Patent Publication Number: US-10324416-B2

Title: Method for maintaining and regulating the frequency of a timepiece resonator

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a divisional of and claims the benefit of priority under 35 U.S.C. § 120 from U.S. application Ser. No. 14,917,780, filed Mar. 9, 2016, which is a National Phase Application in the United States of International Patent Application PCT/EP2015/050588, filed Jan. 14, 2015, which claims the benefit of priority under 35 U.S.C. § 119 to European Patent Application No 14155425.3, filed Feb. 17, 2014. The entire disclosures of the above patent applications are hereby incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The invention concerns a method for maintaining and regulating the frequency of a timepiece resonator mechanism around its natural frequency during the operation of said resonator mechanism, wherein said method implements at least one regulator device, acting on said resonator mechanism with a periodic motion, wherein said periodic motion imposes a periodic modulation of the resonant frequency and/or the quality factor and/or the position of the point of rest of said resonator mechanism, with a regulation frequency of said regulator device which is comprised between 0.9 times and 1.1 times the value of an integer multiple of said natural frequency, said integer being greater than or equal to 2 and less than or equal to 10. 
     The invention concerns the field of time bases in mechanical watchmaking. 
     BACKGROUND OF THE INVENTION 
     The search for improvements in the performance of timepiece time bases is a constant preoccupation 
     A significant limitation on the chronometric performance of mechanical watches lies in the use of conventional impulse escapements, and no escapement solution has ever been able to avoid this type of interference. 
     EP Patent Application No 1843227A1 by the same Applicant discloses a coupled resonator including a first low frequency resonator, for example around a few hertz, and a second higher frequency resonator, for example around one kilohertz. The invention is characterized in that the first resonator and the second resonator include permanent mechanical coupling means, said coupling making it possible to stabilise the frequency in the event of external interference, for example in the event of shocks. 
     CH Patent Application No 615314A3 in the name of PATEK PHILIPPE SA discloses a movable assembly for regulating a timepiece movement, including an oscillating balance maintained mechanically by a balance spring, and a vibrating member magnetically coupled to a stationary member for synchronising the balance. The balance and the vibrating member are formed by the same single, movable, vibrating and simultaneously oscillating element. The vibration frequency of the vibrating member is an integer multiple of the oscillation frequency of the balance. 
     SUMMARY OF THE INVENTION 
     The invention proposes to manufacture a time base that is as accurate as possible. 
     To this end, the invention concerns a method for maintaining and regulating the frequency of a timepiece resonator mechanism around its natural frequency during the operation of said resonator mechanism, wherein said method implements at least one regulator device, acting on said resonator mechanism with a periodic motion, wherein said periodic motion imposes a periodic modulation of the resonant frequency and/or the quality factor and/or the position of the point of rest of said resonator mechanism, with a regulation frequency of said regulator device which is comprised between 0.9 times and 1.1 times the value of an integer multiple of said natural frequency, said integer being greater than or equal to 2 and less than or equal to 10, characterized in that said periodic motion imposes a periodic modulation of the quality factor of said resonator mechanism, by acting on the losses and/or damping and/or friction of said resonator mechanism. 
     The invention also concerns a method for maintaining and regulating the frequency of a timepiece resonator mechanism around its natural frequency during the operation of said resonator mechanism, wherein said method implements at least one regulator device, acting on said resonator mechanism with a periodic motion, wherein said periodic motion imposes a periodic modulation of the resonant frequency and/or the quality factor and/or the position of the point of rest of said resonator mechanism, with a regulation frequency of said regulator device which is comprised between 0.9 times and 1.1 times the value of an integer multiple of said natural frequency, said integer being greater than or equal to 2 and less than or equal to 10, characterized in that said method is applied to a said resonator mechanism including at least one sprung balance assembly comprising a balance, and in that the quality factor of said resonator mechanism is modified, under the action of said regulator device, by causing the oscillation of secondary sprung balances having a high residual unbalance mounted off-centre on said balance. 
     The invention also concerns a method for maintaining and regulating the frequency of a timepiece resonator mechanism around its natural frequency during the operation of said resonator mechanism, wherein said method implements at least one regulator device, acting on said resonator mechanism with a periodic motion, wherein said periodic motion imposes a periodic modulation of the resonant frequency and/or the quality factor and/or the position of the point of rest of said resonator mechanism, with a regulation frequency of said regulator device which is comprised between 0.9 times and 1.1 times the value of an integer multiple of said natural frequency, said integer being greater than or equal to 2 and less than or equal to 10, characterized in that said method is applied to a said resonator mechanism including at least one balance comprising a collet holding a torsion wire which forms an elastic return means of said resonator mechanism, and in that at least one said regulator device is made to act by causing a periodic variation in the tension of said torsion wire. 
     The invention also concerns a method for maintaining and regulating the frequency of a timepiece resonator mechanism around its natural frequency during the operation of said resonator mechanism, wherein said method implements at least one regulator device, acting on said resonator mechanism with a periodic motion, wherein said periodic motion imposes a periodic modulation of the resonant frequency and/or the quality factor and/or the position of the point of rest of said resonator mechanism, with a regulation frequency of said regulator device which is comprised between 0.9 times and 1.1 times the value of an integer multiple of said natural frequency, said integer being greater than or equal to 2 and less than or equal to 10, characterized in that said method is applied to a said resonator mechanism including at least one tuning fork and in that at least one said regulator device is made to act on the attachment of said tuning fork, and/or on a mobile element exerting pressure on at least one arm of said tuning fork. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other features and advantages of the invention will appear upon reading the following detailed description, made with reference to the annexed drawings, partially and schematically showing parametric oscillators corresponding to various implementation modes and variants of the invention, and wherein: 
         FIG. 1  shows, a schematic, partial plan view of a parametric resonator mechanism regulated according to the invention, comprising a timepiece sprung balance, forming a resonator, and whose inertia and/or quality factor is modulated by weights arranged radially or tangentially via springs and excited at a frequency double the frequency of the sprung balance resonator incorporating the balance, whose balance spring is not shown; this balance carries on its rim elements that vibrate radially or tangentially during the pivoting motion of the balance. 
         FIG. 2  shows a schematic, partial plan view of a balance comprising four radial springs connected to the rim and carrying weights, and subjected to regulating excitation at a frequency double the frequency of the sprung balance resonator incorporating the balance, whose balance spring is not shown. 
         FIG. 3  shows a schematic, partial plan view of a balance carrying loosely mounted built-in sprung balances each having a high unbalance. 
