A mechanical watch

The mechanical watch addresses the challenge of low torque energy efficiency and accuracy by using a mechanical oscillator with curved transitions on the pallets and escape wheel teeth, ensuring continuous contact and reliable energy transfer.

EP4498173A1Inactive Publication Date: 2025-01-29FLEXOUS MECHANISMS IP BV
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Patent Information

Application Number
EP2023188471
Authority / Receiving Office
EP · EP
Patent Type
Applications
Current Assignee / Owner
Filing Date
2023-07-28
Publication Date
2025-01-29
Estimated Expiration
Not applicable · inactive patent

AI Technical Summary

Technical Problem

Mechanical watches face challenges in maintaining energy efficiency and accuracy at low torque levels supplied by storage springs, while also ensuring robustness against shocks.

Method used

The mechanical watch incorporates a mechanical oscillator with pallets on an anchor or flexures and an escape wheel with teeth, where at least one of the pallets and the teeth feature a dead face and an impulse face with curved transitions. These curved transitions ensure continuous contact during the impulse phase, optimizing energy transfer even at low torque levels.

Benefits of technology

This configuration allows the mechanical watch to operate efficiently and accurately at low torque levels, maintaining robustness against shocks and ensuring reliable energy transfer, thereby extending the watch's running time.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present disclosure relates to a mechanical oscillator (1) of or for a watch, comprising: pallets (15, 16) on an anchor or on flexures; and an escape wheel (14) carrying teeth (17), wherein at least one of the pallets (15, 16) and the teeth (17) comprise a dead face (18, 25) and an impulse face (19; 21). According to the present disclosure transitions between the dead faces (18, 25) and the impulse faces (19; 21) comprise a curvature.
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Description

[0001] The present disclosure relates to a mechanical oscillator and a watch comprising such an oscillator.

[0002] Mechanical watches are disclosed in, for example, NL-2024076 and in EP-4145228 in the name of the same applicant as the present disclosure. Alternate prior art is disclosed in JP-2011128153 and CH-713144, in the names of other manufacturers.

[0003] The present disclosure is directed at improving energy efficiency and accuracy at low levels of torque supplied by storage springs, preferably without compromising qualities such as robustness against shocks.

[0004] According to the invention a mechanical watch is now proposed with features of one or more of the appended claims, and in particular the appended independent claim.

[0005] Although different embodiments according to the invention are feasible, the mechanical oscillator of or for a watch, both according to the present disclosure, comprises: pallets on an anchor or on flexures; and an escape wheel carrying teeth, wherein at least one of the pallets and the teeth comprise a dead face and an impulse face, and transitions between the dead faces and the impulse faces comprise a curvature.

[0006] Preferably, the curvature of the transitions is designed to maintain contact between the teeth and the pallets at least at the start of an impulse imparting phase, in which the escape wheel is partially released for rotation and one of the teeth pushes a contacting pallet away. Preferably, the curvature of the transitions is determined, dependent on at least a torque of the escape wheel, which decreases in time, as a driving spring or coil winds down. Then, the torque of the escape wheel, at which curvature of the transitions is determined, may be a low torque, at which the oscillator is still properly operable. The low torque may be at most 30%, more preferably less than 20% and most preferably at least approximately 10% of the full torque after full rewinding.

[0007] Preferably, the curvature of the transitions is determined on the basis of a trajectory of one of the teeth and one of the pallets relative to one another, after transitioning to the impulse face, and the curvature at least bridges any distance there between. Then, at least impulse faces may be are formed to extend beyond the trajectory. Additionally or alternatively, the trajectory may be determined based on a simulation, and the simulation may then optionally be based on a point mass as an approximation of the anchor (4), condensed into a free end tip thereof. Additionally or alternatively, the curvature of the transitions may be determined on the basis of a mathematical formula defining the trajectory.

[0008] Preferably, the curvature of the transitions is devoid of any discontinuity, in the form of sudden change in directions of tangent lines, when moving through the transition from dead face to impulse face.

[0009] Preferably, effective lengths of the dead faces are unaffected by the curved transitions.

[0010] As noted above, the present disclosure also relates to a regulator for a watch to regulate watch movement, comprising the oscillator, pallets, and escape wheel according to any one of the preceding claims. As also noted above, the present disclosure also relates to a mechanical watch, comprising an oscillator and a dial with underlying drives, together configured to keep time.

[0011] The invention will hereinafter be further elucidated with reference to the drawing of exemplary embodiments of elements of a mechanical watch according to the invention that is not limiting as to the appended claims.

