WO2019141789A1 - Oscillateur horloger - Google Patents

Oscillateur horloger Download PDF

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Publication number
WO2019141789A1
WO2019141789A1 PCT/EP2019/051188 EP2019051188W WO2019141789A1 WO 2019141789 A1 WO2019141789 A1 WO 2019141789A1 EP 2019051188 W EP2019051188 W EP 2019051188W WO 2019141789 A1 WO2019141789 A1 WO 2019141789A1
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WO
WIPO (PCT)
Prior art keywords
oscillator
pivot
pivots
inertial
coupler link
Prior art date
Application number
PCT/EP2019/051188
Other languages
English (en)
Inventor
Mohammad Hussein KAHROBAIYAN
Ilan Vardi
Simon Henein
Billy NUSSBAUMER
Etienne THALMANN
Original Assignee
Ecole polytechnique fédérale de Lausanne (EPFL)
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
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Publication date
Application filed by Ecole polytechnique fédérale de Lausanne (EPFL) filed Critical Ecole polytechnique fédérale de Lausanne (EPFL)
Priority to EP19700538.2A priority Critical patent/EP3740820B1/fr
Publication of WO2019141789A1 publication Critical patent/WO2019141789A1/fr

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Classifications

    • G—PHYSICS
    • G04—HOROLOGY
    • G04B—MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS
    • G04B17/00—Mechanisms for stabilising frequency
    • G04B17/04—Oscillators acting by spring tension
    • G04B17/045—Oscillators acting by spring tension with oscillating blade springs
    • G—PHYSICS
    • G04—HOROLOGY
    • G04B—MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS
    • G04B17/00—Mechanisms for stabilising frequency
    • G04B17/04—Oscillators acting by spring tension
    • G04B17/06—Oscillators with hairsprings, e.g. balance
    • G—PHYSICS
    • G04—HOROLOGY
    • G04B—MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS
    • G04B17/00—Mechanisms for stabilising frequency
    • G04B17/20—Compensation of mechanisms for stabilising frequency
    • G04B17/28—Compensation of mechanisms for stabilising frequency for the effect of imbalance of the weights, e.g. tourbillon

Definitions

  • the present invention relates to the technical field of horology. More particularly, it relates to horological oscillators comprising at least two coupled inertial masses.
  • Coupled horological oscillators are known in the documents EP2491463, CH700747 and FR322419.
  • the oscillator comprises two balance wheels are coupled to each other by means of teeth. These teeth are either provided on the periphery of the balances, or on gear wheels concentric with each balance, such that the balances turn synchronously in opposite directions.
  • a restoring force is provided by a hairspring associated with each balance, and an escapement is arranged to interact with one or both balances.
  • the aim of these arrangements is to improve the isochronism of the oscillator, and to minimize the influence of gravity and shocks thereupon.
  • This coupler link itself rotates about an anchor point fixed near the center of the system in order to couple the translations of the oscillating inertial bodies such that when one translates to the right, the other translates to the left and vice versa.
  • Such an arrangement is clearly susceptible to rotational shocks and accelerations in the plane of the oscillator, since such accelerations will augment or diminish the amplitude of oscillation depending on the direction of the rotational shock in relation to the direction of translation of the inertial bodies at the moment of the application of the shock, and hence cannot give satisfactory isochronism.
  • US 9 465 363 describes an oscillator system in which four inertial bodies, supported by flexure pivots, are connected in a square in a rotationally- symmetric manner by flexible blade flexures. These flexures are all joined at one end to a central ring arranged to be driven in a circular or oval pathway by a crank, and the other ends of the flexures are attached to respective levers extending away from the inertial bodies.
  • the inertial bodies are hence obliged to oscillate in opposite directions by opposed pairs, each pair acting at 90° to the other.
  • This arrangement results in undesired bending of the flexures during oscillation, which causes variations in the distances between the ends of the flexures where they join rigid levers attached to the inertial bodies.
  • This hence results in the oscillations of each opposed pair of inertial bodies significantly influencing the other, lending component to the oscillation of each pair which is determined by the state of the other pair. This is again clearly unsatisfactory from an isochronism perspective.
  • US 1 595 169 describes an oscillator comprising a single inertial body arranged to translate in two directions in its plane, according to a substantially circular pathway. This arrangement is clearly influenced by both translational and rotational shocks and is hence unsatisfactory.
  • figure 57 of WO 2015/104692 describes an oscillator based on an orbiting inertial body describing a bidirectional translation in a plane, following a circular or oval pathway. Compensating masses attached to levers serve to eliminate undesired forces. Again, this system is susceptible to shocks and is hence unsuitable for use in portable applications such as wristwatches.
  • An object of the present invention is thus to propose horological oscillators which are exempt from the above-mentioned drawbacks, and thereby to create oscillators which substantially satisfy Newton’s model for isochronism and are insensitive to gravity, linear shocks and angular shocks. Such oscillators are hence suitable for integration in a wristwatch or similar.
  • the invention relates to a horological oscillator comprising a first inertial body arranged to rotate with respect to a first axis, and a second inertial body arranged to rotate about a second axis parallel to said first axis.
  • These inertial bodies can, for instance, be balance wheels of any convenient form.
  • At least one elastic element is provided, this elastic element being arranged to apply a restoring torque to at least one of said inertial bodies so as to urge said inertial body towards a neutral position.
  • this elastic element may be arranged between an inertial body and a supporting framework which may be fixed or mobile.
  • the oscillator further comprises a substantially rigid coupler link comprising at least one bar or rod attached directly or indirectly at a first pivot point to said first inertial body and likewise directly or indirectly at a second pivot point to said second inertial body such that said inertial bodies are able to rotate synchronously about their respective axes in the same or opposite directions of rotation, depending on the geometry of the oscillator.
  • These pivot points can be constituted either by pin pivots, or flexure pivots such that the inertial bodies can pivot with respect to the coupler link at these points.
  • the angular velocities of these inertial bodies may be of the same magnitude or, in the case that the moment of inertia and/or the radius at which the coupler link is attached to each inertial body is different, may be of different magnitudes.
  • Said pivot points are distinct from, and hence remote from, the axes of rotation of the inertial bodies, and the coupler link is in consequence arranged to couple the inertial bodies by transmitting force between them according to a vector joining said first and said second pivot points.
  • said first inertial body is mounted pivotally on a supporting element such as a fixed frame or the coupler link of another oscillator by means of a first flexure pivot and said second inertial body is mounted pivotally on said supporting element by means of a second flexure pivot, said flexure pivots not only serving as pivots, but also as said elastic elements.
  • the coupler link is subject to a restoring torque with respect to each of said inertial bodies, said restoring torque being provided at at least one, preferably at each, of said first and second pivot points, for instance by means of an appropriate elastic element such as a coupling spring or by the inherent elasticity of a flexure pivot.
  • said coupler link is attached said first inertial body by means of a further flexure pivot, and is attached to said second inertial body by means of a yet further flexure pivot, said flexure pivots constituting said elastic elements.
  • the flexure pivots serve also to provide the restoring torque between the coupler link and the inertial bodies. Simplicity and efficient manufacture are thus assured.
  • a first line joining said first axis to said first pivot point is parallel to a second line joining said second axis to said second pivot point.
  • Said first and second lines are preferably perpendicular to a third line joining said first pivot point to said second pivot point when said oscillator is in a neutral position, i.e. when the net force generated by the various elastic elements are not tending to urge the coupler link in any particular direction.
  • This geometry results in an oscillator that is insensitive to gravity, linear shocks and angular shocks, and which is also dynamically balanced for longer stroke than in any other case.
  • the oscillator comprises at least two masses mounted movably, e.g. slidably, on said coupler link, one on either side of the center of mass of said coupler link.
  • These masses which can be displaced against friction or otherwise be provided with suitable blocking means to ensure that they remain in position during oscillation, permit modification of isochronism defect without affecting the nominal frequency of oscillation.
  • This latter can be modified in the normal way, for instance by means of adjustable masses such as screws provided on at least one of the inertial bodies.
  • a first and second horological oscillator according to the invention can be combined together into an oscillator system, these oscillators being coupled in series or in parallel.
  • This provides an oscillator system with two degrees of freedom that can easily be driven by a crank arrangement.
  • the isochronism can thus be improved, and the influence of gravity and shocks can be diminished.
  • the inertial bodies of the first horological oscillator can each be mounted pivotally on the coupler link of the second horological oscillator such that the two oscillators preferably act perpendicularly to one another.
  • the coupler link of the second oscillator can be shaped accordingly, e.g.
  • Such an oscillator system can be driven simply by a pin-and-slot crank arrangement, with the pin being situated on the coupler link of the first oscillator. This pin can then describe unidirectional two-dimensional trajectories which are ideally circular but may also be elliptical or oval.
  • Such an oscillator system if properly dynamically balanced, is insensitive to gravity, linear shocks and angular shocks.
  • the oscillator system can be arranged in parallel, i.e. with both oscillators being joined at a common point and each oscillating with respect to a frame.
  • the first horological oscillator and the second horological oscillator are preferably arranged to act at substantially 90° to each other, and are coupled by means of a rigid body from which extend respective linkages each attached to a respective coupler link.
  • This rigid body can, e.g. support a pin which can be driven as part of a pin-and-slot crank arrangement as mentioned above.
  • At least one of the linkages may comprise one of:
  • Robert’ s four-bar linkage comprising pinned pivots or flexure pivots
  • the first horological oscillator and the second horological oscillator are arranged such that they are related by a 90° rotation in the plane of the oscillator system.
