis of the pivoting member. Said pivot axis of the pivoting member is mounted pivoted on an element of the frame of the watch mechanism. The first rotary element 104 has for example the shape of a triangular ring as on the figure 1 and 2 or circular. It is made integral in rotation with the pivot axis of the pivoting member, for example by driving on said axis or any other suitable fixing means.

In accordance with the invention, the elastic arm 102 has at the other of its ends a second rotary element 106 also pivotally mounted. Thus, the two ends of the spring 100 are advantageously pivoted.

According to one embodiment of the invention, the second rotating element 106 of the spring 100 is pivotally mounted on an element of the frame of the timepiece mechanism. It can be pivotally mounted, for example on a pin secured to said frame or by any other suitable mounting means.

According to another embodiment of the invention, the second rotary element 106 of the spring 100 is pivotally mounted on a movable element of the pivoting member arranged to be movable relative to the pivot axis of said pivoting member. It can be pivotally mounted, for example on a pin or a tenon secured to said movable element of the pivoting member or by any other suitable mounting means.

The second rotary element 106 has for example the shape of a circular ring as shown in the figure 1 or triangular as shown in the picture 2 .

It will clearly appear to those skilled in the art that instead of being made up of a single elastic arm, the spring 100 could comprise several elastic arms connecting the two rotating elements 104, 106, depending on the intensity of the force desired product. A spring comprising a single elastic arm, however, has the advantage of greater compactness, which may be advantageous depending on the application.

The spring 100 is here considered as a whole as a part comprising the two rotating elements 104 and 106 connected by the elastic arm 102. The two rotating elements 104 and 106 are intended to rotate on themselves, only the elastic arm 102 deforming during operation of the mechanism.

In a variant not shown, the first rotating element 104 can form a single piece with its pivoting member.

Spring 100 is preferably one-piece. It is for example made of metal, alloy, silicon, plastic, mineral glass or metallic glass. It can be produced by machining or by the LIGA technique, in particular in the case where it is made of a metal or alloy, by deep reactive ion etching called DRIE, in particular in the case where it is made of silicon, by molding, in particular in the case where it is made of plastic or metallic glass, or by laser cutting, in particular in the case where it is made of mineral glass.

For the understanding of the invention, the behavior of the spring 100 considered globally and in isolation, that is to say with its two ends pivoted, but free of any interaction with the rest of the watch mechanism with which it is associated, is described below. -below. The figure 1 and 2 represent this isolated spring.

Due to the specific shape of its elastic arm 102, the spring 100 has a privileged direction of rotation of its rotary elements 104, 106 with respect to their rest position, this direction being defined as that which allows, from a rest state of the isolated spring 100 in which its elastic arm 102 is at rest, the greatest relative angular displacement of the rotary elements 104 and 106 with respect to their rest position. This privileged direction of rotation is the clockwise direction for the first rotary element 104 of the picture 2 and counterclockwise for the second rotating element 106 of the picture 2 , wherein the first rotating element 104 in white is in its rest position, and the first rotating element in black is in a constrained state after one clockwise rotation. The two rotary elements 104 and 106 pivot in the opposite direction but with different angles, which vary in particular according to the center distance E between the first element 104 and the second rotary element 106, i.e. the distance between the centers of rotation of said rotary elements 104, 106.

θ is called the angular position of the first rotating element 104 of the isolated spring 100 in a constrained state with respect to its rest position, θ being equal to zero when the isolated spring 100 is at rest, that is to say when its elastic arm 102 is at rest, and increases with the angular displacement of the first rotary element 104, when the spring 100 is constrained, relative to its rest position in the preferred direction of rotation of said first rotary element 104.

Generally, when the first rotating element 104 is in the angular position in which θ=x°, the spring 100 is said to be armed with x.

The spring 100 differs from conventional elastic structures. Its properties are based on a sinuous shape of its elastic arm 102 which deforms so as to generate, in particular when its section is constant, a moment which decreases over a predetermined range of angular positions of its first rotary element 104 with respect to its position of rotation. rest, the spring 100 then having a negative stiffness over said range, or a substantially constant moment over a predetermined range of angular positions of its first rotary element 104 with respect to its rest position, the spring 100 then having a substantially zero stiffness over said range, when the two ends of the spring are pivoted.

Obtaining such an elastic arm 102 requires a specific and parameterized design. The geometric shape of the elastic arm 102 can for example be obtained by topological optimization using parametric polynomial curves such as Bézier curves. A detailed description of this optimization method is described in the publication WO 2020/016818 of the applicant to obtain an elastic arm 102 whose geometric shape is a Bézier curve or a succession of Bézier curves whose control points have been optimized to take into account, in particular, the dimensions of the spring 100 to be designed as well as obtaining a constant moment of 5% over a predetermined angular range.

The geometric shape of the arm 102 used in the present invention can be obtained according to the method described in said publication WO 2020/016818 to produce blades designed, in particular by their shape, to exert a substantially constant moment (constancy of 5%) in a spring comprising a pivoted end and a recessed end as detailed in said publication, but the blade obtained then being used in a spring 100 whose two ends are pivoted in accordance with the present invention.