[0012] In the drawing: Fig. 1 schematically shows selected parts forming an oscillator of a mechanical watch according to the prior art in a frontal view; Fig. 2 schematically shows selected forming an oscillator of a mechanical watch according to more traditional prior art of a deadbeat escapement, also in a frontal view; Fig. 3 illustrates a configuration of contacting impulse faces on teeth and pallets; Fig. 4 illustrates a troublesome jump occurring in operation of the oscillator; Fig. 5 illustrates a proposed solution to remedy or mitigate issues caused by the troublesome jump in Fig. 4; Fig. 6 illustrates a corresponding proposed solution for the configuration of contacting impulse faces on teeth and pallets; and Fig. 7A and Fig. 7B illustrate the issues caused by the troublesome jump at respectively low and high torque.

[0013] Wherever in the figures the same reference numerals are applied, these numerals refer to the same or similar parts.

[0014] In the drawing, parts that are not essential to understanding of the prior art or the invention have been omitted, and Fig. 1 depicts features that a prior art watch and one according to the invention may have in common.

[0015] For proper understanding of the invention, hereinafter first a brief discussion of the prior art mechanical watch will be provided with reference to Fig. 1. Fig. 1 depicts a portion of a mechanical watch, forming or comprising an oscillator 1. The oscillator 1 is, in the shown configuration, embodied with vibratory masses 2, 3 mounted on a frame 5. Frame 5 can be considered a part of the oscillator 1 or of other portions of the watch, depending on interpretation. However, such a distinction is immaterial for the teaching of the present disclosure. Herein each of the masses 2, 3 connects to at least one flexural member 6-13. Fig. 1 shows the application of two masses 2, 3, but this number is arbitrary; there should at least be one vibratory mass.

[0016] The oscillator 1 further comprises an escape wheel 14 with teeth 17, and pallets 15, 16 on anchor 4. The pallets 15, 16 (that could also be referred to as anchor teeth, also in embodiments according to the present disclosure) would be arranged on a more traditional anchor (having a shape of an anchor), that may, for example be driven by a hairspring or balance spring. However, in this prior embodiment, the anchor is not traditional but in accordance to the present applicant's own prior art publications NL-2024076 and EP-4145228, in which the pallets 15, 16 are indirectly connected with the vibratory mass or masses 2, 3. The pallets 15, 16 cooperate with the teeth 17 on the escape wheel 14, wherein motions of the pallets 15, 16 depend on motions of one or more of those flexural members 10, 11, 12, 13 that provide connections between the vibratory masses 2, 3 without said flexural members 10, 11, 12, 13 connecting directly to the frame 5. In order to realize that the motions of the pallets 15, 16 depend on motions of one or more of said flexural members 10, 11, 12, 13, the pallets 15, 16 are mounted on anchor 4, forming a movable rigid portion of the oscillator 1, while the flexural members 10, 11, 12, 13 provide connections between the vibratory masses 2, 3 without said flexural members 11, 12 connecting directly to the frame 5. Other configurations are disclosed on NL-2024076 and / or EP4145228, or yet further configurations may be prior art relative to these specifically mentioned publications.

[0017] The oscillator 1 in Fig. 1 is therefore embodied with a frame 5 supporting a vibratory mass or masses 2, 3, wherein each vibratory mass 2, 3 connects to at least one flexural member 6-13. Further, the oscillator 1 comprises an escape wheel 14 with teeth 17 extending outward, and pallets 15, 16 on anchor 4 that are indirectly connected with the vibratory mass or masses 2, 3. The pallets 15, 16 cooperate with the teeth 17 on the escape wheel 14, wherein motions of the pallets 15, 16 depend on motions of a selection of one or more of the flexural members 10, 11, 12, 13 that provide connections between the vibratory masses 2, 3 without said flexural members 10, 11, 12, 13 connecting directly to the frame 5.

[0018] In this prior art configuration, a selection of the flexural members 10, 11, 12, 13 that provide connections between the vibratory masses 2, 3 without connecting directly to the frame 5 are free from rigid sections and support an anchor 4 forming a movable rigid portion of the oscillator 1 that is separate from the flexural members 10, 11, 12, 13, which anchor 4 is suspended from the movable masses 2, 3 through said flexural members 10, 11, 12, 13 that are free from rigid sections.

[0019] In the embodiment of figure 1, the pallets 15, 16 are directly provided on a separate movable rigid portion, which acts in a manner comparable with a traditional anchor 4.