  • they can be arranged such that one is a mirror reflection of the other about a plane equidistant from the coupler link of each horological oscillator, said plane being perpendicular to the plane of the oscillator system.
  • the influence of gravity, linear and angular shocks can be all be minimized, and the mirror reflection arrangement is particularly compact.
  • the first and second horological oscillators are coupled by means of a two-layer coupling system.
  • the first horological oscillator comprises a first rigid body arranged in a first layer and attached to the coupler link of said first horological oscillator
  • the second horological oscillator comprises a second rigid body arranged in a second layer and attached to the coupler link of said second horological oscillator.
  • the system is arranged such that the rigid bodies are constrained to translate together and are free to pivot one with respect to the other by means of a rotary joint, flexures or similar.
  • Such an arrangement permits great flexibility in design, and can utilize particularly advantageous arrangements of flexures or conventional pivots so as to achieve the desired guidance in translation of the rigid bodies. More than two layers can be provided if desired.
  • the invention also relates to a timepiece movement comprising an oscillator or an oscillator system as defined above.
  • the timepiece movement comprises a source of energy kinematically connected with said oscillator or said oscillator system by means of a crank attached to at least one coupler link.
  • the oscillator or oscillator system can thus regulate the running of the timepiece movement without any energy being lost to ticking.
  • FIG. 1 an embodiment of an oscillator according to the invention in plan view
  • - Fig. 16 and 17a, b examples of flexure-based pivots which can be used with oscillators according to the invention
  • - Fig. 18 a 2-DOF example of an oscillator with two 1-DOF oscillators in series;
  • FIG. 23 an embodiment of an oscillator system according to the invention comprising two individual oscillators arranged in parallel;
  • - Fig. 30 an embodiment of an oscillator system according to the invention in a series arrangement and based around flexure pivots;
  • Fig. 32 an embodiment of a flexure-based oscillator system according to the invention.
  • Fig. 33a-b and 34 diagrams illustrative of oscillators according to the invention provided with certain measurements;
  • Fig. 35a-b examples of oscillators according to the invention provided with means for adjusting isochronism
  • Fig. 36a-e an oscillator system according to the invention, respectively in: front view (Fig. 36a), rear view (Fig. 36b), front isometric view (Fig. 36c), exploded view (Fig. 36d), front isometric view with certain components removed (Fig. 36e); and - Fig. 37a-b: simplified views of crank arrangements suitable for driving oscillators and oscillator systems according to the invention.
  • An element can be described as being“rigid” in one or more directions and“flexible” in others, however if an element is simply described as“rigid”, it is“rigid” in every direction. An element simply described as “flexible” in one direction can be presumed “rigid” in the others. Also, tolerances as are usual in the art are to be assumed for all relations, ratios, measurements, directions etc., even when the term“substantially” is not used.
  • a“rotation” means that that the angular orientation of an element changes with respect to the framework element or elements upon which it is mounted. In other words, the element in question pivots with respect to its support. This is distinct from a two-dimensional translation as in some of the prior art discussed above, in which the angular orientation of the element in question remains substantially unchanged with respect to said framework, the element undergoing a translation in an orbital motion in a plane according to a circular or oval pathway.
  • a “rotation” in the sense of the present invention will always have an axis of rotation contained within or passing through the element in question (or an element rotationally-integrated therewith) at a predetermined, substantially unchanging point, whether this axis is defined by a conventional pinned pivot or by a flexure pivot.
  • the axis will typically be defined by the intersection of the extension of respective longitudinal axes of a pair of flexures, considered in their unstressed state.
  • the central point of an orbital translation on the other hand, will intersect the element in question at an ever- changing point, and the element in question will not change its angular orientation with respect to the framework.
  • Figure 1 illustrates a first embodiment of an oscillator according to the invention.
  • This oscillator comprises a first inertial body (141) and a second inertial body (143), each anchored to a fixed frame (140) by a respective pivot (A), (D).
  • These pivots (A), (D) are arranged such that the inertial bodies (141), (143) can rotate (i.e. pivot) about respective axes which are mutually parallel, these axes being defined by the pivots (A) and (D).
  • Inertial bodies (141) and (143) are illustrated as having the form of conventional balance wheels connected to each other by a coupler link (142) which can be a substantially rigid rod or bar of any convenient cross-section, this rigidity being present in every direction, as is equally the case in every embodiment.
  • Other forms of inertial bodies (141), (143) are also possible, and this point also applies to all the embodiments below and need not be repeated each time.
  • the inertial bodies contribute at least 70%, preferably at least 75% or even at least 85% of the inertia which, together with the restoring torque (see below), determines the frequency of oscillation of the oscillator. This applies equally to all embodiments and need not be repeated below.
  • Coupler link (142) is attached pivotably to first inertial body (141) at a first pivot point by a pivot (B), and is likewise attached pivotably to second inertial body (143) at a second pivot point by a further pivot (C). All pivots in this embodiment are typical pinned pivots, and are remote from the axes of rotation (A), (D) of the inertial bodies (141), (143). This latter point is equally the case in all of the embodiments discussed below, since no rotational coupling could occur between the inertial bodies (141), (143) if the pivot points (B), (C) each corresponded to a respective axis of rotation (A), (D).
  • coupler link (142) is of unitary construction and is substantially rigid over at least a certain portion of its length, which is to say that it is unarticulated and cannot undergo any deformation in any direction that may influence its function or its interaction with the inertial bodies (141), (143) under the influence of the forces to which it is subject during operation of the oscillator.
  • the coupler link (142) is at least 10 times, preferably at least 20 times, at least 50 times or at least 100 times stiffer than said flexure pivots.
  • the rigid part of the coupler link extends at least 50%, preferably at least 80% or at least 90% of the distance between the pivot points (B), (C). This applies to all embodiments. In the case of pinned pivots at the pivot points (B), (C), the rigid part of the coupler link extends at least between said pivot points, and would typically extend beyond them: in other words, in such a case the entire coupler link (142) is substantially rigid. It should also be noted that the rigidity of the coupler link (142) assures that it substantially cannot bend or articulate perpendicular to an axis intersecting the pivot points (B), (C) and is thus constrained to move only as permitted by the rotational displacements of the inertial bodies (141), (143).
  • the coupler link (142) substantially cannot be displaced in a direction perpendicular to an axis intersecting the pivot points (B), (C) at any given moment under the forces applied during operation. Furthermore, the trajectory of the coupler link (142) is defined exclusively by the relative positions of the axes of rotation (A), (D) and of the pivot points (B), (C). Again, all of this applies to all embodiments.
  • the coupler link (142) is substantially massless and its contribution to the oscillations of the oscillator can be ignored.
  • the moment of inertia of the coupler link (142) around pivot is substantially massless and its contribution to the oscillations of the oscillator.
  • (A) is at least one order of magnitude, preferably at least two orders of magnitude, less than that of first inertial body (141), and likewise about pivot
  • the coupler link (142) transmits force between the two inertial bodies (141), (143) according to a force vector substantially aligned along an axis l2 joining the first and second pivot points (B), (C), which is also the case in all other embodiments and is independent of the geometry of the coupler link (142), and indeed more complex coupler link shapes are described below in the context of other embodiments.
  • the force vector substantially obeys this condition at all times. A moment about each axis of rotation (A), (D) is thus applied by the coupler link (142) to each of the inertial bodies (141), (143).
  • the coupler link (142) is not attached to any framework element, and is supported exclusively on the inertial bodies (141), (143).
  • Afirst elastic element (144) such as a hairspring or any other convenient spring arranged to apply a restoring torque is attached between first inertial body (141) and the fixed frame (140) so as to urge the first inertial body (141) towards a neutral position.
  • a second elastic element (147) is similarly arranged between rigid body (143) and the fixed frame (140) to apply a similar restoring torque. It should be noted that one of the elastic elements (144) or (147) can be omitted if desired.
  • a first coupling spring (145) is attached between the first inertial body (141) and the coupler link (142) so as to also apply a restoring torque between these two elements and to tend to bring them into a predetermined mutual angular orientation, and a second coupling spring (146) is likewise attached between the second inertial body (143) and the coupler link (142).
  • / 141 is the moment of inertia of first inertial body (141) about its pivot point (A)
  • / 143 is the moment of inertia of second inertial body (143) about its pivot point (D)
  • w 141 is the angular velocity of first inertial body (141)
  • w 143 is the angular velocity of second inertial body (143).
  • the oscillator is insensitive to gravity, linear shocks and angular shocks, for s certain stroke, and can be driven via a pin and crank arrangement (not illustrated on figure 1 ; see figure 37b), with the pin being situated at a convenient location on coupler link (142), similarly to that described below in the context of other embodiments.
  • this oscillator can cooperate with a conventional escapement in the known manner, which also applies to the other 1-DOF embodiments mentioned below.
  • Figure 1 represents the general case of this type of oscillator according to the invention. Several special cases will now be discussed below, without there being a need to re-describe them in detail.
  • J 141 is the moment of inertia of first inertial body (141) about its pivot point (A)
  • J 143 is the moment of inertia of second inertial body (143) about its pivot point (D)
  • AB is the distance between pivots (A) and (B)
  • CD is the distance between pivots (C) and (D)
  • CE is the distance between pivots (C) and (E)
  • BE is the distance between pivots (B) and (E)
  • E is the intersection point of the lines l 1 and l 3
  • l 1 is the straight line connecting pivots (A) and (B)
  • l 3 is the straight line connecting pivots (C) and (D).
  • the oscillator in this configuration is insensitive to gravity, linear shocks and angular shocks. It should be noted that this oscillator is dynamically balanced for short strokes.