Indeed, such elastic blades can work in bending (positive stiffness) and in buckling (negative stiffness). Mounting the spring 100 comprising such a blade with its two ends pivoted in accordance with the present invention makes it possible to advantageously modify the behavior of the blade by increasing the buckling. In particular, this can very advantageously make it possible to obtain a negative stiffness in at least part of the predetermined range on a blade of constant thickness which had, at the base, a substantially zero stiffness with only one pivoted end, as in the publication WO 2020/016818 .

Any other form of curve making it possible to obtain an elastic blade which can work in bending (positive stiffness) and in buckling (negative stiffness) so as to present globally a negative or zero stiffness, in particular for a blade of constant section, and more particularly a negative stiffness for a blade of constant section, in at least part of the predetermined range, when the two ends of the spring 100 are pivoted, can be used as an elastic arm in the invention.

In a particularly advantageous manner, the spring 100 can be configured to present a negative or zero stiffness in at least part of the predetermined range of winding angles, depending on the intended application for the pivoting member.

The predetermined range of winding angles is the predetermined range of the angular positions of the first rotary element 104 with respect to its position of rest, this range being preferably at least 10°, preferably at least 15°, the chosen minimum winding angular position preferably being greater than 5°.

Preferably, spring 100 can be configured to have negative or zero stiffness over substantially all of the predetermined range.

Preferably, for certain applications intended for the pivoting member, the spring 100 can be configured to present a negative stiffness in substantially all of the predetermined range. For other applications of the pivoting member, the spring 100 can be configured to have zero stiffness in substantially all of the predetermined range.

According to one embodiment, the center distance E between the first rotary element 104 and the second rotary element 106, that is to say the distance between the centers of rotation of said rotary elements 104, 106, can be advantageously chosen so that the spring 100 has a negative stiffness in said at least part of the predetermined range, preferably in substantially all of the predetermined range.

According to one embodiment, the center distance E varies between 96% and 200% of the developed length of the elastic arm 102.

According to one embodiment, the or each elastic arm 102 has a constant section, and the spring 100 with its two pivoted ends, is configured to have a negative stiffness in said at least part of the predetermined range, preferably in substantially all the predetermined range, unlike a spring of the same shape with one end pivoted and the other end recessed, which has zero stiffness.

More particularly, according to a preferred embodiment, the center distance E varies between 96% and 200% of the developed length of the elastic arm 102 and the elastic arm 102 is of constant section, the spring 100 with its two pivoted ends having a negative stiffness in said at least part of the predetermined range, preferably in substantially all of the predetermined range.

• Distance entre le centre de rotation du premier élément rotatif 104 et le point de jonction du bras élastique 102 audit premier élément rotatif 104: 0,5 mm ;
• Distance entre les deux extrémités du bras élastique 102: 2 mm Distance entre le point de jonction du bras élastique 102 et le centre de rotation du second élément rotatif 106: 0,5 mm;
• Longueur développée du bras élastique 102: 2,4 mm ;
• Soit un entraxe E de 3 mm, égal à 125% de la longueur développée du bras élastique 102 ;
• Epaisseur (largeur) constante du bras élastique 102: 30 µm ;
• Hauteur du ressort 100: 0,3 mm.

Using this principle, the applicant has designed a spring 100 as shown in the figure 1 , having the following dimensions:

• Distance between the center of rotation of the first rotary element 104 and the junction point of the elastic arm 102 with said first rotary element 104: 0.5 mm;
• Distance between the two ends of the elastic arm 102: 2 mm Distance between the junction point of the elastic arm 102 and the center of rotation of the second rotating element 106: 0.5 mm;
• Developed length of elastic arm 102: 2.4 mm;
• Consider a center distance E of 3 mm, equal to 125% of the developed length of the elastic arm 102;
• Constant thickness (width) of the elastic arm 102: 30 µm;
• Spring height 100: 0.3 mm.

The curve C2 of the picture 3 represents the results of a simulation of the evolution of the normalized moment of the spring 100 thus produced as a function of the angular position θ of its first rotary element 104 with respect to its rest position, the two ends of the spring 100 being pivoted in accordance with the invention. For comparison, curve C1 of the picture 3 represents the evolution of the normalized moment of a similar spring but of which only one end is pivoted, the other end being embedded, as described in the publication WO 2020/016818 .

The simulation carried out considers a spring 100 made of an amorphous alloy based on zirconium, titanium, nickel, copper and beryllium, more precisely in a metallic glass of the Vitreloy 1b type, but any suitable material can be used. For example, materials such as other metallic glasses, other alloys such as Nivaflex ^® 45/18 (alloy based on cobalt, nickel and chromium), nickel-phosphorus or CK101 (unalloyed structural steel), silicon, typically coated with silicon oxide, or plastic are also suitable. It is important to take into account the ratio between the elastic limit and the Young's modulus of the material to choose the material constituting the elastic arm 102.

The stiffness of a spring, more precisely of its elastic arm, is the derivative of the function M(θ) defined respectively by the curves represented on the picture 3 .

• pour un angle θ compris entre 0 et une première valeur θ_a, soit θ1_a pour la courbe C1 et θ2_a pour la courbe C2, le moment augmente avec la position angulaire θ ;
• pour un angle θ compris entre la première valeur θ_a et une deuxième valeur θ_b, le moment décroît pour la courbe C2, le ressort présentant alors une raideur négative entre θ2_a et θ2_b, alors que le moment est sensiblement constant pour la courbe C1, le ressort présentant alors une raideur sensiblement nulle entre θ1_a et θ1_b. On entend par moment « sensiblement constant » un moment ne variant pas de plus de 10%, de préférence 5%, plus préférentiellement 3%, étant entendu que ce pourcentage peut être diminué davantage ;
• pour un angle θ au-delà de la valeur θ_b, le moment augmente à nouveau jusqu'à atteindre une valeur limite qui dépend des propriétés du matériau dans lequel le ressort est réalisé et correspond à la contrainte maximale que peut subir ce ressort.