[0020] In the embodiment of Fig. 1 the anchor 4 is supported by parallel flexural members 10, 11 and parallel flexural members 12, 13 that provide connections between the vibratory masses 2, 3 through the anchor 4 without said flexural members 10, 11, 12, 13 connecting directly to the frame 5.

[0021] However, the teachings of the present disclosure may be applicable to more and other configurations of anchors and escape wheels to form oscillator 1, than those shown in Fig. 1. For example a very traditional configuration of a so-called 'deadbeat escapement' is shown in Fig. 2.

[0022] In the deadbeat escapement, pallets 15, 16 each have a 'dead' face 18 and an angled 'impulse' face 19.

[0023] Dead faces 18 of pallets 15, 16 have a circular curvature (indicated with the dashed lines) centered on a rotation axis 20 about which anchor 4 rotates. When a tooth 17 of the escape wheel 14 abuts an outward oriented dead face 18 of the left side pallet 15, while the anchor 4 pivots, escape wheel 14 doesn't rotate and remains locked in place, precisely because of the curvature of the dead face 18, and recoil is prevented. This locked state of the escape wheel 14 is referred to as the dead phase.

[0024] In Fig. 2, as the anchor 4 with the pallet 15 thereon pivots in the direction of the arrow in the dashed line (representing the rotation of the anchor 4 at the moment in time as well as curvature of the dead face), the tooth 17 previously abutting the dead face 18, transitions to abutting the impulse face 19 and is thereby already partially released for rotational movement, for the system to enter the phase of imparting an impulse . The impulse face 19 is angled such that the tooth 17 of the escape wheel 14 gives a push against the slanted impulse face 19, and hence the expression `impulse face' 19. When this tooth 17 falls of the slanted impulse face 19, escape wheel 14 is briefly released entirely for rotation. Such a time of free rotation (which can also be expressed as an angle of free rotation), should be kept as brief (small angle) as possible, as such time / angle of free rotation directly results in a loss of energy. However, this time / angle of free rotation cannot be made zero, as the oscillator 1 would then not work. Moreover, pallets 15, 16 and teeth 17 have non-zero dimensions (thicknesses), whereby a goal of zero free rotation time or angle is impossible.

[0025] Length of the dead faces 18 of the pallets 15, 16 along the respective dashed curvature lines corresponds with a time period during which the escape wheel 14 needs to be arrested to prevent recoil. A length of the impulse faces 19 corresponds with the time during which contact between one of the teeth 17 of escape wheel 14 and the impulse face of one of the pallets 15, 16 is required to impart the desired impulse.

[0026] After the left pallet 15 releases the tooth 17 of the escape wheel 14, another tooth 17 of escape wheel 14 is caught on inward oriented dead face 18 of right pallet 16, to arrest the escape wheel 14 for a next portion of the swing of the anchor 4. In the shown deadbeat configuration (also known as the graham escapement) it's undesirable for the another tooth 17 to bounce on dead face 18 of the right pallet 16, as this would affect the frequency of the oscillator. Lateron - as the anchor 4 pivots - that tooth 17 transitions from engaging the inward dead face 18 of pallet 16 (dead phase) to engaging the slanted impulse face 19, in an impulse imparting phase, in which the teeth 17 on the escape wheel 14 push the pallets 15, 16 away. Thereafter this tooth 17 falls off the slanted impulse face 19 of the right pallet 16 in a free rotation phase. Thereafter, the other pallet 15 catches opposite tooth 17 to begin a new dead phase.

[0027] Above, different important design parameters are identified. In one particular attempt to reduce energy losses, dead faces 18 and impulse faces 19 on both the pallets 15, 16 as well as dead faces 25 and impulse faces 21 on the teeth 17 of escape wheel 14 have been introduced. In such a configuration, teeth 17 on escape wheel 14 are also provided with slanted impulse faces 21, and instead of a pointed end of teeth 17 (as in Fig. 2), a combined contact of the impulse faces 19, 21 sliding over one another contributes to generating the required impulse, after the tooth 17 has slid off the dead face 18 and contact is established between the impulse face 19, 21. As a consequence, the pallets 15, 16 may be made thinner at the free end thereof, where the impulse face 19 is arranged. For clarity, this thickness of the pallets 15, 16 is the dimension of the pallets 15, 16 in tangential direction relative to the rotational direction of the escape wheel 14. This allows a distance between teeth 17 of escape wheel 14 to be reduced, and with that a reduction of the free rotation time or angle can be achieved. Furthermore, acceleration time of the escape wheel 14 is shortened and with that the velocity at the end of the acceleration, reducing the chance of a bounce of a tooth 17 when being caught on and by dead face 18 of one of the pallets 15, 16.

