EP4369113A2 - Mechanism for displaying the phases of the moon - Google Patents

Abstract

The invention relates to a moon phase display mechanism driven by a clockwork movement, this moon phase display mechanism (1) comprising a transparent support (98) provided with an upper face (100) and a lower face (102) which extends at a distance from the upper face (100), a representation (104) of the Moon being transferred to one of the upper (100) or lower (102) faces of this support transparent (98), a substrate (106) being arranged under the transparent support (98), at a distance from the lower face (102) of the latter, the moon phase display mechanism (1) also comprising a shutter ( 94) which is driven by drive means (72) driven by the clockwork movement and which is arranged to move between the transparent support (98) and the substrate (106), the shutter (94) and the substrate (106) having display contrasts reversed relative to each other, the shutter (94) being moved from an initial position to a final position for a duration of a lunar cycle, so as to reveal day after day to an observer the aspect of the Moon which passes from the new moon to the first quarter moon, then from the first quarter moon to the full moon, then to the last quarter moon and finally to the new moon, the the shutter (94) being recalled by the drive means from its final position to its initial position at the end of the lunation.

Description

Technical field of the invention

The present invention relates to a moon phase display mechanism. More precisely, the moon phase display mechanism according to the invention is intended to equip a small portable object such as a timepiece, in particular a wristwatch.

Technological background of the invention

Timepieces, in particular wristwatches, equipped with a moon phase display mechanism have been known for a long time. These moon phase display mechanisms are nevertheless more decorative than they provide information allowing the owner of the watch to easily determine in which quarter of the moon he is located. The simplest moon phase display mechanisms include a needle indicator that points to the different representations of the phases of the Moon (first quarter, full moon, last quarter, new moon). Other known moon phase display mechanisms include a disc which carries two representations of the Moon, part of this disc being visible through a suitably shaped opening in the dial of the watch and successively revealing a waxing moon , a full moon, a waning moon and a new moon. Such a presentation of the different phases of the Moon is very advantageous from an aesthetic point of view; nevertheless, the way in which the Moon is represented has only a distant relationship with the way in which the lunar body appears in the sky. Yet another moon phase display mechanism includes a two-color sphere that makes a complete rotation on itself each lunar cycle. Such a moon phase display mechanism makes it possible to represent the face of the Moon in a manner realistic. However, because such a moon phase display mechanism uses a sphere to represent the different quarters of the Moon, it is thick and takes up a lot of space, so that it is difficult to integrate into a movement of the Moon. horology in particular a wristwatch.
We also know of the document WO91/11756 a device for representing the moon, particularly on the dial of a watch.

Summary of the invention

The present invention aims to provide a moon phase display mechanism which provides a moon phase display which is notably more faithful to reality and more easily understandable for the owner of the watch.

To this end, the present invention relates to a moon phase display mechanism driven by a clockwork movement according to claim 1 of the patent.

Thanks to the combined use of a plano-concave lens, preferably aspherical, and a shutter with a curved profile, preferably but not limited to the hyperbolic type, the observer sees a terminator, that is to say the curve which separates the illuminated part from the dark part of the Moon, whose profile is very realistic and very faithful to what the user can see when observing the Moon in the sky. Furthermore, the moon phase display mechanism is more compact than a moon phase display mechanism using a sphere and can thus be accommodated in a smaller volume such as that of a one-piece box. wristwatch type timepieces. By way of example, we consider that for a representation of the Moon of the same diameter, the moon phase display mechanism according to the invention is half as thick as a moon phase display mechanism using a sphere. Of Likewise, we understand that, as the surface which receives the representation of the Moon is flat, the moon phase display mechanism according to the invention does not hinder the movement of the hands on the surface of the dial.

According to a special embodiment of the invention, the drive means comprise a rectilinear rack which is driven by the clockwork movement and with which the shutter is coupled in a fixed manner in translation.