As can be seen on the M(θ) curves of the picture 3 , the moment follows an evolution in three phases:

• for an angle θ between 0 and a first value θ _a , ie θ1 _a for curve C1 and θ2 _a for curve C2, the moment increases with the angular position θ;
• for an angle θ between the first value θ _a and a second value θ _b , the moment decreases for the curve C2, the spring then having a negative stiffness between θ2 _a and θ2 _b , whereas the moment is substantially constant for the curve C1, the spring then having substantially zero stiffness between θ1 _a and θ1 _b . “Substantially constant” moment is understood to mean a moment not varying by more than 10%, preferably 5%, more preferably 3%, it being understood that this percentage can be further reduced;
• for an angle θ beyond the value θ _b , the moment increases again until it reaches a limiting value which depends on the properties of the material in which the spring is made and corresponds to the maximum stress which this spring can undergo.

Over the range of angular positions [θ2 _a , θ2 _b ] the stiffness of the spring 100 used in accordance with the invention is negative. In the present invention, we place ourselves in this range [θ2 _a , θ2 _b ] or at least partly in this range.

It emerges from the analysis of the results presented on the picture 3 that a decreasing moment is obtained during a displacement of the first rotary element 104 of the spring 100 studied, its two ends being pivoted, with respect to its rest position from an angular position θ2 _a = 5° to an angular position θ2 _b =20°, that is to say over a range of 15° over which the stiffness of the spring 100 is negative.

By way of comparison, with a spring of the same shape but having a pivoted end and a recessed end, a substantially constant moment is obtained during movement of its pivoted rotary element with respect to its recessed end, from an angular position θ1 _a =18° at an angular position θ1 _b =30°, ie over a range of 12° over which the stiffness of the spring is zero.

The Ct2 curve of the figure 4 represents the results of a simulation of the evolution of the normalized stress on the spring 100 as a function of the angular position θ of its first rotary element 104 with respect to its rest position, the two ends of the spring 100 being pivoted in accordance with the invention. For comparison, the Ct1 curve of the figure 4 represents the evolution of the normalized stress on a similar spring but of which only one end is pivoted, the other end being embedded, as described in the publication WO 2020/016818 .

The curves of figure 3 and 4 show that with the spring 100 at both ends pivoted in accordance with the invention, with a center distance E varying from 96% to 200% of the developed length of said elastic arm 102, a negative stiffness is obtained over the range [θ2 _a , θ2 _b ] with a spring, with an elastic arm 102 of constant section, which, at the base, had zero stiffness and only one pivoted end, the other being embedded. With such a spring 100 comprising an elastic arm 102 of constant section and mounted in accordance with the invention, it is no longer necessary, to obtain a negative stiffness, to have an elastic arm of variable section as described in the publication WO 2020/016818 .

In addition, the spring 100 mounted with its two ends pivoted in accordance with the invention, makes it possible to simplify the assembly, the watchmaker having only to insert the second rotary element 106 along a pin fixed to the frame, instead of having to lodge the end of the spring between two pins to achieve a recess, as described in the publication WO 2020/016818 .

Furthermore, the spring 100 mounted according to the invention requires a minimum winding of approximately 5° to have a negative stiffness, with a wide range of angles over which the stiffness is negative, whereas a spring with a recessed end requires a minimum reinforcement of 18° to present zero stiffness, and over a narrower range.

In addition, such a spring 100 mounted in accordance with the invention makes it possible to divide the torque almost by a ratio of 3 and to divide the stress almost by 2 with respect to the same spring, one end of which is embedded, at least on a part of the predetermined range. The assembly of the spring 100 according to the invention therefore makes it possible to reduce the torque and the stress significantly compared to a spring at one end embedded, which makes it possible to be able to increase the thickness of the elastic arm 102, without exceeding the allowable stress. of the material. For example, for a center distance E of 3 mm, the thickness can be multiplied by approximately 1.4. An increase in the thickness of the elastic arm 102 reinforces the robustness of the mechanism. The torque will be less sensitive to dimensional variations related to the manufacture of the elastic arm. Furthermore, the reduction in stress is appreciable for a material such as silicon.

It is possible to adjust the negative stiffness value of a spring 100 having an elastic arm of constant section configured to present a certain negative stiffness, by designing the spring 100 with an elastic arm 102 of variable section.

To this end, the or each elastic arm 102 has a variable section whose variation is chosen to make it less negative, or even zero depending on the variation of the thickness, the stiffness of the spring 100 in said at least part of the predetermined range, preferably in substantially all of the predetermined range, with respect to an elastic arm of the same shape but of constant section and configured to present a stiffness negative.

The figure 5 shows different curves representative of the normalized moment M(θ) exerted in a spring with pivoted ends and embedded by an elastic arm of constant section of 30 μm (curve C1) and in the spring 100 at the two pivoted ends in accordance with the invention, by an elastic arm 102 with a constant section of 30 μm (curve C2) and by arms of different variable sections (other curves) for a center distance of 3 mm corresponding to 125% of the developed length of the elastic arm 102, the spring being moreover identical to the spring 100 described above.