[0028] In view of the knowledge above, and already incorporated into the present disclosure, the configuration of a deadbeat escapement in Fig. 2 and the configuration of contacting impulse faces on teeth and pallets in Fig. 3 may encounter another problem associated with a jump from the transition between the dead face and the impulse face (affecting energy efficiency and frequency stability), exemplified in Fig. 4. Fig. 4 illustrates a configuration of an escape wheel 14 with teeth 17 that have a dead face 25 and an impulse face 21 while the pallet 15, 16 is pointed at a free end of the dead face 18 (different from both configurations of Fig. 2 and Fig. 3). The jump may result in partial or entire contact loss between the impulse face 21 of the tooth 17 and the pointed end of the pallet 16.

[0029] With the present disclosure, it is intended to be able to furnish an oscillator 1 that is capable of running longer, i.e. at lower torque, while maintaining a desired accuracy. At the same time, it is envisaged that the impulse for the right and left pallets 15, 16 is equal and / or symmetric.

[0030] Depicted in Fig. 4 is a situation in which pallet 16 may respond sluggishly when the tip of the dead face 18 transitions from the dead face 25 to the impulse face 21 of a tooth 17. Such a situation may in particular occur, when torque is running low and the anchor 4 is moving reciprocally at high speeds. As the dead face 18 on the pallet 16 is withdrawn in the direction of the arrow drawn in the pallet 16, and a tip thereof moves past edge 22 between the dead face 25 and the impulse face 21 on tooth 17, it will practically be impossible for the escape wheel 14 to start its rotation in the phase of imparting an impulse immediately in the direction of the arrow on the tooth 17, in particular if speed of movement of the pallets 15, 16 is high relative to the velocity of the teeth 17 on escape wheel 14, with a risk that the tip of the dead face 18 on the pallet 16 will jump from and over the edge 22 onto the impulse face 21 of the tooth 17, with detrimental effect on frequency stability, or that the imparted impulse is not strong enough as the tip of the dead face 18 of the pallet 16 and the impulse face 21 of the tooth 17 on the escapement wheel 14 are not in contact over the length of the impulse face 21. In an extreme situation, the tooth 17 can mis contact with the tip of the dead face 18 of pallet 16 altogether. During the phase of imparting an impulse, the transfer of energy is less reliable and / or predictable.

[0031] A similar situation may arise in a conventional configuration like the deadbeat escapement of Fig. 2 and / or a configuration of contacting impulse faces on teeth and pallets of Fig. 3 (but driven at higher than conventional anchor speeds), and the proposed manner of addressing this issue is the same.

[0032] The proposed adaptation to overcome or at least mitigate this issue, is illustrated in Fig. 5 for the configuration of Fig. 4 and in Fig. 6 for the configuration of contacting impulse faces on teeth and pallets of Fig. 3, and the same approach may be deployed for the configuration of Fig. 2.

[0033] To arrive at the configuration of Fig. 5 with an extended or re-formed impulse face 21', a trajectory 24 of the tip of the dead face 18 the pallet 16 was determined, as illustrated in fig. 7A for low torque and in Fig. 7B for higher torque. To this end, a non-limiting simulation was used, based on the assumption of a point mass as an approximation of the anchor 4, compressed into the tip at the end of the dead face 18 on the pallet 16 thereof. More in particular, the trajectory of the tip of the dead face 18 of the pallet 16 and the straight impulse face 21 of the tooth 17 as in Fig. 4 relative to one another was determined. Fig. 7A illustrates the resulting trajectory of the tip relative to straight impulse face 21 on tooth 17, with said originally straight impulse face 21 projected here as stationary, and the tip of the pallet 16 moving relative thereto, but in reality both move relative to one another. Based thereon, the straight impulse face 21 of the tooth 17 in Fig. 4 may be adapted to the determined trajectory 24 to exhibit re-formed impulse face 21' in Fig. 5, but in Fig. 7 the re-formed impulse face 21' is set slightly beyond the determined trajectory 24, relative to the straight face 21.