  • a pin (not illustrated) or similar attachment means can be provided on the coupler link (142), or alternatively principle on one of the inertial bodies (141), (143). Optimally, this pin can be provided at the mid-point (O) of coupler link (142). The pin can then be driven by any convenient crank mechanism (see for instance figure 37b), the axis of the crank being subject to a driving torque produced by a motor (e.g. a mainspring).
  • This driving torque causes the oscillator to oscillate, which serves to regulate the rate at which the crank turns.
  • an eccentric crank and connecting rod attached to the coupler link (142) is suitable (see figure 37b), although other types of crank are also possible. Since such cranks are well-known in mechanics, it is not necessary to illustrate them in detail. This applies equally to all other embodiments where no specific driving arrangement is mentioned.
  • li and l 3 are parallel in the resting state of the oscillator, which implies a relatively longer or shorter connecting link (142) than that illustrated in figure 1 , or moving one of the pivot points (A) or (B) so as to bring these axes parallel.
  • the oscillator is dynamically balanced when:
  • CD J 141 AB / 143
  • / 141 is the moment of inertia of first inertial body (141) about its pivot point (A)
  • / 143 is the moment of inertia of second inertial body (143) about its pivot point (D)
  • AB is the distance between pivots (A) and (B)
  • CD is the distance between pivots (C) and (D).
  • CD J 141 AB J 143 (2)
  • J 141 is the moment of inertia of first inertial body (141) about its pivot point (A)
  • J 143 is the moment of inertia of rigid body (143) about its pivot point (D)
  • AB is the distance between pivots (A) and (B)
  • CD is the distance between pivots (C) and (D).
  • This oscillator is insensitive to gravity, linear shocks and angular shocks.
  • This oscillator is dynamically balanced for longer strokes compared to the case where l 2 is not perpendicular to the lines l 4 and l 3 .
  • the trajectory of point (O) of this oscillator is a better approximation for a straight line compared the case where l 2 is not perpendicular to the lines l 4 and l 3 .
  • Figure 5 illustrates the general case of an oscillator according to the invention, in which the coupler link (152) is not presumed to be essentially massless. In horological applications, even an almost-negligible coupler link mass can introduce errors which decrease chronometric precision over the millions of cycles that such oscillators carry out.
  • the mass of the coupler link (152) is compensated by having inertial bodies (151), (153) whose centers of mass do not lie on their axes of rotation. As defined by pivots (A) and (D).
  • the oscillator illustrated in figure 5 comprises a first inertial body (151) and a second inertial body (153), each anchored to a fixed frame (150) by a respective pivot (A), (B).
  • Inertial bodies (151) and (153) are connected to each other by a coupler link (152) which is substantially rigid, with first inertial body
  • the center of mass of inertial bodies (151) and (153) and coupler link (152) are denoted by (G j J, (G 3 ), and (G 2 ) respectively.
  • d 2 is the line connecting (B) to (G 2 )
  • d' 2 is the line connecting (C) to (G 2 )
  • d 3 is the line connecting (D) to (G 2 ).
  • l 1 is the line connecting (A) and (B)
  • l 2 is the line connecting (B) and (C)
  • l 3 is the line connecting (C) and (D).
  • the angle between l 1 and d 1 is f 1
  • the angle between l 2 and d 2 is f 2
  • the angle between l 2 and d' 2 is f' 2
  • the angle between l 3 and d 3 is (ps-
  • the oscillator of this embodiment is dynamically balanced when:
  • m 3 DG 3 BC m 2 BG 2 CD, (3)
  • AG 1 is the distance between (A) and (G ⁇
  • BC is the distance between (B) and (C)
  • CG 2 is the distance between (C) and (G 2 )
  • AB is the distance between (A) and (B)
  • DG 3 is the distance between (D) and (G 3 )
  • BG 2 is the distance between (B) and (G 2 )
  • CD is the distance between (C) and (D).
  • q is the vector of the total angular momentum of the oscillator about an arbitrary fixed point (q).
  • the oscillator of this embodiment is insensitive to gravity, linear shocks and angular shocks, for short stroke. [0056] As before, several special cases will now be described.
  • Figure 6 illustrates a special case of the oscillator of figure 5, in which the lines l 1 and l 3 intersect at a point (E) when the oscillator is in a neutral position.
  • This oscillator is dynamically balanced when:
  • m 3 DG 3 BC m 2 BG 2 CD, (5)
  • m 1 , m 2 and m 3 are the mass of first inertial body (151), connecting link (152) and second inertial body (153), respectively.
  • AG 1 is the distance between (A) and (G ⁇
  • BC is the distance between (B) and (C)
  • CG 2 is the distance between (C) and (G 2 )
  • AB is the distance between (A) and (B)
  • DG 3 is the distance between (D) and (G 3 )
  • BG 2 is the distance between (B) and (G 2 )
  • CD is the distance between (C) and (D).
  • Equation (6) can be rewritten as follows,
  • RE is the distance between (B) and (E) and CE is the distance between (C) and (E).
  • the oscillator of this embodiment is insensitive to gravity, linear shocks and angular shocks, for short strokes.
  • Figure 7 illustrates a special case of the oscillator of figure 5, where the lines l 1 and l 3 are parallel.
  • This oscillator is dynamically balanced when:
  • m 3 DG 3 BC m 2 BG 2 CD, (7)
  • m 1 , m 2 and m 3 are the mass of first inertial body (151), connecting link (152) and second inertial body (153), respectively.
  • AG 1 is the distance between (A) and (G ⁇
  • BC is the distance between (B) and (C)
  • CG 2 is the distance between (C) and (G 2 )
  • AB is the distance between (A) and (B)
  • DG 3 is the distance between (D) and (G 3 )
  • BG 2 is the distance between (B) and (G 2 )
  • CD is the distance between (C) and (D).
  • Equation (8) can be rewritten as follows,
  • E is the distance between (B) and (E) and CE
  • CE is the distance between (C) and (E).
  • Figure 8 illustrates a special case of the oscillator of figure 5, wherein the center of mass of the coupler link ( G 2 ) lies on the line l 2 connecting pivots (B) and (C).
  • This oscillator is dynamically balanced when:
  • m 1 , m 2 and m 3 are the mass of first inertial boy (151), coupler link (152) and second inertial body (153), respectively.
  • AG 1 is the distance between (A) and (G j J
  • BC is the distance between (B) and (C)
  • CG 2 is the distance between (C) and (G 2 )
  • AB is the distance between (A) and (B)
  • DG 3 is the distance between (D) and (G 3 )
  • BG 2 is the distance between (B) and (G 2 )
  • CD is the distance between (C) and (D).
  • This oscillator is insensitive to gravity, linear shocks and angular shocks, for short strokes.
  • Figure 9 illustrates a special case of the oscillator of figure 5, wherein the lines l 1 and l 3 are parallel.
  • This oscillator is dynamically balanced when:
  • AG is the distance between (A) and (G ⁇
  • BC is the distance between (B) and (C)
  • CG 2 is the distance between (C) and (G 2 )
  • AB is the distance between (A) and (B)
  • DG 3 is the distance between (D) and (G 3 )
  • BG 2 is the distance between (B) and (G 2 )
  • CD is the distance between (C) and (D).
  • CD J 151 AB / 153
  • / 151 is the moment of inertia of first inertial body (151 ) about pivot point (A) and / 153 is the moment of inertia of second inertial body (153) about pivot point (D).
  • This oscillator is insensitive to gravity, linear shocks and angular shocks, for longer strokes as compared to the previous case.
  • Figure 10 illustrates a special case of the oscillator of figure 9, where the center of the coupler link ( G 2 ) is at point (O), the mid-point of the line segment BC, and also the line l 2 is perpendicular to the lines l 1 and l 3 when the oscillator is in a neutral position, i.e. all the torques provided by the elastic elements are balanced such that there is no net force or torque tending to try to displace the coupler link.
  • This oscillator is dynamically balanced when:
  • AG 1 is the distance between (A) and (G ⁇
  • BC is the distance between (B) and (C)
  • AB is the distance between (A) and (B)
  • DG 3 is the distance between (D) and (G 3 )
  • CD is the distance between (C) and (D).
  • CD J 151 AB / 153
  • / 151 is the moment of inertia of first inertial body (151) about pivot point (A) and / 153 is the moment of inertia of second inertial body (153) about pivot point (D).
  • This oscillator is insensitive to gravity, linear shocks and angular shocks, for relatively long strokes.
  • the coupler link (152) extends beyond pivot
  • This oscillator is dynamically balanced when:
  • AG 1 is the distance between (A) and (G j J
  • BC is the distance between (B) and (C)
  • CG 2 is the distance between (C) and (G 2 )
  • AB is the distance between (A) and (B)
  • DG 3 is the distance between (D) and (G 3 )
  • BG 2 is the distance between (B) and (G 2 )
  • CD is the distance between (C) and (D).
  • j£ 51 is the moment of inertia of first inertial body (151 ) about pivot (A)
  • / 52 is the moment of inertia of coupler link (152) about pivot (B)
  • / 53 is the moment of inertia of second body (153) about pivot (D).
  • the oscillator is insensitive to gravity, linear shocks and angular shocks, for long strokes.
  • Figure 12 illustrates a variant of the embodiment of figure 1 , in which the simple pin pivots (A) and (D) have been replaced by coupled back to back crossed pivots.
  • This embodiment comprises a first inertial body (1306) attached to a fixed frame (1308) by two crossing rods (1301) and (1302) which cross one another.
  • the crossing rods (1301) and (1302) are each attached to the fixed frame (1308) on one of their extremities by respective pivots (1310) and (1315) and to the rigid body (1306) on their other extremities by respective pivots (1309) and (1316).