         FIG. 4  shows a schematic, partial plan view of a balance suspended by two diametrically opposite radial springs, the trajectory of the centre of gravity of the balance corresponding to the common direction of the two springs. 
         FIGS. 5A, 5B, 5C  show schematic, partial plan views of a balance carrying on its rim elements that pivot during the pivoting motion of the balance. 
         FIG. 6  shows a schematic, partial plan view of a balance in proximity to which an aerodynamic brake pad is movable at a frequency double that of the sprung balance resonator incorporating the balance, whose balance spring is not shown. 
         FIG. 7  shows a similar balance to that of  FIG. 3  with two sprung balances with high unbalances, loosely mounted on the same diameter and in a position of alignment of the unbalances (at the point of rest), which are different from those of  FIG. 3  and either in in-phase or anti-phase vibration. 
         FIG. 8  shows a schematic, partial plan view of a tuning fork, one arm of which is in contact with a friction pad excited at double the frequency of the frequency of the tuning fork resonator. 
         FIG. 9  illustrates a resonator mechanism comprising a balance including a collet holding a torsion wire, wherein a resonator device controls a periodic variation in tension with a frequency double that of the resonator comprising the balance and torsion wire. 
         FIG. 10  shows a schematic view of a regulated parametric resonator mechanism according to the invention, comprising a timepiece sprung balance, wherein the outer coil of the balance spring is pinned to a balance spring stud to which a regulator device imparts a periodic motion, said stud being movable in a translational, pivoting and tilting motion in space to twist the balance spring if necessary. 
         FIG. 11  shows a schematic view of a balance spring provided with an index mechanism with pins, with a crank rod system for actuating a continuous motion of the index, for a continuous variation in the active length of the balance spring. 
         FIG. 12  shows a schematic view of a balance spring on which a cam rests, for a continuous variation in the active length of the balance spring and/or in the position of the point of attachment and/or in the geometry of the balance spring. This Figure is a simplified representation wherein a single cam rests on the balance spring on only one side; it is evidently possible to combine two cams arranged to clamp the balance spring on both sides. 
         FIG. 13  shows a partial, schematic view of the balance spring of a sprung-balance assembly, with an additional coil fixed to the balance-spring and locally lining the outer terminal curve of the balance spring, and a regulator device actuating one end of this additional coil. 
         FIG. 14  illustrates a balance spring with, in proximity to its terminal curve, another coil which is held at a first end by a support operated by a regulator device, and which is free at a second end arranged to periodically come into contact with the terminal curve under the action of the regulator device on this support. 
         FIG. 15  illustrates the regulation obtained with a resonator of the type shown in  FIG. 2 . 
         FIGS. 16A and 16B  illustrate a modification of the centre of gravity of the resonator, with a sprung balance resonator comprising a balance carrying substantially radial springs attached to the rim and carrying oscillating inertia blocks, some towards the interior and some towards the exterior of the rim. 
         FIGS. 17A and 17B  illustrate, in a similar manner to  FIG. 5 , another balance system having wings with a flexible pivot making it possible to modify aerodynamic losses and inertia. 
         FIGS. 18A to 18D  illustrate modulation of the centre of gravity, based on a resonator like that of  FIG. 3  or  FIG. 7 , comprising built-in sprung balances. 
         FIG. 19  illustrates an example embodiment of a parametric oscillator with a balance collet carrying a silicon spring bearing a peripheral inertia block weighted with a gold layer, the spring-inertia block assembly oscillating at a regulation frequency ωR. 
         FIG. 20  shows a balance comprising spring-inertia blocks assemblies similar to that of  FIG. 19 . 
         FIG. 21  shows a tuning fork one branch of which carries a loosely pivotally mounted secondary sprung balance. 
         FIG. 22  shows a tuning fork one branch of which carries a spring-inertia block assembly mounted for free vibration. 
         FIG. 23  shows a block diagram of a watch including a mechanical movement with a resonator mechanism regulated according to the invention by a double frequency regulator device. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     It is an object of the invention to produce a time base for making a timepiece, in particular a mechanical timepiece, especially a mechanical watch, as accurate as possible. 
     One method of achieving this consists in associating different resonators, either directly or via the escapement. 
     To overcome the factor of instability linked to an escapement mechanism, a parametric resonator system makes it possible to reduce the influence of the escapement mechanism and thereby render the watch more accurate. 
     A parametric oscillator uses, for maintaining oscillations, a parametric actuation which consists in varying at least one of the parameters of the oscillator with a regulation frequency ωR. 
     By convention and in order to differentiate clearly between them, “regulator” 2 refers here to the oscillator used for maintaining and regulating the frequency of the other maintained system, which is referred to here as “the resonator” 1. 
     The Lagrangian L of a parametric resonator of dimension 1 is:
 
 L=T−V= ½ I ( t ) {dot over (x)}   2 −½ k ( t )[ x−x   0 ( t )] 2  
 
where T is the kinetic energy and V the potential energy, and the inertia I(t), stiffness k (t) and rest position x 0 (t) of said resonator are a periodic function of time, x is the generalized coordinate of the resonator.
 
     The forced and damped parametric resonator equation is obtained via the Lagrange equation for the Lagrangian L by adding a forcing function f(t) and a Langevin force taking account of the dissipative mechanisms: 
                     ∂   2     ⁢   x         ∂   2     ⁢   t       +       γ   ⁡     (   t   )       ⁢       ∂   x       ∂   t         +         ω   2     ⁡     (   t   )       ⁡     [     x   -       x   0     ⁡     (   t   )         ]         =     f   ⁡     (   t   )             
where the coefficient of the first order derivative at x is:
 
γ( t )=[β( t )+ İ ( t )]/ I ( t ),
 
β(t)&gt;0 being the terms describing losses,
 
and where the coefficient of zero order term depends on the resonator frequency ω(t)=√{square root over (k(t)/I(t))}.
 
     The function f(t) takes the value 0 in the case of a non-forced oscillator. This function f(t) may also be a periodic function, or be representative of a Dirac impulse. 
     The invention consists in varying, via the action of a maintenance oscillator called a regulator, one and/or the other or all of the terms β(t), k(t), I(t), x 0 (t), with a regulation frequency ωR that is comprised between 0.9 times and 1.1 times the value of an integer multiple, (particularly two) of the natural frequency ω0 of the oscillator system to be regulated. 
     To understand this phenomenon, it can be likened to the example of a pendulum whose length is varied. The damped oscillator equation is as follows: 
                     ∂   2     ⁢   x         ∂   2     ⁢   t       +       β   ⁡     (   t   )       ⁢       ∂   x       ∂   t         +         ω   2     ⁡     (   t   )       ⁡     [     x   -       x   0     ⁡     (   t   )         ]         =     f   ⁡     (   t   )             
where the first order term at x is the loss term, and where the zero order term is the frequency term of the resonator, and where x 0  (t) corresponds to the position of rest of the resonator.