[0034] Determining the trajectory 24 for adjusting the re-formed impulse face 21', starting from the straight impulse face 21, was done with low torque as a starting point. Preferably, a situation was taken into account with the lowest working torque, that still yields proper operation of the oscillator 1, and of the watch in which the oscillator 1 is deployed. Although the adjusted or re-formed impulse face 21' may follow the expected or calculated trajectory 24 or be wider than trajectory 24, in an additional or alternative embodiment, the adjusted impulse face 21', reformed on the basis of the determined trajectory, follows a curvature outside or along the trajectory 24 at low torque, up to a point where a tangent line is oriented in parallel to the unadjusted impulse face 21, and then flattens off, as shown at the dashed line 26 in Fig. 7A and 7B. For example, a remaining torque of 30% may be used to calculate or determine the trajectories of the tip of the dead face 18 of the pallet 16 and the straight impulse face 21 of the tooth 17 relative to one another, to re-form the straight impulse face 21 of the teeth. Alternatively, such a threshold may be below 20% or at least approximately equal to 10%. The watch may be expected to never be operating at a lower torque, since the owner is likely to tension the coils thereafter, by rewinding the watch, before such low torque occurs. Under other circumstances, i.e. with high(er) torque, the escape wheel 14 will respond less sluggish and more quickly, and - if at all jumping - then jumping closer to edge 22 than if a low torque situation exists, as will be appreciated from comparison of the trajectories 24 in Fig. 7A for low torque and in Fig. 7B for higher torque.

[0035] It is noted that by taking the low torque into account for determining the trajectory 24 and re-forming of the straight impulse face 21 into impulse face 21', the high torque situation will automatically also improve. Fig. 7A illustrates in dashed lines a determined trajectory 24 of the tip of the dead face 18 of the pallet 16 relative to the straight impulse face 21 on the tooth 17 in Fig. 4 for a situation with low torque, while Fig. 7B illustrates an alternative trajectory for higher torque. Forcing the tip of the pallet 16 to follow the trajectory along reformed impulse face 21' (determined from a low torque situation and extending beyond the low torque trajectory 24) even in a situation of high(er) torque of Fig. 7B has no detrimental effects; the required impulse is imparted, and any jump is prevented.

[0036] Preferably, the re-formed impulse face 21' is rounded / blunted (at what was the discontinuous edge 22) so as not to be able to pointedly identify any such discontinuous edge 22 to the impulse face 21 as in Fig. 4 anymore; only a smooth transition range 23. Preferably, the transition from dead face to impulse face 21' on tooth 17 does not have any discontinuity, in the form of for example a sudden change in directions of tangent lines, when moving through the transition from dead face 25 to impulse face 21', that could result in loss of contact between the tip of dead face 18 of pallet 16 and impulse face 21 on tooth 17. Preferably, re-formed impulse face 21' extends (slightly) into or beyond the determined trajectory 24 of the tip of the dead face 18, as illustrated in Fig. 7A and Fig. 7B, to not just maintain contact, but ensure a secure transfer of energy and impart the required impulse. A time during which the escape wheel 14 is arrested by the anchor 4 or any one of the pallets 15, 16 thereof, must ensure that there's no recoil. Consequently, the lengths of contacting parts of the dead face 18 and any opposite part should not decrease, as a consequence of the adaptation at the transition from dead face 18, 25 to the impulse face 19, 21, 21'.

[0037] In Fig. 6, discontinuous edges between dead faces 18, 25 and impulse faces 19, 21 on pallet 16 / tooth 17 are blunted or rounded in the same or a similar manner as described immediately above in relation to Fig. 5, to yield transitional area 23 to replace any discontinuous edge, like the edge 22 in Fig. 4.

[0038] The trajectory 24 of the tip of the dead face 18 of the pallet 16 in Fig. 7 may be approximated using one or more mathematical formulae. These all suffer from assumptions and simplification, but still allow valuable insight into the reasoning underlying the above proposed solution to the jump issue. Therefore, to approximate the trajectory 24 of the tip of the dead face 18 of the pallet 16 relative to the straight face 21 with an abrupt or discontinuous edge 22 relative to the dead face 18, it may be assumed that the velocity of the escape wheel 14 is constant between transitioning from the dead face 18 onto the angled but straight impulse face 19 and release from the impulse face 19. More accurate formula may be developed, but at the expense of higher complexity and elaborateness. However, the following and relatively simple approximation has already been found to yield very effective approximations of the trajectory 24, and adjustment of the straight impulse face 21 into a re-formed impulse face 21'. Such an approximation could, for instance yield the following formulae to express the trajectory 24: x = ω r anchor t y = τ min r wheel 2 I wheel t 2

[0039] Therein, the following quantities are: t : time in seconds; τ : minimum working torque on the escapement wheel; r wheel : radius of the escapement wheel r anchor : radius of the anchors rotational point to the anchor point ω : angular velocity of the anchor (which is a function of frequency of the oscillator, amplitude of the oscillator and transmission between the oscillator and anchor), and I wheel : Inertia of the escapement wheel

[0040] The change of x, y coordinates in time can also provide a measure of the speed of the pallet and the teeth relative to each other.