  • a first elastic element (1319) such as a hairspring, leaf spring or any other convenient arrangement is attached between the frame (1308) and the rod (1301 ), and a second elastic element (1320) is likewise provided linking the frame (1308) to the rod (1302).
  • These elastic elements (1319), (1320) each provide a restoring force so as to urge the first inertial body (1306) towards a neutral angular position.
  • a second inertial body (1305) is provided, which is again attached to the fixed frame (1308) by two crossing rods (1303) and (1304), each associated with a respective elastic element (1321 ), (1322).
  • the crossing rods (1303) and (1304) are each attached to the fixed frame (1308) on one extremity by respective pivots (131 1) and (1314) and to the second inertial body (1305) on the other extremity by respective pivots (1312) and (1313).
  • First inertial body (1306) and second inertial body (1305) are connected to each other by a coupler link (1307) as before, this coupler link (1307) being is attached to first inertial body (1306) at a first point by pivot (1318) and to second inertial body (1305) at a second point by pivot (1317).
  • the ensemble formed by first inertial body (1306), its rods (1301 ), (1302) and the corresponding elastic elements (1319), (1320) is geometrically related to the corresponding ensemble formed by second inertial body (1305), its rods (1303), (1304) and the corresponding elastic elements (1321 ), (1322) by a 180-degree rotation in the x-y plane. Note that no coupling springs are provided at pivot points (1317) and (1318) which join the coupler link (1307) to each inertial body (1305), (1306).
  • FIGS 13 a-d illustrate further embodiments of oscillators according to the invention. These variants incorporate coupled back-to-back remote center compliance (RCC) pivots rather than the crossed rods of figure 12, and contains similar elements to the coupled pair of crossed pivots described above.
  • the numbering of the elements starting at (1401) correspond to the respective elements numbered starting at (1301 ), and hence need not be repeated at length here.
  • the remote center compliance (RCC) pivots each comprise pairs of beams (1401 ), (1402) and (1403), (1404) whose longitudinal axes intersect at a point in space beyond the extremities of the beams of each respective pair, defining respective centers of rotation R 1 and R 2 which act as respective pivot points.
  • flexible pivots can be used instead of conventional pin-based pivots, and as such can comprise two flexure blades (cf. pivot RCC aides lames from Henein op cit) as illustrated in figure 13d, or two rigid beams with necked-down flexures (e.g. cols) at their extremities (cf. pivot RCC a quatre co/sfrom Henein op cit). More generally, one can replace the pivots (1409)-(1416) by any convenient flexible pivot from the literature.
  • Figure 13c illustrates a variant of the embodiment of figure 13a in which the coupler link 1407 has been placed in a particular manner by overhanging terminal portions of each inertial body (1405), (1406) such that they overlap, the coupler link (1407) being arranged between these overhanging portions.
  • the coupler link (1407) being arranged between these overhanging portions.
  • the inertial bodies (1505) and (1506) are connected to the fixed frame (1508) respectively by flexure blades (1503)-(1504) and (1501 )-(1502). These blades are placed in such way that they form pairs at a 180-degree rotational symmetry with respect to the center of the oscillator (cf. pairs (1501)-(1504) and (1502)-(1503)). This way, their axial loads (due to gravity) are opposite and hence have the same magnitude but opposite signs. As a result, when one beam is subjected to tensile axial load, the other one is subjected to compressive axial load with equal magnitude. This improves the gravity insensitivity of the pivot. Coupler link (1507) is in this case a rigid beam with flexure blades at each end serving to connecting the first inertial body (1505) to the second inertial body (1506) in a similar fashion to the other embodiments described above.
  • the fixed frame (1408) and inertial bodies (1405), (1406) can be exchanged such that the inertial bodies (1405), (1406) become the fixed frame (1408) and the fixed frame (1408) is separated into two inertial bodies (1405), (1406), which are then connected by the coupler link (1407) as illustrated in figure 13b.
  • the position of the center of mass of the oscillator should not change during its rotation. This can be obtained by having the center of mass of each pivot of the pair at its respective center of rotation. More generally, in the case of a coupled pair of ideal pivots, the combination of the following properties guarantee that the overall center of mass does not move:
  • each pair of flexible pivots in each of the oscillators of these figures has one degree of freedom, namely in rotation in the x-y plane.
  • Each pivot of the pair has its own rotation axis (R and R 2 ) but the rotations are coupled.
  • R and R 2 rotation axis
  • the corresponding rotation axis is perpendicular to the x-y plane, and intersects the crossing point of the beams in question.
  • the corresponding rotation axis is perpendicular to x-y plane, intersecting the crossing point of the extension of the longitudinal axis of the beams in question.
  • the inertial bodies can be coupled so as to turn in the same direction as illustrated in figure 12, or in opposite directions as illustrated in figure 14.
  • This latter embodiment couples the two inertial bodies such that when one turns clockwise, the other turns anticlockwise.
  • This same principle can be applied to the flexure-based oscillator of figure 13d, and it is not necessary to describe this further here.
  • Having the inertial bodies turn in the same direction has the advantage of having the intrinsic parasitic shifts of each pivot compensate each other. This reduces the sensitivity to linear accelerations such as gravity. However, such an oscillator is sensitive to angular accelerations. Having one inertial body turn in the opposite direction to the other cancels this sensitivity but does not benefit from parasitic shift compensation.
  • the position where the connecting link (1407), (1507) is attached to the inertial bodies (1405), (1406), (1505), (1506) defines the coupling between the sets of pivots.
  • both sets of pivots rotate the same angle, they need to rotate in the same direction (like in figures 12 and 13 a-d), and the connecting rod needs to have the same length L as the distance a between the rotation axes Ri, R2 of the pivots.
  • the rod must be connected in a way that the vectors r from a connecting point on a pivot to its respective rotation center forms a parallelogram with the other sides being the connecting rod and the segment between the rotation axes of the pivots (see figure 15).
  • a variant of the oscillator of figure 12 can also be implemented using a pivot with four necked-down flexures shown highly schematically in figure 16.
  • This variant applies the pivot presented on p.129 of Helmer and Clavel, Conception systematique de structures cinematiques orthogona!es pour !a microrobodique, These EPFL, No. 3365 (2006).
  • one of the beams (1504) connecting the fixed part (1508) to the inertial body (1505) passes around the structure by means of a frame.
  • This planar architecture is advantageous for easy manufacturing, since no beams are actually required to cross in separate planes parallel to the xy plane.
  • Figures 17a and 17b illustrate this principle applied to the oscillator of figure 13a.
  • a first pivot ensemble (1501 , 1502) is attached to the second inertial body (1506) on a first side thereof at the point illustrated with a corresponding chain line
  • a second pivot ensemble (1503, 1504) is attached to the first inertial body (1505) on a second side thereof as illustrated by the corresponding chain line.
  • the inertial bodies (1505), (1506) are sandwiched between the pivot ensembles (1501 , 1502), (1503, 1504).
  • Figure 18 illustrates a two degree of freedom (2-DOF) oscillator comprising two inertial bodies (301 ), (302) connected together in series and taking the form of balance wheels. This oscillator does not form part of the invention.
  • First inertial body (301 ) is connected to another inertial body (302) by a pivot (303) situated on an extension of a second inertial body (302) which serves as a coupler link (307) and is fixedly attached to said second inertial body (302) at a second point (307).
  • the second inertial body (302) is itself anchored to a fixed frame (300) by a pivot (304), the part of the second inertial body (302) acting as coupler link (307) extending between the two pivots (304), (303).
  • a torsional spring (305) is arranged between the two inertial bodies (301) and
  • a driving pin (P) is provided on the first inertial body so as to be driven by a crank (see figure 37a), which will drive the oscillators synchronously.
  • first inertial body (301 ) is mounted pivotally on second inertial body (302).
  • first inertial body (301 ) lies on the rotation axis of pivot (304) where second inertial body (302) is mounted pivotally on fixed support 300.
  • / 302 is the moment of inertia of second inertial body (302) together with first inertial body (301) about pivot (304), k 305 is the stiffness of torsional spring (305) and k 306 is the stiffness of torsional spring (306)
  • This oscillator is insensitive to gravity and linear shocks; however it is sensitive to angular shocks.
  • the line d c connecting pivot (303) and the driving pivot (P) is best arranged perpendicular to the line 5 y connecting pivot (303) and pivot (304).
  • the distance between pivots (303) and (P) is chosen to equal the distance between pivots (303) and (304).
  • FIG 19 illustrates an oscillator system comprising two oscillators (Oi) and (O2) according to the invention arranged in series.
  • Each of these oscillators (O1), (O2) comprises an oscillator according to one of the embodiments of figures 1 -1 1 , first oscillator (O1) being mounted on the coupler link (315) of second oscillator (O2).
  • First oscillator (O c ) comprises two inertial bodies (31 1 ) and (313) each fixed to the coupler link (315) of oscillator ( 0 2 ) at appropriate pivot points.
  • coupler link (315) comprises a hollow frame-shaped portion, upon which first oscillator (O c ) is mounted.
  • first oscillator (O ⁇ ) its first inertial body (31 1) is connected to the coupler link (315) of second oscillator ( 0 2 ) by a pivot (A ⁇ .
  • This coupler link (315) thus serves as a support frame for the first oscillator (O ⁇ .
  • second inertial body (313) is connected to the same coupler link (315) by a further pivot (D j J.
  • the inertial bodies (31 1 ) and (313) of oscillator (O c ) are connected to each other by a respective coupler link (312).