Thanks to these characteristics, the present invention provides a moon phase display mechanism making it possible to display the different aspects of the Moon day after day in an original manner and easily intelligible by the user. In particular, the representation of the Moon which is provided by the moon phase display mechanism according to the invention is very close to the real appearance of the Moon in the sky, so that it is much simpler for the user to determine which period of the lunar cycle the Moon is in. The moon phase display mechanism according to the invention is also thinner than those using a sphere rotating on itself, and therefore easier to integrate into a clock movement, in particular a wristwatch. Furthermore, regardless of the district in which the Moon is located, its representation is always visible to the owner of the watch. It will also be noted that the moon phase display mechanism according to the invention makes it possible to obtain a representation of the different phases of the realistic Moon, formed by two surfaces of different colors and separated by a terminator, that is to say say the curve which separates the illuminated part from the dark part of the Moon, whose profile is very realistic and very faithful to what the user can see when observing the Moon in the sky. This is particularly the case during the first and last quarter of the moon, when optical distortions are almost zero and the terminator thus appears perfectly rectilinear.

Brief description of the figures

• la figure 1 est une vue en plan du mécanisme d'affichage de phases de lune selon l'invention ;
• la figure 2 est une vue de détail à plus grande échelle du trou oblong dans lequel la goupille portée par le doigt fait saillie ;
• la figure 3A est une vue de détail à plus grande échelle de la première bascule dans sa position intermédiaire A
• la figure 3B est une vue de détail à plus grande échelle de la première bascule dans sa position extrême B dans laquelle elle est en appui contre le sommet du profil du doigt ;
• la figure 4A est une vue de détail à plus grande échelle du premier râteau dans sa position C dans laquelle son bec palpeur se trouve au sommet du profil de la came ;
• la figure 4B est une vue de détail à plus grande échelle du premier râteau dans sa position D dans laquelle son bec palpeur tombe le long du décrochement de la came ;
• la figure 5 est une vue de dessus du support transparent et de la tôle à partir desquels la lentille plan-concave asphérique et l'obturateur sont obtenus ;
• la figure 6 est une vue en élévation et en coupe de l'ensemble optique formé par la lentille plan-concave asphérique, l'obturateur et le substrat ;
• la figure 7 est une vue schématique de dessus qui illustre l'aspect de la représentation de la Lune tel qu'il peut être perçu par l'observateur lorsque l'obturateur commence à pénétrer dans l'espace qui sépare la lentille plan-concave asphérique du substrat ;
• la figure 8A est une vue schématique du mécanisme d'affichage des phases de lune lorsqu'il se trouve dans sa position extrême E au début d'un cycle lunaire ;
• la figure 8B est une vue analogue à celle de la figure 8A qui illustre le mécanisme d'affichage des phases de lune selon l'invention lorsqu'il se trouve dans sa position extrême F à la fin du cycle lunaire, et
• les figures 9A à 9L illustrent l'aspect du terminateur selon plusieurs positions de l'obturateur à profil courbe, de préférence hyperbolique.

Other characteristics and advantages of the present invention will emerge more clearly from the detailed description which follows of an exemplary embodiment of a moon phase display mechanism according to the invention, this example being given for purely illustrative purposes and non-limiting only in conjunction with the attached drawing in which:

• there figure 1 is a plan view of the moon phase display mechanism according to the invention;
• there figure 2 is a larger-scale detail view of the oblong hole into which the pin carried by the finger protrudes;
• there Figure 3A is a detailed view on a larger scale of the first rocker in its intermediate position A
• there Figure 3B is a detailed view on a larger scale of the first rocker in its extreme position B in which it rests against the top of the profile of the finger;
• there figure 4A is a larger scale detail view of the first rake in its position C in which its feeler tip is at the top of the cam profile;
• there Figure 4B is a detailed view on a larger scale of the first rake in its position D in which its feeler tip falls along the recess of the cam;
• there Figure 5 is a top view of the transparent support and the sheet metal from which the aspherical plano-concave lens and the shutter are obtained;
• there Figure 6 is an elevational and sectional view of the optical assembly formed by the aspherical plano-concave lens, the shutter and the substrate;
• there figure 7 is a schematic top view which illustrates the appearance of the representation of the Moon as it can be perceived by the observer when the shutter begins to penetrate the space that separates the aspherical plano-concave lens from the substrate;
• there Figure 8A is a schematic view of the moon phase display mechanism when it is in its extreme position E at the start of a lunar cycle;
• there Figure 8B is a view analogous to that of the Figure 8A which illustrates the moon phase display mechanism according to the invention when it is in its extreme position F at the end of the lunar cycle, and
• THE Figures 9A to 9L illustrate the appearance of the terminator according to several positions of the shutter with a curved profile, preferably hyperbolic.