 
     The function f(t) takes the value 0 in the case of a non-forced oscillator. This function f(t) may also be a periodic function, or be representative of a Dirac impulse. 
     The invention consists in varying, via the action of a maintenance oscillator or regulator  2 , one and/or the other or all of the terms β(t), k(t), I(t), x 0 (t), with a regulation frequency ωR that is comprised between 0.9 times and 1.1 times the value of an integer multiple, this integer being greater than or equal to 2, of the natural frequency ω0 of the oscillator system to be regulated, in this case resonator  1 . In a particular application, the regulation frequency ωR is comprised between 1.8 times and 2.2 times the natural frequency ω0, and more particularly, regulation frequency ωR is double the natural frequency ω0. 
     Preferably, one or several terms, or all the terms β(t), k(t), I(t), x 0 (t) vary with a regulation frequency ωR thus defined, and which is preferably an integer multiple (particularly two) of the natural frequency ω0 of the resonator system  1  to be regulated. 
     Generally, in addition to modulating the parametric terms, the oscillator used for maintenance or regulation therefore introduces a non-parametric maintenance term f(t), whose amplitude is negligible once the parametric regime is attained [W. B. Case, The pumping of a swing from the standing position, Am. J. Phys. 64, 215 (1996)]. 
     In a variant, the forcing term f(t) may be introduced by a second maintenance mechanism. 
     The maintenance oscillator or regulator  2  also makes it possible to vary, if it is not zero, the term f(t). 
     In the example of the unforced damped oscillator, and in the case where x 0  is a constant, the parameters of the equation are summarized by the frequency term ω and the loss term β, in particular losses through mechanical or aerodynamic or internal or other friction. 
     The oscillator quality factor is defined by Q=ω/β. 
     To better understand the phenomenon, it can be likened to the example of a pendulum whose length is varied. In such case, 
               ω   2     =     g   L           
where L is the length of the pendulum and g the attraction of gravity.
 
     In this particular example, if length L is periodically modulated in time with a frequency 2ω and sufficient modulation amplitude δL (δL/L&gt;2β/ω), the system oscillates at frequency ω without damping.
     [D. Rugar and P. Grutter,  Mechanical parametric amplification and thermomechanical noise squeezing , PRL 67, 699 (1991), A. H. Nayfeh and D. T. Mook,  Nonlinear Oscillations , Wiley-Interscience, (1977)].   

     The zero order term may also take the form ω 2 (A, t), where A is the oscillation amplitude. 
     Thus, the invention concerns a method and a system for maintaining and regulating the frequency of a timepiece resonator mechanism  1  around its natural frequency ω0. According to the method, there is implemented at least one regulator device  2  acting on resonator mechanism  1  with a periodic motion. 
     More specifically, there is implemented at least one regulator device  2  imparting a periodic motion to at least one internal component of resonator mechanism  1 , or to an external component exerting an influence on such an internal component such as an aerodynamic influence or braking, or modulating a magnetic or electrostatic or electromagnetic field or similar exerting a “return” force (used in the broad sense here of attraction or repulsion) on such an internal component of resonator  1 . 
     This periodic motion imposes at least a periodic modulation of the resonant frequency and/or quality factor and/or position of the point of rest of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     With regard to the quality factor, the watch designer will seek to obtain the highest possible value. The quality factor depends on the architecture of the resonator, and also on all the operating parameters of the latter, particularly the natural frequency, and it further depends on the operating environment of the resonator. A first design option may consist in setting the quality factor at a constant value, once this value has been modelled and checked by testing and deemed sufficient. Although this first option appears reassuring, it is ill-suited to the alternate operation of resonators used in watchmaking, and seems especially unrealistic with regard to the areas of reversal of direction or turnaround. 
     Thus the invention selects a second option that takes account of these phenomena related to alternate operation. According the invention, the periodic motion imposes a periodic modulation of the quality factor of resonator mechanism  1  by acting on the losses and/or the damping and/or the friction of resonator mechanism  1 . 
     It is understood that, particularly in the case of a sprung-balance type resonator, although it is impossible to act on the balance itself, this does not preclude acting on the environment surrounding the latter, or on the pivoting position (especially in the case of virtual pivots) to create a modulation of the aerodynamic braking torque and thereby the quality factor. 
     In a particular implementation, the periodic motion imposes a periodic quality factor modulation of resonator mechanism  1 , by acting on the aerodynamic losses of resonator mechanism  1 , through deformation of resonator mechanism  1  and/or through modification of the environment around said resonator mechanism  1 . 
     It is understood that, as regards aerodynamic losses, the situation of a resonator that includes elements making return movements and oscillating about a median position, is completely different from the case of a speed regulator, which generally operates in only one direction. Further, the invention is concerned here with regulating a frequency, and not a speed, which requires a regulating precision of a completely different order of magnitude: although a precision of around 10 −2  is, for example, sufficient for a timepiece striking work regulator having inertia-blocks and/or brake fins, it is not suitable for a resonator intended to ensure that the rate of a movement is constant, and in this latter case, precision or around 10 −5  should be targeted to obtain a daily rate deviation on the order of a second. 
     In a specific implementation, the periodic motion imposes a periodic quality factor modulation of resonator mechanism  1  by modulating the internal damping of the elastic return means comprised in resonator mechanism  1 . 
     In a specific implementation, the periodic motion imposes a periodic quality factor modulation of resonator mechanism  1  by modulating the mechanical friction inside resonator mechanism  1 . 
     In a first specific implementation mode of the invention, this periodic motion imposes a periodic modulation of at least the resonant frequency of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     In a second specific implementation mode of the invention, this periodic motion imposes a periodic modulation of at least the quality factor of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     In a third specific implementation mode of the invention, this periodic motion imposes a periodic modulation of at least the point of rest of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     Naturally, other specific implementation modes of the invention permit a mixture of the first, second and third modes. 
     Thus, in a fourth specific implementation mode of the invention combining the first and second modes, this periodic motion imposes a periodic modulation of at least the resonant frequency and quality factor of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     In a fifth specific implementation mode of the invention combining the second and third modes, this periodic motion imposes a periodic modulation of at least the quality factor and point of rest of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     In a sixth specific implementation mode of the invention combining the first and third modes, this periodic motion imposes a periodic modulation of at least the resonant frequency and point of rest of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     In a seventh specific implementation mode of the invention combining the first, second and third modes, this periodic motion imposes a periodic modulation of at least the resonant frequency, quality factor and point of rest of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of natural frequency ω0, this integer being greater than or equal to 2 and less than or equal to 10. 