The curves located below the curve C2 correspond to an elastic arm 102 whose thickness increases linearly from the first rotary element 104 to the middle of the elastic arm 102 and decreases linearly from the middle of the elastic arm 9 to the second rotary element 106, the thickness in the middle of the elastic arm 102 being 30 μm for each curve, the thickness at the point of junction with the first or second rotary elements 104, 106 being 29 μm for the curve C3 under the curve C2, 28 μm for the curve C4 under curve C2, by 27 μm for curve C5 under curve C2, and so on by decrementation of 1 μm.

It can be seen that with the spring 100 mounted in accordance with the invention, the stiffness becomes less negative (the moment decreases less), or even zero (the moment is substantially constant), in the range of winding angles of interest where the stiffness is negative for an arm of constant section, when the section variation of the elastic arm 102 is increased. On the contrary, the publication WO 2020/016818 showed that an increase in the section variation of the elastic arm of a spring with a pivoted end and a recessed end led to a decrease in the negative stiffness of the spring.

More particularly, the stiffness of the spring 100 mounted in accordance with the invention increases but remains negative when the variation in section of the elastic arm 102 increases but is less than 60%, preferably less than 50%.

When the section variation of the elastic arm is greater than 60%, the stiffness of the spring 100 mounted in accordance with the invention is zero.

It is obvious that other modes of variation of the section of the elastic arm can be chosen.

In general, in the cases where the elastic arm 102 has a variable section, this typically varies in a strictly monotonous manner (it increases or decreases without interruption but not necessarily linearly) over at least a continuous portion of the elastic arm representing 10% , preferably 20%, preferably 30%, preferably 40%, of the (developed) length of the elastic arm. The variation of the section is also chosen to make the stiffness of the elastic arm 102 less negative, or even zero, over the range [θ2 _a , θ2 _b ] or at least over the part of the predetermined range which intersects with the range [θ2 _a , θ2 _b ], compared to an elastic arm of the same shape but of constant section.

It is therefore possible to choose the section of the elastic arm which is constant or variable according to the negative or zero stiffness sought in the range of interest. In addition, an increase in the variation of the section of the elastic arm makes it possible to reduce the moment as well as the stress, so that the section of the arm can also be adapted according to the intended application for the pivoting member.

Thus, a spring 100 having an elastic arm 102 of constant section or varying by less than 60% with a center distance E varying from 96% to 200% of the developed length of said elastic arm 102 and its two pivoted ends, a negative stiffness is obtained. on the range [θ2 _a , θ2 _b ] with a spring which, at the base, had zero stiffness and only one end rotated, the other being embedded.

According to another embodiment, the center distance between the first rotary element 104 and the second rotary element 106 can be chosen so that the spring 100' has zero stiffness in said at least part of the predetermined range, preferably in substantially the entire predetermined range.

According to one embodiment, the center distance E is greater than 200% and less than 300% of the developed length of the elastic arm 102.

According to one embodiment, the or each elastic arm 102 has a constant section, and the spring 100' with its two pivoted ends, is configured to have zero stiffness in said at least part of the predetermined range, preferably in substantially the entire predetermined range.

More particularly, according to a preferred embodiment, the center distance E is greater than 200% and less than 300% of the developed length of the elastic arm 102 and the elastic arm 102 is of constant section, the spring 100' with its two ends pivoted having zero stiffness in said at least part of the predetermined range, preferably in substantially all of the predetermined range.

Using this principle, the applicant has designed another spring 100' as shown in the figure 1 , having a distance between the two ends of the elastic arm 102 of 4 mm, ie a center distance E of 5 mm, equal to 208% of the developed length of the elastic arm 102; the other dimensions of the spring 100' are identical to those of the spring 100 described above.

The curve C2' of the figure 6 represents the results of a simulation of the evolution of the normalized moment of the spring 100' thus produced as a function of the angular position θ of its first rotary element 104 with respect to its rest position, the two ends of the spring 100' being pivoted in accordance with the invention. For comparison, curve C1 of the picture 3 which represents the evolution of the normalized moment of a similar spring but of which only one end is pivoted, the other end being embedded, with a center distance E of 5 mm, the moment not varying according to the center distance when the second end is embedded.

• pour un angle θ compris entre 0 et une première valeur θ_a, soit θ1_a pour la courbe C1 et θ2'_a pour la courbe C2', le moment augmente avec la position angulaire θ ;
• pour un angle θ compris entre la première valeur θ_a et une deuxième valeur θ_b, le moment est sensiblement constant (moment ne variant pas de plus de 10%, de préférence 5%, plus préférentiellement 3%), pour la courbe C2', le ressort 100' présentant alors une raideur sensiblement nulle entre θ2'_a et θ2'_b, et le moment est sensiblement constant pour la courbe C1, le ressort présentant une raideur sensiblement nulle entre θ1_a et θ1_b;
• pour un angle au-delà de la valeur θ_b, le moment augmente à nouveau jusqu'à atteindre une valeur limite qui dépend des propriétés du matériau dans lequel le ressort est réalisé et correspond à la contrainte maximale que peut subir ce ressort.