  • This coupler link (312) is attached to first inertial body (31 1 ) by a pivot (B ⁇ and is attached to second inertial body (313) by a pivot (CY).
  • the second oscillator ( 0 2 ) comprises two respective inertial bodies (314) and (316) coupled together by a respective coupler link (315).
  • Inertial body (314) is anchored to a fixed frame (310) by a pivot (A 2 ), and inertial body (316) is anchored thereto by a pivot ( D 2 ).
  • the coupler link (315) of the second oscillator ( 0 2 ) is attached to inertial body (314) by pivot ( B 2 ) and attached to inertial body (316) by pivot ( C 2 ).
  • a torsional spring (317) is arranged between inertial body (311) and the coupler link (315) of the second oscillator ( 0 2 ), and another torsional spring (318) is arranged between inertial body (311) and the coupler link (312) of the first oscillator (O ⁇ . Furthermore, a torsional spring (319) is arranged between inertial body (313) and the coupler link (312) of the first oscillator (O ⁇ , another torsional spring (320) between inertial body (313) and the coupler link (315) of the second oscillator (0 2 ).
  • a torsional spring (321) is arranged between inertial body (314) and the fixed frame (310)
  • another torsional spring (322) is arranged between inertial body (314) and the coupler link (315)
  • another torsional spring (323) is arranged between inertial body (316) and the coupler link (315)
  • a torsional spring (324) is arranged between inertial body (316) and the fixed frame (310).
  • the driving pin (P) which is driven by a crank, is attached to the coupler link (312) of oscillator (O c ) at a convenient location, for instance at the mid-point thereof.
  • Oscillators (O ⁇ and ( 0 2 ) are dynamically balanced as described above in the context of figures 1-11. Note that the total mass and moment of inertia of the coupler link of oscillator ( 0 2 ) comprise the mass and moment of inertia of the coupler link (315) of the second oscillator ( 0 2 ) as well as the mass and moment of inertia of oscillator (O ⁇ .
  • the two oscillators (O ⁇ and ( 0 2 ) are arranged such that they act perpendicularly to each other. A movement of the pin exclusively in the y direction will cause the first oscillator (O c ) to be actioned without disturbing the second oscillator ( 0 2 ), whereas a movement of the pin exclusively in the x direction will cause the second oscillator ( 0 2 ) to be actioned without disturbing the first oscillator (O ⁇ . Moving the pin (P) in a circular or oval trajectory will cause both oscillators ⁇ O ⁇ , ( 0 2 ) to be actioned synchronously. This applies to all the oscillator systems described below, and need not be repeated each time.
  • FIG. 20 illustrates a variant of the oscillator system of figure 19, in which each oscillator (O ⁇ , ( 0 2 ) is similar to that of figure 10 in that in a neutral position the axes joining adjacent pivot points intersect at right angles. Furthermore, the line l c connecting pivots ( B 2 ) and ( C 2 ) is perpendicular to the line connecting pivots ( A 2 ) and ( B 2 ) and also to the line connecting pivots ( C 2 ) and ( D 2 ). The line y connecting pivots (B ⁇ and (CY) is perpendicular to the line connecting pivots (A ) and (B ⁇ and also to the line connecting pivots (CY) and (Oi)
  • This oscillator is insensitive to gravity, linear shocks and angular shocks for long strokes.
  • Figures 21 and 22 illustrate solutions for coupling 1 -DOF oscillators in parallel so as to form a 2-DOF oscillator system.
  • Figure 21 illustrates a three-bar coupling element, in which a rigid body (400), which supports a driving pin ( P ), is connected to a first oscillator (O ⁇ by two parallel rigid bars (401) and (407) and connected to a second oscillator ( 0 2 ) by a further single rigid bar (402).
  • Rigid bar (401 ) is connected to rigid body (400) by pivot (403) and is connected to second oscillator (O x ) by pivot (405).
  • Rigid bar (407) is connected to rigid body (400) by pivot (408) and is connected to first oscillator (O c ) by pivot (409).
  • Rigid bar (402) is connected to rigid body (400) by pivot (404) and is connected to second oscillator (0 2 ) by pivot (406).
  • Oscillators (O c ) and ( 0 2 ) can be of any convenient above-mentioned type.
  • FIG. 22 The coupling arrangement of figure 22 differs from that of figure 21 in that only one rigid bar (401 ) links rigid body (400) to the first oscillator (O ⁇ .
  • the longitudinal axis of bar (401 ) extends such that it intersects driving pin (P) when the system is in a neutral position with no resultant force tending to try to displace the rigid body 400.
  • Figure 23 illustrates an oscillator comprising two oscillators (O ⁇ and ( 0 2 ) each according to the oscillator of figure 10, coupled functionally in parallel by means of the coupling arrangement of figure 22 such that the axis of action of one oscillator is substantially orthogonal to that of the other, i.e. the directions of displacement of the coupler links of each oscillator (O ⁇ , ( 0 2 ) during oscillation is substantially orthogonal. This is the case in all of the parallel- coupled oscillators described below.
  • the optimal connecting point at which the coupling element is connected to each of the oscillators is the mid-point of each coupler link (417), (418) respectively.
  • This attachment is effected by means of a respective pivot (415), (416), the former lying on the mid-point of the coupler link (417) of first oscillator (Oi), and the latter lying on the mid-point of the coupler link (418) of second oscillator ( 0 2 ).
  • Displacement of the driving pin (P) in the y direction thus excites first oscillator (O ⁇ , and displacement of the driving pin (P) in the x direction excites second oscillator ( 0 2 ).
  • Circular displacements of the driving pin (P) excites both oscillators (O ⁇ , ( 0 2 ) synchronously.
  • Figure 24 illustrates a variant of a coupling arrangement in which the above- mentioned parasitic shift is compensated by means of double parallelogram pivots.
  • rigid body (420) supporting the driving pin (P) is connected indirectly to the oscillators (O c ) and ( 0 2 ).
  • Rigid body (420) is connected by two rigid bars (421 ) and (422) to an intermediate stage (423).
  • Intermediate stage
  • Rigid bar (421 ) is connected to rigid body (420) by pivot (430) and is connected to intermediate stage (423) by pivot (433).
  • Rigid bar (422) is connected to rigid body (420) by pivot (431) and connected to intermediate stage (423) by pivot (432).
  • Rigid bar (425) is connected to first oscillator (O c ) by pivot (435) and connected to intermediate stage (423) by pivot (434).
  • Rigid body (420) is connected by a rigid bar (426) to intermediate stage (423).
  • Intermediate stage (423) is connected to second oscillator ( 0 2 ) by two rigid bars (428) and (429).
  • Rigid bars (426), (428), and (429) are parallel.
  • Rigid bar (426) is connected to rigid body (420) by pivot (438) and connected to intermediate stage (423) by pivot (439).
  • Rigid bar (428) is connected to second oscillator ( 0 2 ) by pivot (443) and connected to intermediate stage (423) by pivot (442).
  • Rigid bar (429) is connected to second oscillator ( 0 2 ) by pivot (440) and connected to intermediate stage (423) by pivot (441 ).
  • rigid bars (421 ), (422), (424), and (425) are perpendicular to rigid bars (426), (428) and (429) when the system is in a neutral position.
  • the trajectories of pivots (440) and (443) are substantially parallel to the x-axis and the trajectories of pivots (435) and (437) are substantially parallel to the y-axis.
  • the trajectories of pivots (430) and (431 ) with respect to first oscillator (O c ) are approximately straight lines parallel to the x- axis.
  • the trajectory of pivot (438) with respect to oscillator ( 0 2 ) is approximately a straight line parallel to the y-axis, and any parasitic shift is substantially eliminated.
  • Figure 25 illustrates a further coupling arrangement based on a pair of Robert’s four-bar linkages, which convert rotational motions to approximately straight- line motions.
  • the rigid body (470) supporting the driving pin (P) is connected to each of oscillators (O c ) and ( 0 2 ) by a respective Robert’s four-bar linkage.
  • Rigid body (470) is connected to rigid body (471 ) by pivot (478).
  • Rigid body (471 ) is connected to first oscillator (O c ) by two rigid bars (472) and (473).
  • Rigid bar (472) is connected to rigid body (471 ) by pivot (475) and connected to first oscillator (O c ) by pivot (474).
  • Rigid bar (473) is connected to rigid body (471 ) by pivot (477) and connected to first oscillator (O c ) by pivot (476).
  • Rigid body (470) is connected to rigid body (479) by pivot (486).
  • Rigid body (479) is connected to second oscillator ( 0 2 ) by two rigid bars (480) and (481).
  • Rigid bar (480) is connected to rigid body (479) by pivot (483) and connected to second oscillator ( 0 2 ) by pivot (482).
  • Rigid bar (481 ) is connected to rigid body (479) by pivot (485) and connected to second oscillator (0 2 ) by pivot (484).
  • Pivot (478) lies on the straight line connecting pivots (474) and (476).
  • the line connecting pivots (475) and (477) is parallel to the line connecting pivots (474) and (476).
  • the distances between pivots (474) and (475); (475) and (478); (478) and (477); and (477) and (476) are equal.
  • the distance between pivots (474) and (476) is two times the distance between pivots (475) and (477).
  • Pivot (486) lies on the straight line connecting pivots (484) and (482).
  • the line connecting pivots (485) and (483) is parallel to the line connecting pivots (484) and (482).
  • the distances between pivots (482) and (483); (483) and (486); (486) and (485); and (485) and (484) are equal.
  • the distance between pivots (484) and (482) is two times the distance between pivots (485) and (483).