     In a specific implementation of these various implementation modes of the method, all the modulations are performed either with the same frequency ωR or with frequencies ωR that are multiples of each other. 
     The first three main implementation modes of the invention will be set out in detail below. 
     In a specific implementation of the first mode of the invention, the periodic motion imposes a periodic modulation of the resonant frequency of resonator mechanism  1  by acting on the stiffness and/or the inertia of resonator mechanism  1 . More specifically, the periodic motion imposes a periodic modulation of the resonant frequency of resonator mechanism  1  by imposing both a modulation of the stiffness of resonator mechanism  1  and a modulation of the inertia of resonator mechanism  1 . 
     Different advantageous variants permit different means of achieving the invention in this first implementation mode. 
     In a first variant of the first implementation mode, this periodic motion imposes a periodic modulation of the resonator frequency of resonator mechanism  1 , by imposing a modulation of the inertia of resonator mechanism  1  through modulation of the mass of resonator mechanism  1 , and/or through modulation of the shape of resonator mechanism  1  (as seen in  FIG. 1, 2 or 3 ), and/or through modulation of the position of the centre of gravity of resonator mechanism  1  as seen, for example, in the sketch of  FIG. 4 . 
     Still in this first variant of the first mode,  FIGS. 16A and 16B  also illustrate a modification of the centre of gravity of the resonator, and of its inertia. 
     Still in this first variant of the first mode,  FIGS. 18A to 18D  illustrate a modulation of the centre of gravity, based on a resonator like that of  FIG. 3  or of  FIG. 7 . A system of this type includes secondary in-built sprung balances  260 . These secondary sprung balances  260  are advantageously replaced by systems with no arbors, i.e. with flexible bearings, which is easier to achieve given that their amplitude of oscillation is not necessarily high. In that case, only the inertia of the main sprung balance is modified. Depending on the angular position of the unbalances of the small sprung balances, it is therefore possible to create a system whose centre of gravity is modulated. 
     This modulation of the centre of gravity position is preferably a dynamic modulation acting on one or more of the components of resonator  1 . Inertia modulation can be achieved through shape modulation, through a change in mass, or through a change in the centre of gravity of the resonator relative to its centre of rotation, for example with the use of a flexible balance. It is also possible to use built-in resonators, with a dissymmetry having a suitable phase ratio, as seen in  FIG. 7 , where the unbalances are either in phase or in anti-phase vibration. 
     In a second variant of the first mode, this periodic motion imposes a periodic modulation of the resonant frequency of resonator mechanism  1 , by imposing a modulation of the stiffness of an elastic return means comprised in resonator mechanism  1  or a modulation of a return force exerted by a magnetic or electrostatic or electromagnetic field within resonator mechanism  1 . More specifically, in this second variant, the periodic motion imposes a periodic modulation of the resonant frequency of resonator mechanism  1 , by imposing a modulation of the active length of a spring comprised in resonator mechanism  1  (as seen in  FIGS. 11 and 12 ), or a modulation of the cross-section of a spring comprised in resonator mechanism  1  (as seen in  FIGS. 13 and 14 ), or a modulation of the modulus of elasticity of a return means comprised in resonator mechanism  1 , or a modulation of the shape of a return means comprised in resonator mechanism  1 . The modulation of the modulus of elasticity of a component of resonator  1  can be obtained by implementing a piezoelectric system, an electrical field (electrodes), by periodic localised heating, by the action of a magnetic field subjecting specific alloys to expansion, by optomechanical resonant systems, by torsion or by twisting, in particular for shape memory materials. 
     In a third variant of the first mode resulting from a combination with the third implementation mode of the invention, the periodic motion imposes a periodic modulation of the resonant frequency of resonator mechanism  1  by imposing both a modulation of the stiffness of resonator mechanism  1  and a modulation of the position of the point of rest of resonator mechanism  1 . 
     To act on stiffness, the phenomena of magnetostriction can advantageously be used, periodically modifying stiffness by subjecting a component, made of a suitable material, of resonator  1  to a magnetic field (internal magnetisation and/or external field), or to shocks. 
     To act on the modulus of elasticity, it is also possible to use the phenomenon of magnetostriction, but also to employ a periodic temperature rise, shape memory components, the piezoelectric effect, or non-linear regimes achieved through the use of specific stresses. 
     In a specific implementation of the second implementation mode of the invention, this periodic motion imposes a periodic modulation of the quality factor of resonator mechanism  1  by acting on the losses and/or the damping and/or the friction of resonator mechanism  1 . Action may be taken in different ways: 
     in a first variant of this second mode, the periodic motion imposes a periodic modulation of the quality factor of resonator mechanism  1 , by acting on the aerodynamic losses of resonator mechanism  1 , through deformation of resonator mechanism  1  (as seen in  FIG. 5  on a balance provided with pivoting wings, or in  FIG. 17 ), and/or through modification of the environment around resonator mechanism  1  (as seen in  FIG. 6  where a pad moved by a periodic motion modifies the flow of air around the balance); 
     in a second variant of this second mode, the periodic motion imposes a periodic modulation of the quality factor of resonator mechanism  1  by modulating the internal damping of the elastic return means comprised in resonator mechanism  1 , for example with a flow of liquid in a hollow body (for example the balance spring or balance of a sprung balance assembly), or under the effect of a torsion periodically applied to a balance spring or similar, resulting in modifications both in the stiffness and the damping of the resonator containing the spring. In a specific case, internal losses can be modified, without modifying stiffness: two springs replace a single spring with overall equivalent stiffness, the internal losses are then higher; two springs can, in particular, be placed in series, or in parallel according to the case, and one of the springs may be prestressed. Another means of modifying losses while maintaining the same stiffness is to use, on a spring, either heat compensation by doping of silicon, or a thermo-elastic effect with a heat transfer between two different parts of the coil of a spring. 
     in a third variant of this second mode, the periodic motion imposes a periodic modulation of the quality factor of resonator mechanism  1 , by modulating mechanical friction within resonator mechanism  1  with a similar effect to a virtual increase in gravity.  FIG. 8  shows an example where a friction strip cooperates, in a modulated manner, with a tuning fork arm. 