As can be seen on the M(θ) curves of the figure 6 , the moment follows an evolution in three phases:

• for an angle θ between 0 and a first value θ _a , ie θ1 _a for curve C1 and θ2′ _a for curve C2′, the moment increases with the angular position θ;
• for an angle θ between the first value θ _a and a second value θ _b , the moment is substantially constant (moment not varying by more than 10%, preferably 5%, more preferably 3%), for curve C2' , the spring 100' then having substantially zero stiffness between θ2' _a and θ2' _b , and the moment is substantially constant for curve C1, the spring having substantially zero stiffness between θ1 _a and θ1 _b ;
• for an angle beyond the value θ _b , the moment increases again until it reaches a limiting value which depends on the properties of the material in which the spring is made and corresponds to the maximum stress which this spring can undergo.

Over the range of angular positions [θ2' _a , θ2' _b ] the stiffness of the spring 100' used in accordance with the invention is substantially zero. In this embodiment of the invention, we place ourselves in this range [θ2′ _a , θ2′ _b ] or at least partly in this range.

It emerges from the analysis of the results presented on the figure 6 that a substantially constant moment is obtained during a displacement of the first rotary element 104 of the spring 100' studied, its two ends being pivoted, with respect to its rest position from an angular position θ2' _a = 5° to a angular position θ2' _b = 15°, that is to say over a range of 10° over which the stiffness of the spring 100' is zero. It is recalled that for the spring having a pivoted end and a recessed end, the moment is substantially constant during a displacement of its rotary element pivoted relative to its recessed end, from an angular position θ1 _a = 18° to an angular position θ1 _b = 30°.

The Ct2' curve of the figure 7 represents the results of a simulation of the evolution of the normalized stress on the spring 100' as a function of the angular position θ of its first rotary element 104 with respect to its rest position, the two ends of the spring 100' being pivoted in accordance with the invention. For comparison, the Ct1 curve of the figure 4 which represents the evolution of the normalized stress on a similar spring but of which only one end is pivoted, the other end being embedded, with a center distance E of 5 mm, the stress not varying according to the center distance when the second end is recessed.

The curves of figure 6 and 7 show that with the spring 100' at both ends pivoted in accordance with the invention, having an elastic arm 102 of constant cross-section with a center distance E greater than 200% and less than 300% of the developed length of said elastic arm 102, one obtains zero stiffness over the range [ _θ2'a , _θ2'b ] with a spring that basically had zero stiffness and only one end rotated, the other being recessed, but with much reduced moment and stress. Indeed, such a spring 100 'mounted in accordance with the invention makes it possible to divide the torque almost by a ratio of 10 and to divide the stress almost by 4 with respect to the same spring, one end of which is embedded, at least on a part of the predetermined range. As seen above for the spring 100, this makes it possible to increase the thickness of the elastic arm 102, without exceeding the allowable stress of the material.

In addition, the spring 100' mounted according to the invention requires a minimum winding of approximately 5° to have zero stiffness, whereas the same spring with a recessed end needs to be wound at a minimum of an angle of 18° to have zero stiffness.

Moreover, as for the spring 100 previously described, the spring 100' makes it possible to simplify assembly.

According to another embodiment in which the center distance E is greater than 200% and less than 300% of the developed length of the elastic arm 102, the elastic arm 102 is of variable section, the stiffness of the spring 100' with its two ends rotated remaining zero at least in part of the predetermined range, preferably in substantially all of the predetermined range.

When the center distance E is greater than 200% and less than 300% of the developed length of the elastic arm 102, the variation in the section of the arm does not modify the stiffness of the spring 100' which remains zero at least in part of the predetermined range, preferably within substantially the entire predetermined range. However, an increase in the variation of the section of the elastic arm makes it possible to reduce the moment as well as the stress, so that the section of the arm can be adapted according to the intended application for the pivoting member and the values desired for timing and stress.

On the other hand, according to another embodiment, as seen above, it is possible to obtain zero stiffness with a spring 100 having an elastic arm 102 of section varying by more than 60% with a center distance E varying from 96% to 200% of the developed length of said elastic arm 102 and its two pivoted ends, with a very reduced moment and stress, close to the moment and stress obtained with a similar spring 100' but with a center distance greater than 200% of the developed length of the elastic arm.

For more compactness, it is therefore possible to choose to replace a spring 100' with a spring 100 of appropriate configuration, having a smaller center distance by reducing the length of the elastic arm 102.

Very advantageously, the spring 100, 100' mounted according to the invention can be configured so as to adapt its stiffness to the function of the pivoting member with which it is associated.

According to certain embodiments, the pivoting member can be subjected to the action of a single spring 100, 100'.

According to other embodiments, the pivoting member can be subjected to the action of at least two springs 100, 100' respectively having zero or negative stiffness at least over the same predetermined range and arranged to generate a torque of pivoting on the pivoting member.

Advantageously, said pivoting member is and/or cooperates with, for example, a rocker, a hammer, a lever, a rake, a finger, a slider, a hook, a wheel such as an escape wheel, a regulating member or an energy source.

According to one embodiment, the second rotary element 106 of the spring 100, 100' is pivotally mounted on a frame of the timepiece mechanism.