  • the trajectories of pivot (482) and (484) are approximately two straight lines parallel to the x-axis.
  • the trajectories of pivot (474) and (476) are approximately two straight lines parallel to the y-axis.
  • the trajectory of pivot (478) with respect to first oscillator (O c ) is approximately a straight line parallel to the x-axis.
  • the trajectory of pivot (486) with respect to second oscillator ( 0 2 ) is approximately a straight line parallel to the y-axis.
  • a similar arrangement can be formed using flexure pivots rather than pinned pivots.
  • Figures 26a-c illustrate another variant of a coupling element, in this case distributed over two layers (Z ⁇ ) and (L 2 ). These figures are partial and schematic, and do not illustrate all the details of the entire oscillator system.
  • First oscillator (O c ) is in or adjacent to layer (Z ⁇ ) and second oscillator ( 0 2 ) is in or adjacent to layer ( 2 ).
  • These oscillators can be of any type disclosed in the present specification, each hence comprising two inertial bodies, for a total of four inertial bodies for the oscillator system.
  • rigid body (450) is connected to first oscillator (O ⁇ by two rigid bars (451 ) and (452), these bars (451 ) and (452) notably being connected to the coupler link of said first oscillator ⁇ O ⁇ .
  • Rigid bar (451 ) is connected to rigid body (450) by pivot (453) and is connected to first oscillator (O c ) by pivot (454).
  • Rigid bar (452) is connected to rigid body (450) by pivot (455) and connected to first oscillator (O c ) by pivot (456).
  • Rigid bars (451 ) and (452) are related to each other by a 180-degree in-plane rotation about the mid-point of the line segment (453)- (455).
  • the center of mass of rigid body (450) lies on the mid-point of the line segment (453)-(455).
  • the trajectories of pivots (454) and (456) are approximately straight lines parallel to the y-axis.
  • the trajectory of the mid-point of the line segment (453)-(455) is approximately a straight line parallel to the x-axis.
  • rigid body (460) is connected to second oscillator (0 2 ) by two rigid bars (461 ) and (462), these bars (461) and (462) likewise being connected to the coupler link of said second oscillator (0 2 ).
  • Rigid bar (461 ) is connected to rigid body (460) by pivot (463) and connected to second oscillator (0 2 ) by pivot (464).
  • Rigid bar (462) is connected to rigid body (460) by pivot (465) and connected to second oscillator (0 2 ) by pivot (466).
  • Rigid bars (461 ) and (462) are related to each other by a 180-degree in-plane rotation about the mid-point of the line segment (463)-(465).
  • the center of mass of rigid body (460) lies on the mid-point of the line segment (463)-(465).
  • the trajectories of pivots (464) and (466) are approximately straight lines parallel to the x-axis.
  • the trajectory of the mid-point of the line segment (463)-(465) is approximately a straight line parallel to the y-axis.
  • Rigid body (450) of oscillator (O c ) is connected to the rigid body (460) of the second oscillator ( 0 2 ) by pivot (457), which may be of any convenient type ensuring that the rigid bodies (450), (460) are unified such that they are constrained to translate together but can rotate with respect to each other.
  • the driving pin (P) can be attached to either rigid body (450) or rigid body (460).
  • Other arrangements of two-layer coupling elements which constrain the first and second oscillators (O ⁇ , ( 0 2 ) to oscillate at 90° to each other, and in which the rigid bodies (450), (460) are constrained to translate in translation but can rotate with respect to each other are also possible.
  • figure 27a illustrates a flexure-based dynamically balanced 1-DOF oscillator based on that of figure 10.
  • the first inertial body (41 ) is anchored to the frame (40) by a flexure pivot comprising two blades (43) and (44), the extension of whose longitudinal axes cross at point (A) so as to form a remote center compliance (RCC) pivot.
  • Point (A) is the center of rotation (and hence the axis of rotation) of the pivot in question.
  • the second inertial body (42) is similarly anchored to the fixed frame (40) by two further blades (45) and (46) the extension of whose axes cross at point (D), which likewise forms the center of rotation and hence axis of rotation of the pivot in question.
  • Inertial bodies (41) and (42) are connected to each other by a coupler link comprising a rigid beam (47) with a flexible blade at each extremity thereof.
  • first inertial body (41 ) lies on point (A) and the center of mass of second inertial body (42) lies on point ( D ).
  • Inertial bodies (41) and (42) are substantially dynamically identical, i.e. they each have equal masses and moments of inertia about their respective centers of mass.
  • Each point on the midline of coupler link (47) is substantially equidistant from point (A) and point ( D ).
  • Flexible blades (43) and (45) are substantially elastically identical and related to each other by a 180-degree in-plane rotation about the mid-point ( O) of coupler link (47).
  • Flexible blades (44) and (46) are substantially elastically identical and related to each other by a 180-degree in-plane rotation about the mid-point (O) of coupler link (47).
  • Figure 27b illustrates a special case of the oscillator of figure 27a in which the line passing through (A) and ( D) is the perpendicular bisector of the bar (57) serving as the coupler link and vice-versa when the oscillator is at rest.
  • the reference signs (50)-(57) correspond respectively to the reference signs (40)-(47) of figure 27a, and need not be re-described here.
  • a pin can be provided as appropriate on one of the inertial bodies or on the coupler link, arranged to be driven by a crank as discussed above in the context of figure 1. Again, this applies to each of the following embodiments where appropriate.
  • Figure 28 illustrates a further variant of an oscillator according to the invention, wherein the coupler link (508) is a substantially rigid beam with negligible mass. This embodiment is analogous to that of figure 1
  • This oscillator comprises first and second inertial bodies (507) and (509) connected by a coupler link (508) with negligible mass.
  • First inertial body (507) is anchored to a fixed frame (500) by an RCC (remote center compliance) pivot comprising two flexible blades (501 ) and (502) whose extended axes cross at point (A), which is on the midline on the inertial body (507).
  • Second inertial body (509) is likewise anchored to the fixed frame (500) by a further RCC (remote center compliance) pivot comprising two flexible blades (504) and (505) whose extended axes cross at point (D), which is again on the midline of corresponding inertial body (509).
  • the coupler link (508) is connected to first inertial body (507) by a single-blade flexure pivot (503), whose center of rotation lies at the mid-point (B) of the flexible blade (503).
  • the coupler link (508) is furthermore connected to second inertial body (509) by a further single-blade flexure pivot (506) having its center of rotation of the pivot lies at the mid-point (C) of the flexible blade (506).
  • Inertial bodies (507) and (509) are substantially dynamically identical, i.e. they have the same mass and the same moment of inertia about their respective pivot points. They are related to each other by a 180-degree in-plane rotation about point (O), which is the mid-point of line segment BC.
  • the length of line segment AB is equal to the length of line segment CD.
  • the flexible blades of each of the pairs (501 ) and (504); (502) and (505); (503) and (506) are kinematically substantially identical and are related to each other by a 180- degree in-plane rotation about point (O) to cancel the effect of gravity on oscillator stiffness.
  • the center of mass of coupler link (508) lies on point (O).
  • line BC is perpendicular to lines AB and CD.
  • Figure 29 illustrates an embodiment of an oscillator according to the invention wherein the coupler link (530) has significant mass and moment of inertia, and is analogous to that of figure 10.
  • First inertial body (529) is anchored to a fixed frame (520) by an RCC (remote center compliance) pivot comprising two flexible blades (521 ) and (522) crossing at point (A), which is at the center of rotation of the pivot.
  • Second inertial body (531 ) is anchored to the fixed frame (520) by a further RCC (remote center compliance) pivot likewise comprising two flexible blades (525) and (526) crossing at point (D).
  • the coupler link (530) is connected to first inertial body (529) by an RCC flexure pivot comprising two yet further flexible blades (523) and (524) the extensions of whose longitudinal axes cross at a point (B), which is the center of rotation of the pivot.
  • the coupler link (530) is likewise connected to second inertial body (531 ) by a yet further RCC flexure pivot comprising another two flexible blades (527) and (528), the extension of whose longitudinal axes crosses at point (C), which is again the center of rotation of the pivot.
  • Inertial bodies (529) and (531 ) are dynamically substantially identical, i.e. they have the same mass and the same moment of inertia about their respective pivot points, and are related to each other by a 180-degree in-plane rotation about point (O), the mid-point of line segment BC.
  • the length of line segment AB is equal to the length of line segment CD.
  • the flexible blades of each of the pairs: (521 ) and (525); (522) and (526); (523) and (527); (524) and (528) are kinematically identical and are related to each other by a 180-degree in- plane rotation about point (O) to cancel the effect of gravity on oscillator stiffness.
  • Figure 30 illustrates a flexure implementation of a 2-DOF dynamically balanced oscillator system comprising two serially connected double inertial bodies. This oscillator system is flexure-based version of that of figure 19, where the rigid pivots and torsional springs are replaced by flexure pivots.
  • First inertial body (541) of second oscillator ( 0 2 ) is anchored to a fixed frame (540) by an RCC pivot comprising two flexible blades (547) and (548) whose longitudinal axes cross at point ( A 2 ).
  • Second inertial body (543) of the second oscillator ( 0 2 ) is anchored to the fixed frame (540) by an RCC pivot comprising two flexible blades (557) and (558) whose axes cross at point ( D 2 ).
  • Inertial bodies (541) and (543) are connected to each other by a coupler link (542).
  • the coupler link (542) is connected to first inertial body (541) by an RCC pivot comprising two flexible blades (549) and (550) whose longitudinal axes cross at point ( B 2 ), and is connected to inertial body (543) by an RCC pivot comprising two flexible blades (559) and (560) whose longitudinal axes cross at point (C 2 ).