     In a specific implementation of the third mode of the invention, this periodic motion imposes a periodic modulation of the point of rest of resonator mechanism  1 , by modulating the position of attachment of resonator mechanism  1  and/or by modulating the equilibrium between the return forces acting on resonator mechanism  1 . Modulation of the position of attachment of resonator mechanism  1  can be performed on at least one point of attachment of resonator  1 . For example, in a resonator  1  with a sprung balance  3 , it is possible to act on the balance spring stud and/or on the collet  7  for attaching balance spring  4  on at least one pivot point by action on the pivot shock absorber elements. Some functions of the movement can be used for this purpose, for example in a conventional escapement mechanism, the percussion of the lever on springs or suchlike. 
     more specifically in a first variant of this third mode, the periodic motion imposes a periodic modulation of the point of rest of resonator mechanism  1 , by modulating the equilibrium between the return forces acting on resonator mechanism  1  generated by mechanical elastic return means and/or magnetic return means and/or electrostatic return means. To modulate this equilibrium, the simplest solution is to subject the resonator to several return forces of different origin; it is sufficient to modulate at least one of the return forces in time, in intensity and/or direction. These forces are not necessarily all of the same nature, some may be mechanical (springs) and others connected to the application of a field. A specific example is the application to a sprung balance  3  provided with two springs, modulation of the position of only one of the balance spring studs is sufficient to modulate the equilibrium. Twisting a balance spring, at angle Ψ of  FIG. 10  is a good means of modifying the balance of forces applied to resonator  1 , and thus to modulate their equilibrium. It is noted in this regard that the six degrees of freedom can be applied to the stud, the Figure showing a specific simplified application, and in particular rotation about axis Z may be advantageous: 
     in a second variant of this third mode, modulation of the position of the point of rest is combined with stiffness modulation according to the first mode: indeed, often, if the equilibrium of forces is modified, the overall stiffness is also modified. The action of modulating the point of rest is thus combined with an action of modulating stiffness. 
     Preferably, when the component whose stiffness can be modulated is formed of several elements, and modulation is performed on at least one of such elements. 
     In another implementation mode of the invention, the periodic motion imposes a periodic modulation of the quality factor of resonator mechanism  1 , and according to the invention, the periodic motion is imparted at the same regulation frequency ωR both to a component of resonator mechanism  1  and to a loss generation mechanism on at least one component of resonator mechanism  1 . 
     In yet another implementation mode of the invention, compatible with each of the various modes presented above, regulator mechanism  2  imposes a periodic modification of the frequency of resonator mechanism  1  with a higher relative amplitude than the inverse quality factor of resonator mechanism  1 . 
     In an easy-to-implement mode of the invention, regulator device  2  acts on at least one attachment of resonator mechanism  1 . 
     As regards frequency ωR, although it is possible to imagine that the periodic modulation of the various characteristics: resonant frequency, quality factor, point of rest, occurs in each case at different multiples of frequency ω0 (for example, stiffness modulation with double the basic frequency and quality factor modulation at quadruple the basic frequency), this does not provide any particular advantage, because the maximum effect and stability of parametric amplification is obtained when the frequency is double the basic frequency. Further, it is not easy to envisage a system wherein each characteristic is modulated differently, except if there is a plurality of regulators  2 , which would make the system complex. Therefore, modulation of all the parameters preferably occurs at the same frequency ωR. 
     Different applications of the invention are possible. 
     In a conventional application, the invention is applied to a resonator mechanism  1  comprising at least one elastic return means  40 , and at least one such regulator device  2  is made to act by causing a periodic variation in the frequency of resonator mechanism  1  and/or in the quality factor of resonator mechanism  1 . 
     In a normal watchmaking application, the invention is applied to a resonator mechanism  1  comprising at least one sprung balance assembly  3  including a balance  26  with at least one spring  4  as the elastic return means  40 . More specifically, as seen in  FIG. 3 , the inertia and quality factor of resonator mechanism  1  are modified by regulator device  2  setting in motion secondary sprung balances  260  having a high residual unbalance  261  eccentrically mounted on balance  26  and oscillating according to the speed of resonator  1 . 
     In another variant of the application to a sprung balance assembly  3  comprising a balance  26  with at least one spring  4  as elastic return means  40 , the quality factor of resonator mechanism  1  is modified through modification of the air friction of balance  26 , generated by a local modification of the geometry of balance  26 , under the action of regulator device  2 , the device is on balance  26  here. For example, as seen in  FIG. 5 , balance  26  may carry modulation wings (to be differentiated from the brake fins that a simple speed regulator may include, as explained above), particularly modulation fins with the profile of aircraft wings hinged to the periphery of balance  26 , particularly by flexible guide members or similar, these fins being preferably reversible and thus capable of tilting fully in the direction of motion. Preferably, these flaps are held by flexible strips. At intermediate speed, the flaps are close to the rim, in  FIG. 5A . At maximum speed in  FIG. 5B , an aerodynamic effect lifts them up (aircraft wing effect), when the flaps change to the other side as seen in  FIG. 5C . In this example, the inertia is modified with a frequency that is 4 times the natural frequency of the sprung balance resonator. Air friction of the aerobraking type is thus obtained, with a flap at the periphery of the balance having an influence on the quality factor and/or inertia. This flap may be loosely pivotally mounted or pivotally mounted and returned by a balance spring or flexible guide member or similar. One variant may consists of a balance rim of variable geometry. Thus, in such a variant, the quality factor of resonator mechanism  1  is modified through modification of the air friction of balance  26  generated by a local modification of the geometry of balance  26  under the action of regulator device  2 . It will be noted that regulator  2  can move independently of the speed of resonator  1 . A specific variant consists in combining this variant with the preceding variant where eccentric sprung balances  260  are set in oscillation. 
     In another variant where the environment is acted upon rather than the actual balance, the quality factor of resonator mechanism  1  is modified through a modification of the air friction of balance  26  generated by a local modification of the geometry of the environment around balance  26  under the action of regulator device  2  as seen in  FIG. 6  where a pad moved by a periodic motion modifies the flow of air around the balance. 
     The invention is therefore also applicable to resonator mechanisms  1  with no mechanical return means. Thus, in specific applications (not shown), the periodic motion of regulator mechanism  2  imposes modulation of the frequency and/or quality factor and/or position of the point of rest of resonator mechanism  1  via a remote electrical or magnetic or electromagnetic force. 
     Another variant application of the invention, seen in  FIG. 9 , concerns a resonator mechanism  1  comprising at least one balance  26  comprising a collet  7  holding a torsion wire  46  which forms elastic return means  40  where at least one regulator device  2  is made to act by causing a periodic variation in the tension of torsion wire  46 . In a similar variant, the torsion wire is replaced by a flexible guide member. 