Advantageously, a spring thus mounted in accordance with the invention, configured to present a negative stiffness in at least part of the predetermined range, and preferably in substantially all of the predetermined range, as described above, can be associated with a pivoting member which is and/or cooperates with a rocker, a rake or any other cam follower, resting on a cam of variable radius. Such a snail cam arms and disarms (partially) successively, one or more times per revolution of said cam follower. In the context of the present invention, the term "cam follower" means a member which cooperates with the periphery of a cam, typically to read information, without having any function of maintaining the cam in determined positions in normal operation. of the mechanism, unlike for example a jumper or a pawl cooperating with a toothed wheel to position it.

The spring mounted and configured in accordance with the invention to have a negative stiffness advantageously makes it possible to exert a constant torque on the cam of variable radius, the negative stiffness compensating for the variation in radius. This makes it possible to have a lower energy consumption and to limit the jolts.

Advantageously, a spring thus mounted in accordance with the invention, configured to have zero stiffness in at least part of the predetermined range, and preferably in substantially all of the predetermined range, as described above, can be associated with a pivoting member which is, for example, a rocker without support, a player, a hook, or a wheel such as an escapement wheel. Such a spring is less sensitive to its positioning than a spring of negative stiffness, which requires less effort on assembly precision.

In particular when the pivoting member cooperates with an escape wheel, it can be arranged to be subjected to the action of two springs mounted in accordance with the invention, configured to respectively have zero stiffness at least over the same predetermined range as described above, of slightly different thicknesses and having elastic arms of opposite directions, the subtraction of the two torques at zero stiffness generating on the pivoting member a very low constant pivoting torque. Zero stiffness is obtained according to the different configurations described above. Such a pivoting member is grafted onto the escape wheel to deliver a constant torque at each alternation.

When the pivoting member is a player, the spring of zero stiffness can be mounted directly on said player, so that the axis of the rocker of the player has a constant torque return spring. The gear opposite the slider will always see the same effort. This makes it possible to make the machining imperfections of the player and of said gear less noticeable.

A spring with zero stiffness can be mounted directly on a shaft without support, as a source of energy or as a return torque for a function. For example, when the pivoting member is a hook, the spring of zero stiffness can be mounted directly on the axis of said hook. Such a spring of zero stiffness in accordance with the invention has a very low torque which is perfectly suited to the pivoting torque corresponding to this application.

The figure 8 represents an embodiment of a watch mechanism comprising a pivoting member according to the invention in which the second rotary element 106 of the spring 100 is pivotally mounted on a frame 1a of said watch mechanism.

In this example, the pivoting member cooperates with a rocker resting on a cam of variable radius and the spring 100, with an elastic arm 102 of constant section, is configured to present a negative stiffness over the entire predetermined range, and the mechanism 1 is an instantaneous minute counter mechanism of a chronograph. Said mechanism 1 is mounted on the frame 1a, and comprises a rocker 2 pivoted in O and having a feeler 3 cooperating with a snail cam 4 mounted on, and driven by, the chronograph axis 5. This chronograph axis 5 carries its upper end the chronograph seconds indicator hand 6 and is integral in rotation with the chronograph wheel 7 and the heart for resetting the chronograph seconds 8. The rocker 2 is held in abutment against the periphery of the snail cam 4 by a rocker return spring 100 acting on the axis 10 of a finger 11, this finger 11 itself acting on the rocker 2. The cooperation between the finger 11 and the rocker 2 is of the bearing type. The finger 11 indeed interacts with the wall of a recess 12 of the rocker 2 in the manner of meshing, almost without friction. Rocker 2 and finger 11 thus rotate in opposite directions.

In this example, the finger 11 constitutes the pivoting member mounted on its pivot axis 10 and subjected to the action of its spring 100. The first rotary element 104 of the spring 100 is driven onto the axis 10 of the finger 11 and the second rotary element 106 is pivotally mounted on a pin 108 secured to frame 1a.

A hook 13 is pivoted at P on the free end of the rocker 2 and is subjected to the action of a hook return spring 14, mounted on the rocker 2, tending to apply the beak 15 of the hook 13 against the wolf tooth toothing of a 16 minute counter wheel.

The hook return spring 14 could be replaced by a spring configured in accordance with the invention to have zero stiffness over a predetermined range and whose first rotary element is mounted directly on the axis of the hook, the second rotary element being mounted on a pin secured to the frame 1a.

Spindle 17 of minute counter wheel 16 carries a chronograph minute indicator 18, such as a hand (as shown) or disc, displaying the chronograph minutes in cooperation with the chronograph dial. A chronograph minute reset core 19 is integral in rotation with the minute counter wheel 16. The minute counter wheel 16 is held in determined angular positions between its successive actuations by a jumper 20 on which acts a jumper return spring 21.

In the example illustrated, the snail cam 4 has a slot 22 in its end part, in accordance with the teaching of the patent application EP 2241944 , but it could have a more classic shape, without this slot 22.

The snail cam 4 has a variable radius between its lower part B and its upper part H, so that at each turn of rotation of the snail cam 4, the feeler 3 of the rocker 2 slides from the lower part B towards the part high H of cam 4. Rocker 2 rises gradually by rotating finger 11 in the opposite direction, spring 100 winding up as it goes.

Each minute, the feeler 3 and with it the entire rocker 2 falls from the upper part H to the lower part B of the snail cam 4 under the action of the spring 100. During this fall, the hook 13 advances one step the minute counter wheel 16 to instantly change the value indicated by the chronograph minute indicator 18. Then, during the progressive rewinding of the spring 100 via the rocker 2 again gradually raised by the snail cam 4, hook 13 passes from between the teeth of the minute counter wheel 16 in which it was during the fall at the previous inter-tooth against the action of its return spring 14, to again advance the minute counter wheel 16 by one step during the next fall of the seesaw 2.