  • first inertial body (544) is connected to the coupler link (542) of the second oscillator ( 0 2 ) by an RCC pivot comprising two flexible blades (551) and (552) whose longitudinal axes cross at point (A ⁇ .
  • second inertial body (546) is connected to coupler link (542) by an RCC pivot comprising two flexible blades (554) and (555) whose longitudinal axes cross at point (D ⁇ .
  • Inertial bodies (544) and (546) are connected to each other by corresponding coupler link (545).
  • Coupler link (545) is connected to inertial body (544) by a single-blade flexure pivot (553) and is connected to inertial body (546) by a single-blade flexure pivot (556).
  • the mid-points of flexible blades (553) and (556) lie substantially on points (B ⁇ and (CY), respectively.
  • the driving pin (P) lines substantially on the intersection of the lines l c and y when the system is at rest, where l c is a straight line connecting ( B 2 ) and ( C 2 ), and y is a straight line connecting (B ⁇ and (CY). It should be noted that the lines l c and y are substantially perpendicular.
  • the driving pin (P) lies on the mid-point of line segment B ⁇ and also on the mid-point of line segment B 2 C 2 .
  • the flexible blades of the following pairs are related to each other by a 180- degree in-plane rotation about (P) to cancel the effect of gravity on stiffness of the oscillator; (547) and (557); (548) and (558); (549) and (559); (550) and (560); (551 ) and (554); (552) and (555); (553) and (556).
  • the pin (P) is advantageously be biased away from the intersection of lines l c and y when the crank is not rotating and the movement is at rest. This permits the crank to apply sufficient force when subject to a driving torque to cause the oscillator system to self-start without having to be displaced manually or subjected to a shock.
  • Figures 31a and 31 b illustrate a particular variant of the double-layer coupling element of figure 26 specially adapted for a flexure-based construction, in which two layers (Z ⁇ ), (L 2 ), are superposed one with respect to the other.
  • Z ⁇ two layers
  • L 2 two layers
  • a rigid body (701 ) is connected to first oscillator (O c ) by two rigid bars (700) and (702), these bars (700) and (702) notably being connected to the coupler link of the first oscillator (O ⁇ .
  • Rigid bar (700) is connected to first rigid body (701 ) by a single-blade flexure pivot (704) and is connected to first oscillator (O c ) by another single-blade flexure pivot (705).
  • Rigid bar (702) is likewise connected to second rigid body (701) by single-blade flexure pivot (706) and is connected to first oscillator (O c ) by single-blade flexure pivot (707).
  • First rigid body (701 ) has a plurality of mounting holes (709), (710), (71 1 ) and (712), which can be of any number or can be substituted by other mounting means.
  • the mid-points of flexible blades (704) and (706) lie on a straight line which is perpendicular to rigid bars (700) and (702).
  • Rigid body (700), flexible blade (704) and flexible blade (705) are respectively related to rigid body (702), flexible blade (706) and flexible blade (707) by a 180-degree in-plane rotation.
  • second rigid body (721 ) is connected to second oscillator (0 2 ) by two rigid bars (720) and (722), these bars (720) and (722) likewise being connected to the coupler link of the second oscillator (0 2 ).
  • Rigid bar (720) is connected to rigid body (721 ) by single-blade flexure pivot (724) and connected to second oscillator ( 0 2 ) by another single-blade flexure pivot (725).
  • Rigid bar (722) is connected to rigid body (721 ) by single-blade flexure pivot
  • Rigid body (723) also has mounting holes (729), (730), (731 ) and (732) corresponding to those of the first layer (Z ⁇ ), and is connected to rigid body (721 ) by a flexure pivot comprising two flexible blades (728) and (733) situated in different planes parallel to the xy plane. A single blade flexure in this role is also sufficient.
  • the mid-points of flexible blades (724), (726) and the crossing point of blades (728) and (733) lie on a straight line which is perpendicular to rigid bars (720) and (722).
  • Rigid body (720), flexible blade (724) and flexible blade (725) are respectively related to rigid body (722), flexible blade (726) and flexible blade (727) by a 180-degree in-plane rotation about the crossing point of blades (728) and (733).
  • First oscillator (O c ) has a DOF along the y-axis and second * oscillator ( 0 2 ) has a DOF along the x-axis.
  • Rigid bodies (701 ) and (723) are connected to each other by four screws passing through the corresponding mounting holes, or by other convenient means such as welding, soldering, glue, pins, or similar.
  • Figure 32 illustrates a flexure implementation of the oscillator system of figure 23. This system comprises two independent double inertial body 1-DOF oscillators connected in parallel to form a 2-DOF oscillator system.
  • Rigid body (740) supporting the driving pin (P) is connected to first oscillator (Oi) by a rigid bar (741) which is connected to rigid body (740) by a single- blade flexure pivot (747) and is connected to first oscillator (O c ) by a single- blade flexure pivot (743).
  • Rigid body (740) is likewise connected to second oscillator ( 0 2 ) by a further rigid bar (742) which is connected to rigid body (740) by another single-blade flexure pivot (748) and is connected to second oscillator ( 0 2 ) by a further single-blade flexure pivot (744).
  • Rigid bars (741 ) and (742) extend in superposition to their respective oscillators (O ⁇ , ( 0 2 ) without impinging on them.
  • the coupler link (745) of first oscillator (O c ) is substantially oscillates parallel to the y-axis and the coupler link (746) of second oscillator ( 0 2 ) is substantially oscillates parallel to the x-axis.
  • the mid-points of flexible blade (743) and coupler link (745) are coincident, as are the mid-points of flexible blade (744) and coupler link (746).
  • Figures 33a and 33b illustrate the variables used below in the following discussion of tuning the isochronism of a 1-DOF oscillator according to figure 10.
  • this oscillator comprises two substantially identical inertial bodies each with moment of inertia J 1 about their respective pivot points (A) and ( D ).
  • the inertial bodies are connected to each other by a coupler link of mass m 2 and moment of inertia J 2 about its center of mass which lies on the mid-point ( O) of the line segment BC.
  • the distance between (A) and ( B) is equal to the distance between (Q and ( D) and is denoted by H.
  • the distance between (B) and (C) is denoted.
  • Isochronism can be achieved up to second order by setting
  • Figure 34 which corresponds to the oscillator of figure 28, illustrates the effect of parasitic shift of the pivots on isochronism.
  • this oscillator comprises two substantially identical inertial bodies of mass m 1 and moment of inertia J 1 about their respective centers of rotation (A) and ( D ).
  • the inertial bodies are connected to each other by a coupler link of mass m 2 and moment of inertia J 2 about its center of mass which lies on the mid-point ( O) of the line segment BC.
  • Each of the flexure pivots anchoring the inertial bodies to the fixed frame comprises two identical flexible blades of length and angle 2 a with respect to each other.
  • the distance between the points where the flexible blades are attached to the inertial bodies and the crossing point of the extensions of the axes of each pair of flexible blades is r.
  • the distance between A and B ⁇ s H which is equal to the distance between Cand D.
  • Figures 35a and 35b illustrate the application of the above-mentioned teaching on isochronism to practical oscillators which permit the adjustment of isochronism independently of the frequency of oscillation.
  • the oscillator of figure 35a corresponds to that of figure 10
  • that of figure 25b corresponds to that of figure 28.
  • the coupler link (800), (810) of each oscillator carries a pair of slidable masses (801 ) and (802) in figure 35a, and (81 1) and (812) in figure 35b. Displacement of these masses (801), (802), (811), (812) along the respective coupler link (800), (810) tunes the isochronism of the oscillator since such displacement changes the moment of inertia of the coupler link J 2 without changing mass of the coupler m 2 . Sufficient friction, or other suitable blocking means, are provided so as to ensure that the slidable masses (801), (802) remain in position. Hence, isochronism can be tuned without changing the nominal frequency.
  • the respective masses (801), (802); (811), (812) should be moved symmetrically with respect to the center of mass of the coupler link (800), (810).
  • an asymmetric movement may be advantageous if it is required to move the center of mass of the coupler link (800), (810) in order to balance the oscillator.
  • FIGs 36a to 36e illustrate an embodiment of an oscillator system according to the invention, which incorporates the above teachings.
  • This oscillator system comprises two independent dynamically balanced 1- DOF oscillators (O ⁇ , ( 0 2 ) mounted in parallel in a manner similar to that shown in figure 32.
  • This oscillator comprises a driving pin (P) connected to each 1-DOF oscillator by a two-bar coupling element similar to that of figure 32, each connection incorporating a substantially rigid bar and a pair of single-blade blade flexible pivots.
  • This oscillator also incorporates mechanisms for adjusting isochronism and frequency.
  • the first dynamically balanced 1-DOF oscillator (O c ) comprises two substantially identical inertial bodies, the first of which comprises two relatively heavy masses (905) and (906) rigidly attached to a rigid body (901).
  • a pair of inertia-blocks in the form of radially-adjustable screws (913) and (914) are mounted in appropriate holes located in the periphery of masses (905) and (906) so as to permit the frequency of oscillations to be tuned by modifying the inertia of the inertial body as is generally known.
  • the second inertial body of the first oscillator (O c ) comprises again two relatively heavy masses (907) and (908) rigidly attached to a rigid body (902). Again, radially-adjustable screws (915) and (916) are provided in the periphery of masses (907) and (908) as before.
  • Rigid body (901) is rigidly attached to rigid body (950) and rigid body (902) is rigidly attached to rigid body (949).