     Another variant application of the invention, seen in  FIG. 8 , concerns a resonator mechanism  1  comprising at least one tuning fork, wherein at least one regulator device  2  is made to act by causing a periodic variation in the frequency of resonator mechanism  1  and/or in the stiffness of at least one tuning fork arm defining the quality factor of resonator mechanism  1 . More specifically, regulator device  2  can act on the attachment of the tuning fork, and/or on a wheel set exerting pressure on at least one arm of the tuning fork. It will be noted that this type of tuning fork is not necessarily in the conventional shape of a fork, and may take, among other possible shapes, a heart-shape or H-shape. 
     In a variant, the invention is also applicable to a resonator with a single arm, or to a resonator operating in torsion, or in elongation. 
     Advantageously, the invention makes it possible to use regulator device  2  to start and/or to maintain resonator mechanism  1 . Preferably, this regulator device  2  cooperates with a start and/or maintenance mechanism of resonator mechanism  1  to increase the oscillation amplitude of resonator mechanism  1 . 
     The invention advantageously makes co-maintenance possible: standard low-power maintenance, combined with the parametric method for maintaining oscillation. Regulator device  2  is used for the continuous maintenance of resonator mechanism  1 , alone or in cooperation with a start and/or impulse maintenance mechanism. 
     For example, such maintenance can be obtained with a sprung balance system, comprising a balance including on its rim springs carrying oscillating inertia blocks, according to the configuration of  FIG. 2 . A lever escapement or similar then makes it possible to excite the oscillations of the balance and the small inertia blocks. The springs and inertia blocks oscillate at a frequency, here double the natural frequency of the sprung balance. The inertia blocks oscillate by inertial coupling. The parametric effect occurs, because the inertia of the balance varies at a frequency double that of the sprung balance.  FIG. 15  illustrates regulation obtained with a resonator of this type. It is to be noted that in this case, the aerodynamic losses are also modified. 
     Another example consists in using a detent escapement, which also ensures the counting function, in cooperation with a regulator mechanism  2  acting on the stiffness of balance spring  4  (with pins that move). 
     The invention also concerns a timepiece movement  10  including at least one such resonator mechanism  1 . According to the invention, this movement  10  comprises at least one such regulator device  2 , arranged to act on resonator mechanism  1 , by imposing a periodic modulation of one or more physical characteristics of resonator mechanism  1 : resonant frequency and/or quality factor and/or point of rest, with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of a multiple integer of the natural frequency ω0 of resonator mechanism  1 , said integer being greater than or equal to 2 and less than or equal to 10. 
     In a variant, this regulator device  2  is arranged to act on resonator mechanism  1  by directly imparting a periodic motion thereto with regulation frequency ωR. 
     In a variant, this regulator device  2  acts on at least one attachment of resonator mechanism  1  and/or the frequency, particularly on stiffness and/or inertia, of resonator mechanism, and/or on the quality factor of resonator mechanism  1 , and/or on the losses or friction of resonator mechanism  1 . 
     In a variant, regulator device  2  acts on resonator mechanism  1  by imparting the periodic motion to a component of resonator mechanism  1  and/or to a loss generation mechanism on at least one component of resonator mechanism  1 . 
     The invention also concerns a timepiece  30  including at least one such timepiece movement  10 . 
     The few parametric oscillator examples illustrated here are non-limiting. Some, like those of  FIGS. 15 to 18 , may be inserted straight into existing movements, replacing standard components such as balances, which is an advantages, since the design and manufacture of the mechanical components of the movement concerned are not called into question. 
     One of the advantages of these systems is that it is possible to operate a sprung balance at a high frequency, despite the inherent decrease in the efficiency of the escapement. 
     The easiest principle to implement consists in making one part of the balance oscillate. These oscillations (at a frequency multiple n≥2 of the natural frequency of the sprung balance) either modify the inertia or the centre of gravity or aerodynamic losses. 
     The Figures illustrate simple, non-limiting examples of embodiments of the invention. Some may be very simply implemented, for example by substituting a particular balance for a standard balance. 
     These examples show that the constituents of regulator  2  may be built into some components of resonator  1 . In numerous cases, the invention does not require a secondary excitation circuit, it is the dimensions of the regulator components which enable it to oscillate at a defined frequency ωR in its specific relation to the natural frequency ω0 of resonator  1 . 
       FIG. 1  shows a parametric resonator mechanism  1  regulated according to the invention, comprising a sprung balance  3  with a balance  26  and a balance spring (not shown), forming a resonator. The inertia and/or the quality factor is modulated by inertia blocks  71  arranged radially or tangentially via springs  72 , the latter are fixed at points of attachment  73  to the structure of balance  26 , in particular to its rim. These inertia block-spring assemblies are excited at a frequency double the frequency ω0 of resonator  1  with sprung balance  3 . Resonator  1  carries here the elements of regulator  2  formed by the inertia block-spring assemblies, which vibrate radially and/or tangentially during the pivoting motion of balance  26 . Some may, in particular, be guided in a path  74  comprised in balance  26 . The radial vibration of the inertia blocks affects the inertia and friction term, the tangential vibration affects the dynamic inertia. Balance  26  also carries here arms  85  carrying vibrating strips  84  which oscillate mainly radially. For regulator  2  to be highly efficient, springs  72  are preferably of large volume in comparison to the balance, their radial footprint is, for example, on the order of the radius of the rim of the actual balance, or greater with for example a radial footprint of spring  72  and inertia block  71  equivalent to quadruple the radius of a collet  7 . 
     Preferably, and this is true for all the examples, all the vibrating assemblies comprised in the regulator oscillate at the same frequency ωR defined by the invention. It is also acceptable for some of them to oscillate at frequency that is an integer multiple of frequency ωR defined by the invention relative to natural frequency ω0. 
       FIG. 2  also shows a resonator  1  with a sprung balance  3 , whose balance  26  carries the elements of regulator  2 : four radial springs  72  attached to the rim at points  73  and carrying inertia blocks  71  and subjected to regulation excitation at a frequency double the frequency ω0 of resonator  1 .  FIG. 15  illustrates regulation obtained with a resonator of this type. 
       FIG. 3  shows a very easy solution for replacing an existing balance, with a resonator  1  similar to those of  FIGS. 1 and 2 , comprising a balance  26  carrying loosely pivotally mounted secondary in-built sprung balances  260  each having a high unbalance  261 . There are two embodiments: 
     either the secondary sprung balances  260  are entirely free to rotate, with no amplitude limitation, for example with conventional mechanical pivoting; 
     or the secondary sprung balances  260  are limited in amplitude, and are, for example, made in one-piece with balance  26  in a silicon or similar embodiment, with a flexible pivot and thus limited amplitude. 