[0041] Although the invention has been discussed in the foregoing with reference to exemplary embodiments of the mechanical watch of the invention, the invention is not restricted to these particular embodiments which can be varied in many ways without departing from the invention. The discussed exemplary embodiments shall therefore not be used to construe the appended claims strictly in accordance therewith. On the contrary the embodiments are merely intended to explain the wording of the appended claims without intent to limit the claims to these exemplary embodiments. The scope of protection of the invention shall therefore be construed in accordance with the appended claims only, wherein a possible ambiguity in the wording of the claims shall be resolved using this exemplary embodiment.

[0042] In some prior art, pallets are referred to as anchor teeth, but this has the same meaning here as ion the prior art. Likewise, the escape wheel is sometimes in prior art not considered to constitute a part of the oscillator. However, a regulator or escapement, to which the present disclosure both also relates, would then include the escape wheel with the oscillator and the anchor with the teeth or pallets thereof.

Claims

1. A mechanical oscillator (1) of or for a watch, comprising: - pallets (15, 16) on an anchor (4) or on flexures; and - an escape wheel (14) having teeth (17), - wherein at least one of the pallets (15, 16) and the teeth (17) comprise a dead face (18, 25) and an impulse face (19; 21), and - transitions between the dead faces (18, 25) and the impulse faces (19; 21) comprise a curvature.

2. The mechanical oscillator according to claim 1, wherein the curvature of the transitions is formed to maintain contact between the teeth (17) and the pallets (15, 16) at least at the start of an impulse imparting phase, in which the escape wheel (14) is partially released for rotation and one of the teeth (17) pushes a contacting pallet (15, 16) away.

3. The mechanical oscillator according to claim 1 or 2, wherein the curvature of the transitions is determined, dependent on at least a torque of the escape wheel (14), which decreases over time, as a driving spring or coil winds down.

4. The mechanical oscillator according to claim 3, wherein the torque of the escape wheel (14) at which curvature of the transitions is determined, is a low torque, at which the oscillator (1) is still properly operable.

5. The mechanical oscillator according to claim 4, wherein the low torque is at most 30%, more preferably less than 20% and most preferably at least approximately 10% of the full torque after full rewinding.

6. The mechanical oscillator according to any preceding claim, wherein the curvature of the transitions is determined on the basis of a trajectory of one of the teeth (17) and one of the pallets (15, 16) relative to one another, after transitioning to the impulse face (19; 21), and the curvature bridges any distance there between.

7. The mechanical oscillator according to claim 6, wherein at least impulse faces (19; 21) are formed to extend beyond the trajectory.

8. The mechanical oscillator according to claim 6 or 7, wherein the trajectory is determined based on a simulation.

9. The mechanical oscillator according to claim 8, wherein the simulation is based on a point mass as an approximation of the anchor (4), condensed into a free end tip thereof.

10. The mechanical oscillator according to any of the preceding claims 6 - 9, wherein the curvature of the transitions is determined on the basis of a mathematical formula defining the trajectory.

11. The mechanical oscillator according to claim 10, wherein the formula is x = ω r anchor t y = τ min r wheel 2 I wheel t 2 and wherein: t : time in seconds; τ : minimum working torque on the escapement wheel; rwheel: radius of the escapement wheel; ranchor: radius of the anchors rotational point to the anchor point; ω : angular velocity of the anchor (which is a function of frequency of the oscillator, amplitude of the oscillator and transmission between the oscillator and anchor); and Iwheel : Inertia of the escapement wheel.

12. The mechanical oscillator according to any preceding claim, wherein the curvature of the transitions is devoid of any discontinuity, in the form of sudden change in directions of tangent lines, when moving through the transition from dead face (18, 25) to impulse face (19, 21').

13. The mechanical oscillator according to any preceding claim, wherein effective lengths of the dead faces (18; 25) are unaffected by the curved transitions.

14. A regulator for a watch to regulate watch movement, comprising the oscillator, pallets, and escape wheel according to any one of the preceding claims.

15. A mechanical watch, comprising an oscillator (1) according to any one or more of the preceding claims and a dial with underlying drives, together configured to keep time.

Citation Information

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