The spring 100 is arranged to work in a predetermined range of winding angles, said spring being shaped according to the invention to present here a negative stiffness throughout the predetermined range in order to compensate for the lever arm effect of the cam snail. More specifically in relation to the spring 100 corresponding to the picture 3 , said spring 100 is of constant section, configured so that, at each revolution of the snail cam 4 against the return action of the elastic arm 102, the first rotary element 104 moves in a predetermined range of angular positions with respect to in its rest position, this range being included in the range of angular positions [θ2 _a , θ2 _b ] associated with the spring 100 in which the stiffness of the elastic arm 102 is negative. Preferably, said predetermined range is constituted by this range of angular positions [θ2 _a , θ2 _b ] where the stiffness is negative at each point. The length of the predetermined range is defined by the difference in radius between the upper part H and the lower part B of the cam 4, the position of the rocker 2 and that of the finger 11. In the example illustrated, it is 3 °, which leaves a wide choice of the winding angle at the time of assembly.

The first rotary element 104 is positioned angularly when it is mounted on the axis 10 of the finger 11 so that the spring 100 is armed with θ _arm degrees when the feeler 3 of the rocker 2 is on the lower part B of the snail cam 4, this value θ _arm being chosen within the predetermined range, and may for example be the lower limit of the aforementioned predetermined range, ie here 5°. It is also possible to choose a value θ _arm of 9° for example in order to be situated in a part of the predetermined range, for which the stiffness is even more negative.

Such a spring 100, with its two pivoted ends, makes it possible to fully compensate for the increase in the lever arm of the force applied to the cam 4 by the rocker 2 on one revolution of rotation of this cam during the movement of the rocker 2 from the lower part B to the upper part H, with an elastic arm 102 of constant section, without having to use an arm of variable section as in the publication WO 2020/016818 . This makes it possible to make constant the torque which it exerts indirectly on the cam 4 and thus, on the one hand, to improve the regularity of the oscillations of the regulator organ of the chronograph and therefore the precision of the measurement and, on the other hand, decrease energy consumption.

In addition, the torque obtained by the spring 100, with its elastic arm of constant section and its two pivoted ends, being lower than that obtained with the spring at one pivoted end and the other end embedded described in the publication WO 2020/016818 in the same instantaneous minute counter mechanism of a chronograph, the thickness of the elastic arm 102 could be increased from a 28 µm metallic glass blade to a 40 µm blade to obtain the same torque without exceeding the allowable stress of the material. Mounting the spring 100 in accordance with the invention is simplified, requiring only a single pin 108 and the windage is 9° against 18° for the spring at one end pivoted and the other end embedded.

The use of the intermediate finger 11 between the spring 100 and the rocker 2 makes it possible, by acting on the lever arms, to reduce the size of the mechanism 1 for a given restoring torque applied to the rocker 2. However, this finger 11 could be removed and spring 100 could act more directly on rocker 2, the pivoting member then being the rocker itself. For example, the first rotating element 104 could be mounted directly on the axis of rocker 2. Spring 100 could also form a single piece with rocker 2.

According to another embodiment of the invention, the second rotary element 106 of the spring 100, 100' is pivotally mounted on a movable element of the pivoting member, said movable element being arranged to be movable relatively with respect to the axis pivoting of said pivoting member.

With reference to the figure 9 , there is shown such a pivoting member 110, which in this example is more specifically subjected to the action of a plurality of springs 100, 100' respectively having zero or negative stiffness at least over the same predetermined range and arranged to generate a pivoting torque on said pivoting member 110.

In particular, the pivoting member 110 comprises a hub 112 secured to the pivot axis (not shown) of said pivoting member 110, and an annular rim 114 constituting the movable element of the pivoting member 114.

Each of the second rotating elements 106 of the springs 100, 100' is pivotally mounted on the rim 114, for example by means of pins or tenons 116 distributed around the periphery of the rim 114. The tenons 116 have the advantage of avoiding the out-of-plane displacement of the arms 102 of the springs 100, 100'. The pins or tenons 116 can be attached or form a single piece with the serge 114.

The first rotary elements 104 of the springs 100, 100' are all fixed at least in rotation to the pivot axis of the pivoting member 110.

In the variant represented, the first rotary elements 104 of the springs 100, 100' are advantageously arranged to form a single piece which constitutes the hub 112 of the pivoting member 110. Thus, the hub 112, formed by the union of the first rotary elements 104, and all of the arms 102 terminated by the second rotary elements 106 form a single one-piece piece. It is obvious that each arm 102 can be made independently of the hub, and then assembled to the hub 112. The hub 112 can be mounted integrally on the pivot axis, for example by driving or other equivalent means, or be made in one piece with the pivot axis of the pivoting member 110.

The pivoting member 110 is obtained by assembling on the rim 114 each of the second rotary elements 106 of the arms 102 carried by the hub 112 by means of its tenon 116.