       FIG. 4  shows a similar resonator  1  to those of the preceding Figures, with a balance  26  suspended from one or more structures  50  by two diametrically opposite, substantially radial springs  51 , the trajectory of the centre of gravity of balance  26  corresponding to the common direction of these two springs  51 . In a variant, the balance staff is held by springs. In another variant, balance  26  is not pivoted with a conventional arbor, but only with flexible bearing members; the virtual balance staff is then defined by the direction of the springs. The Figure is deliberately simplified with only two springs; it is naturally possible to envisage suspending balance  26  from, three or more springs  51 . A one-piece embodiment of this entire assembly is possible, within the limits of the desired pivoting amplitude of balance  26 . It is clear that a multi-level embodiment is possible, to distribute the functional components on different planes. 
       FIGS. 5A, 5B, 5C  show another similar resonator  1  incorporating a balance  26  carrying on its rim flaps  60  with an aerodynamic profile, hinged on flexible bearing pivots  81  on the rim of balance  26  and which pivot during the pivoting motion of balance  26 , as explained above. This configuration can operate in a vacuum, with a flap regulation frequency double the natural frequency ω0, or in the air, with a frequency four times ω0. 
       FIG. 6  shows a resonator  1  with a balance  26 . Here regulator  2  is completely separate from resonator  1 : a pad  82  in proximity to the rim of balance  26  forms an aerodynamic brake, is suspended by a spring  83  from a structure  53  and is movable at a frequency double that of the sprung balance resonator  1  incorporating the balance. This mobility may result from an external excitation source, it may also result from a profile, for example a toothed profile, of the balance rim, which creates a variation in the air flow in proximity to pad  82 . 
       FIG. 7  shows a similar balance to that of  FIG. 3  with two secondary sprung balances  260  with high unbalances  261 , loosely mounted on the same diameter and in a position of alignment of the unbalances (at the point of rest), which are different from those of  FIG. 3  and either in-phase or in anti-phase vibration. Preferably, this embodiment is made of silicon or another similar micromachinable material (especially silicon oxide, quartz, “LIGA”®, amorphous metal, or suchlike): the secondary sprung balances and their unbalances  261  are in one-piece with balance  26  relative to which they pivot via flexible connections, and alignment of the unbalances is the rest state of this structure. This type of balance is also a very easy solution for replacing an existing balance to improve chronometric performance. 
       FIG. 8  shows a resonator  1  with a tuning fork  55 , fixed to a structure  50 , and one arm  56  of which is in contact with a friction pad  57  excited at a frequency double the frequency of the tuning fork resonator. 
       FIG. 9  illustrates a resonator mechanism comprising a balance  26  including a collet  7  holding a torsion wire  46 , wherein a resonator device  2  controls a periodic variation in tension with a frequency double that of the balance and torsion wire resonator  1 . 
       FIG. 10  shows a parametric resonator mechanism  1  comprising a sprung balance  3 , wherein the outer coil  6  of the balance spring  4  is pinned to a balance spring stud  5  to which a regulator device  2  imparts a periodic motion, said stud  5  being movable in a translational, pivoting and tilting motion in space to twist balance spring  4  if necessary. 
       FIG. 11  shows another sprung balance  3  resonator  1  with a balance spring  4  provided with an index mechanism with an index  12  and pins  11 , with a regulator system  2  with a crank rod system for actuating a continuous motion of index  12 , for a continuous variation in the active length of balance spring  4 . 
       FIG. 12  shows, in a similar manner, a balance spring  4  on which a cam  14  rests, driven in rotation by a regulator  2  for a continuous variation in the active length of balance spring  4  and/or in the position of the point of attachment and/or in the geometry of the balance spring. This Figure is a simplified representation wherein a single cam rests on the balance spring on only one side; it is evidently possible to combine two cams arranged to clamp balance spring  4  on both sides. 
       FIG. 13  shows, in a similar manner, a balance spring  4  with an additional coil  18  fixed to the balance-spring and locally lining the terminal curve  17  of the balance spring, and a regulator device  2  actuating one end  18 A of this additional coil  18 . 
       FIG. 14  illustrates another balance spring  4  with, in proximity to its terminal curve  17 , another coil  23  which is held at a first end  24  by a support  59  operated by a regulator device  2 , and which is free at a second end  25  arranged to periodically come into contact with terminal curve  17  under the action of regulator device  2  on this support. 
       FIGS. 16A and 16B  illustrate modification of the centre of gravity of resonator  1 , with a sprung balance  3  resonator comprising a balance  26  carrying substantially radial springs  72  attached to the rim and carrying oscillating inertia blocks  71 , similar to  FIG. 2  but some towards the interior and some towards the exterior of the rim. The associated centripetal or centrifugal effects allow for modulation of the position of the centre of gravity of resonator  1 . 
       FIGS. 17A and 17B  illustrate, in a similar manner to  FIG. 5 , another variant balance system  26  having flaps  80  with a flexible pivot  81  for modifying aerodynamic losses and inertia. 
       FIGS. 18A to 18D  illustrate modulation of the centre of gravity, based on a resonator like that of  FIG. 3  or  FIG. 7 , comprising built-in secondary sprung balances  260  with unbalances  261 . 
       FIG. 19  illustrates an example embodiment of a parametric oscillator with a balance collet  7  carrying a silicon spring  72  bearing a peripheral inertia block  71  weighted with a layer  75  of gold or another heavy metal obtained, for example, by galvanic deposition or other means, the spring-inertia block assembly oscillating at a regulation frequency ωR. For example, ω0=10 Hz and ωR=20 Hz.  FIG. 20  shows a balance  26  where these spring-inertia block assemblies extend from collet  7  to the largest diameter of the rim. 
       FIG. 21  shows a tuning fork  55  built into a support  50  and wherein one branch  56  carries a secondary sprung balance assembly  260  with eccentric unbalance  261  loosely pivotally mounted on branch  56 . 
       FIG. 22  shows a tuning fork  55  one branch  56  of which carries a spring  72 -inertia block  71  assembly mounted to vibrate freely. 
     The invention also concerns, in an advantageous embodiment, a timepiece resonator mechanism  1  with forced oscillation, arranged to oscillate at a natural frequency ω0, and comprising, on the one hand, at least one oscillating member  100 , which preferably includes a balance  26  or a tuning fork  55  or a vibrating strip, or similar, and on the other hand, oscillation maintenance means  200  arranged to exert an impact and/or a force and/or a torque on said oscillating member  100 . 