  • Rigid body (949) is anchored to the fixed frame (900) by a flexure pivot comprising two flexible blades (930) and (931), the extension of whose longitudinal axes intersect at the theoretical pivot point that they define.
  • Rigid body (950) is similarly anchored to the fixed frame (900) by a similar flexure pivot comprising blades (932) and (933).
  • Rigid bodies (949) and (950) are connected to each other by a coupler link (951), which is connected to rigid body (949) by a single-blade flexure pivot (934), and to rigid body (950) by another single-blade flexure pivot (935).
  • Sliding masses (938) and (939) are mounted such that they can be translated along coupler link (951) so as to permit tuning of the isochronism by changing the moment of inertia of the coupler link (951 ) around its center of gravity.
  • the second dynamically balanced 1-DOF oscillator ( 0 2 ) is constructed similarly to the first oscillator (O ⁇ .
  • Its first inertial body comprises two relatively heavy masses (909) and (910) rigidly attached to a rigid body (903). Again, two screws (917) and (918) are provided on the masses (909) and (910) to tune the frequency of oscillations by changing the inertia of the inertial body.
  • the second inertial body comprises two relatively heavy masses (911) and (912) rigidly attached to a rigid body (904). Again, two further screws (919) and (920) are provided on masses (911) and (912) to tune the frequency of oscillations by changing the inertia of the inertial body.
  • Rigid body (903) is rigidly attached to rigid body (923) and rigid body (904) is rigidly attached to rigid body (921).
  • Rigid body (921) is anchored to the fixed frame (900) by a flexure pivot comprising two flexible blades (924) and (925), the extension of whose longitudinal axes cross.
  • Rigid body (923) is anchored to the fixed frame (900) by a similar flexure pivot comprising two flexible blades (926) and (927).
  • Rigid bodies (921 ) and (923) are connected to each other by a coupler link (922). This latter is connected to rigid body (921) by a single-blade flexure pivot
  • Sliding masses (936) and (937) mounted slidably on coupler link (922) are again arranged to tune isochronism by changing the moment of inertia of the coupler link (922) around its center of gravity.
  • Driving pin (P) is connected to each of the 1 -DOF oscillators by a flexure-based two-bar coupling element which comprises a rigid body (940) supporting the driving pin (P).
  • This rigid body (940) is connected to the coupler links of the oscillators ⁇ O ⁇ , (0 2 ).
  • Rigid body (940) is connected to coupler link (951 ) by a rigid bar (941) and is connected to coupler link (922) by a rigid bar (942), these rigid bars (941 ), (942) being substantially perpendicular to each other.
  • Rigid bar (941 ) is connected to rigid body (940) by a single-blade flexure pivot (946) and is connected to rigid body (943) by another single-blade flexure pivot (945).
  • Rigid bar (942) is also connected to rigid body (940) by a further single- blade flexure pivot (948) and is connected to rigid body (944) by a yet further single-blade flexure pivot (947).
  • Rigid body (943) is rigidly attached to coupler link (951 ) and rigid body (944) is rigidly attached to coupler link (922)
  • Mid-points of flexible blades (945) and (947) lie on the mid-points of coupler links (951 ) and (922) respectively.
  • Flexible blades (924), (925), (930) and (931 ) are substantially elastically identical to flexible blades (926), (927), (932) and (933), respectively.
  • Flexible blades (924) and (925) are related to flexible blades (926) and (927) by a 180-degree in-plane rotation about the mid-point of coupler link (922).
  • Flexible blades (930) and (931 ) are related to flexible blades (932) and (933) by a 180-degree in-plane rotation about the mid-point of coupler link (951 ).
  • Rigid bar (941 ) is perpendicular to rigid bar (942).
  • Coupler link (922) is perpendicular to coupler link (951 ).
  • This oscillator system is insensitive to gravity, insensitive to all linear and angular shocks. It does not transmit torque to the support, and hence has extremely high Q-factor oscillations.
  • the architecture is particularly compact and suitable for integration in a wristwatch.
  • the isochronism and the frequency can be tuned independently, and each individual oscillator (O ⁇ , ( 0 2 ) is independently tunable.
  • the driving pin (P) moves with a relatively long stroke.
  • Figures 37a and 37b illustrate schematically simple crank arrangements suitable for driving a 2-DOF oscillator system and a 1 -DOF oscillator respectively when these are integrated in a timepiece movement (7). These diagrams are highly schematic and are not to scale.
  • a source of energy (M) such as a driving spring or similar, drives a wheel (1), to which is rigidly attached a bar (2) comprising a slot (3).
  • Bar (2) is typically arranged along a radius of the wheel (1) and extends beyond the outer periphery of the wheel (1 ).
  • Driving pin (P) as described above is located slidingly in the slot (3), and as the source of energy (M) causes the wheel (1) to rotate about its own axis (1a) and the crank to cause the driving pin (P) to translate in orbital motion about the axis (1 a) of the wheel (1 ).
  • This driving system applies to the 2-DOF oscillator of figure 18, and also to all the 2-DOF oscillator systems described above.
  • a source of energy such as a driving spring or similar, drives a wheel (1), to which is pivotally mounted a connecting rod (4) by means of an eccentric (5).
  • This connecting rod (4) is pivotally connected to coupler link (6) of a 1-DOF oscillator of any type mentioned above, the rest of the oscillator not being illustrated.
  • Complete rotations of the wheel (1) thus cause the coupler link (6) to carry out substantially linear oscillations since it is constrained by the geometry of the pivots of the oscillator.
  • the length of stroke of the coupler link (6) (and hence of the oscillator of which it is a part) is determined by the geometry of the wheel (1), eccentric (5) and connecting rod

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Abstract

Oscillateur horloger comprenant : - un premier corps inertiel (141 ; 151 ; 1305 ; 1405 ; 1505 ; 301 ; 311 ; 314 ; 41 ; 51 ; 507 ; 529 ; 544 ; 541 ; 901 ; 903) conçu pour tourner par rapport à un premier axe ; - un second corps inertiel (143 ; 153 ; 1306 ; 1406 ; 1506 ; 302 ; 313 ; 316 ; 42 ; 52 ; 509 ; 531 ; 546 ; 543 ; 902 ; 904) conçu pour tourner par rapport à un second axe parallèle audit premier axe ; - au moins un élément élastique (144, 155, 156, 157 ; 154, 155, 156, 157 ; 1319, 1320, 1321, 1322 ; 1419, 1420, 1421, 1422 ; 1501, 1502, 1503, 1504, 1507 ; 305, 306 ; 317, 318, 319, 320 ; 321, 322, 323, 324 ; 43, 44, 45, 46 ; 53, 54, 55, 56 ; 501, 502, 503, 504, 505, 506 ; 521, 522, 523, 524, 525, 526, 527, 528 ; 551, 552, 553, 554, 555, 556, 547, 548, 549, 550, 557, 558, 559, 560 ; 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935) conçu pour appliquer un couple de rappel à au moins un desdits corps inertiels de façon à solliciter ledit corps inertiel vers une position neutre. Conformément à l'invention, l'oscillateur comprend en outre : - un maillon de coupleur sensiblement rigide (142 ; 152 ; 1307 ; 1407 ; 1507 ; 307 ; 312 ; 315 ; 47 ; 57 ; 508 ; 530 ; 545 ; 542 ; 745 ; 746 ; 800 ; 810 ; 922 ; 951) fixé au niveau d'un premier point de pivotement audit premier corps inertiel (141 ; 151 ; 1305 ; 1405 ; 1505 ; 301 ; 311 ; 314 ; 41 ; 51 ; 507 ; 529 ; 544 ; 541 ; 901 ; 903) et au niveau d'un second point de pivotement audit second corps inertiel de telle sorte que lesdits corps inertiels sont conçus pour tourner de manière synchrone autour de leurs axes respectifs, ledit maillon de coupleur sensiblement rigide (142 ; 152 ; 1307 ; 1407 ; 1507 ; 307 ; 312 ; 315 ; 47 ; 57 ; 508 ; 530 ; 545 ; 542 ; 745 ; 746 ; 800 ; 810 ; 922 ; 951) comprenant une barre ou tige et étant conçu pour transmettre une force entre ledit premier corps inertiel (141 ; 151 ; 1305 ; 1405 ; 1505 ; 301 ; 311 ; 314 ; 41 ; 51 ; 507 ; 529 ; 544 ; 541 ; 901 ; 903) et ledit second corps inertiel (143 ; 153 ; 1306 ; 1406 ; 1506 ; 302 ; 313 ; 316 ; 42 ; 52 ; 509 ; 531 ; 546 ; 543 ; 902 ; 904) en fonction d'un vecteur sensiblement aligné le long d'un axe (λ2) reliant les premier et second points de pivotement.
PCT/EP2019/051188 2018-01-18 2019-01-17 Oscillateur horloger WO2019141789A1 (fr)

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EP3936946A1 (fr) * 2020-07-10 2022-01-12 Patek Philippe SA Genève Oscillateur horloger a pivot flexible
NL2029137B1 (en) * 2021-09-06 2023-03-21 Flexous Mech Ip B V An oscillator for a mechanical watch

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EP4325301A1 (fr) * 2022-08-17 2024-02-21 Patek Philippe SA Genève Mécanisme horloger comprenant un organe horloger rotatif et un dispositif à raideur angulaire prédéfinie

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Publication number Priority date Publication date Assignee Title
EP3936946A1 (fr) * 2020-07-10 2022-01-12 Patek Philippe SA Genève Oscillateur horloger a pivot flexible
NL2029137B1 (en) * 2021-09-06 2023-03-21 Flexous Mech Ip B V An oscillator for a mechanical watch

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