The negative or zero stiffness of the springs 100, 100' as well as for example the thickness of the blades of the arms 102 of the pivoting member 110 are chosen according to the desired application of said pivoting member 110. For example, the springs 100, 100' can have zero or negative stiffness, and preferably zero stiffness, obtained according to the various possibilities described above, with thicker blades than for a similar pivoting member but with second embedded rotating elements, so as to obtain a large constant torque, allowing an application as a source of energy. Thinner blades make it possible to obtain a very low torque for applications of the regulating organ or very low energy source type.

Claims (19)

1. Timepiece mechanism (1) comprising a pivoting member mounted on a pivot spindle and subject to the action of at least one spring (100, 100') arranged to act within a predetermined range of winding angles, said spring (100, 100') comprising at least one elastic arm (102) having, at one of its ends, a first rotary element (104) fixed at least for conjoint rotation with the pivot spindle of the pivoting member, said spring (100, 100') having a zero or negative spring rate over at least one part of the predetermined range, characterised in that the elastic arm (102) has, at the other of its ends, a second rotary element (106) mounted in a pivoting manner.
2. Timepiece mechanism (1) as claimed in claim 1, characterised in that the spring rate of the spring (100, 100') is zero or negative over substantially the whole predetermined range.
3. Timepiece mechanism (1) as claimed in any one of the preceding claims, characterised in that the or each elastic arm (102) is sinuous in shape.
4. Timepiece mechanism (1) as claimed in any one of the preceding claims, characterised in that the geometric shape of the or of each elastic arm (102) is a Bezier curve or a succession of Bezier curves.
5. Timepiece mechanism (1) as claimed in any one of the preceding claims, characterised in that the centre-to-centre distance (E) between the first rotary element (104) and the second rotary element (106) is selected so that the spring (100) has a negative spring rate over said at least one part of the predetermined range, preferably over substantially the whole predetermined range.
6. Timepiece mechanism (1) as claimed in any one of the preceding claims, characterised in that the centre-to-centre distance varies between 96% and 200% of the extended length of the elastic arm (102).
7. Timepiece mechanism (1) as claimed in any one of claims 5 and 6, characterised in that the or each elastic arm (102) has a constant cross-section, the spring rate of the spring (100) being negative over said at least one part of the predetermined range, preferably over substantially the whole predetermined range.
8. Timepiece mechanism as claimed in any one of claims 5 and 6, characterised in that the or each elastic arm (102) has a variable cross-section, the variation in which is selected to render the spring rate of the spring (100) less negative, or even zero, over said at least one part of the predetermined range, preferably over substantially the whole predetermined range, as compared with an elastic arm of the same shape but a constant cross-section.
9. Timepiece mechanism as claimed in any one of claims 1 to 4, characterised in that the centre-to-centre distance (E) between the first rotary element (104) and the second rotary element (106) is selected so that the spring (100, 100') has a zero spring rate over said at least one part of the predetermined range, preferably over substantially the whole predetermined range.
10. Timepiece mechanism as claimed in claim 9, characterised in that the centre-to-centre distance (E) is greater than 200% and less than 300% of the extended length of the elastic arm (102).
11. Timepiece mechanism as claimed in any one of claims 9 and 10, characterised in that the or each elastic arm (102) has a constant cross-section, the spring rate of the spring (100') being zero over said at least one part of the predetermined range, preferably over substantially the whole predetermined range.
12. Timepiece mechanism as claimed in any one of the preceding claims, characterised in that the pivoting member is subject to the action of at least two springs (100, 100') having respectively a zero or negative spring rate at least over the same predetermined range and being arranged to generate a pivoting torque on the pivoting member.
13. Timepiece mechanism (1) as claimed in any one of the preceding claims, characterised in that the pivoting member is and/or cooperates with a lever arm (2), a hammer, a lever, a rack, a finger (11), a sliding gear, a hook, a wheel, a regulating member, a power source.
14. Timepiece mechanism as claimed in any one of the preceding claims, characterised in that the second rotary element (106) of the spring (100, 100') is pivotably mounted on a frame (1a) of the timepiece mechanism (1).
15. Timepiece mechanism (1) as claimed in any one of claims 13 to 14, characterised in that the pivoting member is and/or cooperates with a lever arm (2) bearing against a cam (4) of variable radius, the spring (100) having a negative spring rate.
16. Timepiece mechanism (1) as claimed in any one of claims 13 to 14, characterised in that the pivoting member is a non-bearing lever arm, a sliding gear, a hook, a wheel, the spring (100, 100') having a zero spring rate.
17. Timepiece mechanism as claimed in any one of claims 1 to 13, characterised in that the second rotary element (106) of the spring (100, 100') is pivotably mounted on a movable element of the pivoting member (110) arranged for relative movement with respect to the pivot spindle of said pivoting member (110).
18. Timepiece mechanism as claimed in claim 17, characterised in that the pivoting member (110) is subject to the action of a plurality of springs (100, 100') having respectively a zero or negative spring rate at least over the same predetermined range and being arranged to generate a pivoting torque on the pivoting member (110), in that the pivoting member (110) comprises a hub (112) fixedly attached to the pivot spindle and a felloe (114) forming the movable element of the pivoting member (110), and in that each of the second rotary elements (106) of the springs (100, 100') is pivotably mounted on said felloe (114), the first rotary elements (104) of the springs (100, 100') being arranged to form a single piece forming the hub (112) of the pivoting member (110).
19. Timepiece comprising a timepiece mechanism (1) as claimed in any one of claims 1 to 18.

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