     According to the invention, this oscillating member  100  carries at least one oscillating regulator device  2  whose natural frequency is a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of the natural frequency ω0 of said resonator mechanism  1 , this integer being greater than or equal to 2. The specific values of ωR relative to natural frequency ω0 preferably follow the specific rules set out above. 
     In a first variant, this regulator device  2  includes at least one secondary sprung balance  260  pivoting about a secondary pivot axis, with an eccentric unbalance  261  relative to said secondary pivot axis of said secondary sprung balance  260 , which is loosely pivotally mounted on oscillating member  100 . 
     Specifically, oscillating member  100  pivots about a main pivot axis, and this at least one secondary sprung balance  260  has an eccentric secondary axis relative to the main pivot axis. 
     In a specific embodiment, regulator device  2  includes at least a first secondary sprung balance  260  and a second secondary sprung balance  260  whose unbalances  261 , in a rest state with no stress, are aligned with the secondary pivot axes of secondary sprung balances  260 . More specifically, oscillating member  100  pivots about a main pivot axis, and at least one said secondary sprung balance  260  has an eccentric secondary axis relative to the main pivot axis. 
     In an advantageous embodiment allowed by micromaterial technology, at least one such secondary sprung balance  260  pivots about a virtual secondary axis defined by elastic maintenance means comprised in oscillating member  100  for holding secondary sprung balance  260  and its amplitude of motion is limited relative to oscillating member  100 . 
     Advantageously, at least one such secondary sprung balance  260  is in one-piece with oscillating member  100 . 
     More specifically, at least one said secondary sprung balance  260  is in one-piece with a balance  26  comprised in oscillating member  100 , or which forms said oscillating member  100 . 
     In a second variant, regulator device  2  includes at least one spring-inertia block assembly comprising an inertia block  71  attached by a spring  72  at a point  73  on oscillating member  100 . 
     Specifically, oscillating member  100  pivots about a main pivot axis, and at least one such spring  72  extends radially relative to said main pivot axis. 
     In a specific embodiment, oscillating member  100  carries several such spring-inertia block assemblies, whose springs  72  extend radially relative to the main pivot axis, and wherein at least one assembly carries its inertia block  71  further from the main pivot axis than its spring  72  and wherein at least another assembly carries its inertia block  71  closer to the main pivot axis than its spring  72 . 
     Specifically, oscillating member  100  pivots about a main pivot axis, and at least one such spring  72  extends in a direction tangential to point  73  relative to the main pivot axis. 
     Specifically, at least one such spring-inertia block assembly is free to move relative to oscillating member  100 , except for its point of attachment  73 . 
     In a specific embodiment, the mobility of the spring-inertia block assembly is limited by guide means comprised in said oscillating member  100 , or travels in a path  74  comprised in said oscillating member  100 . 
     In a third variant, regulator device  2  includes at least one flap  80  or a strip  84  that is movable under the effect of aerodynamic variations and attached by a pivot  81  or by an elastic strip or by an arm  85  to oscillating member  100 . 
     In particular, in a specific embodiment, at least one flap  80  or strip  84  can tilt relative to pivot  81  or to the elastic strip or to arm  85  by which it is carried. 
     In an advantageous embodiment which allows for easy adaptation of the invention to existing movements, making it possible to considerably improve their chronometric performance at minimum cost, oscillating member  100  is a balance  26  subjected to the action of oscillation maintenance means  200 , which are return means comprising at least one balance spring  4  and/or at least one torsion wire  46 . 
     In another specific embodiment, oscillating member  100  is a tuning fork  55  of which at least one branch  56  is subjected to the action of oscillation maintenance means  200 . 
     It is clear that these different, non-limiting variants may be combined with each other and/or with yet other variants observing the principles of the invention. 
     The invention also concerns a timepiece movement  10  comprising at least one resonator mechanism  1  arranged to oscillate around its natural frequency ω0. According to the invention, this movement  10  includes at least one regulator device  2  comprising means arranged to act on said resonator mechanism  1  by imposing a periodic modulation of the resonant frequency and/or quality factor and/or position of the point of rest of resonator mechanism  1 , with a regulation frequency ωR which is comprised between 0.9 times and 1.1 times the value of an integer multiple of the natural frequency ω0 of said resonator mechanism  1 , this integer being greater than or equal to 2 and less than or equal to 10. 
     In a first variant, this movement  10  includes at least one such resonator mechanism  1 , whose oscillating member  100  carries at least one said regulator device  2 . 
     In a second variant, movement  10  includes at least one said regulator device  2  distinct from a said at least one resonator mechanism  1 , and which acts either by contact with at least one component of said resonator mechanism  1 , or remote from said resonator mechanism  1  through modulation of an aerodynamic flow or of a magnetic field or of an electrostatic field or of an electromagnetic field. 
     Advantageously, this resonator mechanism  1  includes at least one deformable component of variable stiffness and/or inertia, and said at least one regulator device  2  includes means arranged to deform the deformable component to vary its stiffness and/or inertia. 
     In a specific embodiment, this at least one regulator device  2  includes means arranged to deform resonator mechanism  1  and to modulate the position of the centre of gravity of resonator mechanism  1 . 
     In a specific embodiment, this at least one regulator device  2  includes loss generation means in at least one component of said resonator mechanism  1 . 
     In an embodiment that is advantageous since it is very easy to implement, regulator device  2  includes means for modulating an aerodynamic flow in proximity to oscillating member  100 , these modulation means comprising at least one pad  83  suspended from a structure  50  by elastic return means  83 . 
     The invention also concerns a timepiece  30  particularly a watch, including at least one such timepiece movement  10 . 
     Naturally, it is perfectly possible to apply the invention to another timepiece such as a clock. It is applicable to any type of oscillator comprising a mechanical oscillating member  100 , and particularly to a pendulum. 
     Excitation at frequency ωR as defined above, and more particularly at double the frequency ω0, may be achieved with a square or pulsed signal; it is not essential to have sinusoidal excitation. 
     The maintenance regulator does not need to be very accurate: any lack of accuracy results only in a loss of amplitude, but with no frequency variation unless of course the frequency is very variable, which is to be avoided. In fact, these two oscillators, the regulator that maintains and the maintained resonator, are not coupled, but one maintains the other, ideally (but not necessarily) in a single direction. In a preferred embodiment, there is no coupling spring between maintenance regulator  2  and maintained resonator  1 . 
     The invention also differs from known coupled oscillators in that the frequency of the regulator is double or a multiple of the natural frequency of the resonator (or at least very close to a multiple), and in the mode of energy transfer.