Detailed description of an embodiment of the invention

The present invention proceeds from the general inventive idea which consists of transferring a representation of the Moon on one or the other of the two upper and lower faces of a transparent support which is placed above and at a distance from a substrate, with the interposition of a shutter between the transparent support and the substrate. The face of the Moon can be depicted in a color similar to that of the substrate, while the shutter and the substrate have reverse contrasts: if the substrate is light, then the shutter will be dark, and vice versa, if the substrate is dark, the shutter will be clear. Assuming, as an illustrative example only, that the representation of the Moon and the substrate are dark and the shutter is light, it is understood that when the shutter is not in the space between the transparent support and the dark substrate, the representation of the Moon which is above the dark substrate is not perceptible to the observer. Then, as the light shutter penetrates the space which separates the transparent support from the dark substrate, the representation of the Moon gradually becomes perceptible to the user. The present invention thus provides a more compact mechanism that moon phase display mechanisms which include a sphere and which make it possible to display the moon phases in an original and much more realistic manner than most art moon phase display devices allow prior. Consequently, the observer has a much easier time understanding which period of the lunar cycle he or she is in. Furthermore, the realism is further increased if, in accordance with a special form of execution of the invention, the transparent support is given a plano-concave profile preferably but not necessarily aspherical and such a transparent support is combined with a curved shutter, preferably hyperbolic in profile. Such a combination makes it possible to obtain a terminator whose profile is very faithful to that observed in reality as the Moon grows, becomes full, then decreases and the lunar cycle resumes.

Housed for example in a timepiece such as a wristwatch, the moon phase display mechanism 1 according to the invention is driven by a clockwork movement, that is to say a mechanism whose the operation depends on the division of time. More precisely, the clock movement comprises a timer mobile of which a pinion (not visible in the figures) drives a 24-hour wheel 2 which, as its name indicates, is arranged so as to complete one complete revolution per day.

The 24-hour wheel 2 carries a finger 4 on an axis 6 of which this finger 4 is mounted free to rotate. To be able to pivot relative to the 24-hour wheel 2, the finger 4 is mounted on the axis 6 with a slight axial play thanks to a ring 8 engaged on this axis 6. Furthermore, the finger 4 is provided with a pin 10 which projects into an oblong hole 12 made in the thickness of the 24-hour wheel 2 and which limits the freedom of pivoting of the finger 4 relative to the 24-hour wheel 2 (see figure 2 ). We therefore understand that when the pin 10 abuts against an interior wall 14 of the oblong hole 12, it is rotated by the 24-hour wheel 2 and in turn drives the finger 4 which, too, makes a complete revolution in 24 hours.

The moon phase display mechanism 1 according to the invention also comprises a first rocker 16 which is pivotally mounted around a pivot axis 18 and which is applied elastically against a first part 20a of a profile 20 of the finger 4 by an upper spring 22. We also note in the drawing the presence of a star 24 whose position is indexed by a jumper 26 which is held elastically against a toothing 28 of this star 24 by a lower spring 30.

The 24-hour wheel 2 turns clockwise, driving with it the finger 4. The first rocker 16 thus slides along the first part 20a of the profile 20 of the finger 4 and, after passing through a position intermediate A ( Figure 3A ), finds itself in an extreme position B ( Figure 3B ) in which it is supported by a foot 32 against a vertex 34 of the profile 20 of the finger 4. Furthermore, the first rocker 16 comes into engagement via a nose 36 with the teeth 28 of the star 24. When, for example around midnight, the finger 4 advances further, the first rocker 16 exceeds the extreme position B in which it rests against the vertex 34 of the profile 20 of the finger 4, and drives the star 24 one step in the direction counterclockwise. This movement is made possible by the fact that at the moment when the first rocker 16 exceeds the vertex 34 of the profile 20 of the finger 4, a leverage effect occurs on the finger 4 which causes the pivoting of this finger 4 and the concomitant movement of the pin 10 which, abutting against one end of the oblong hole 12 made in the thickness of the 24-hour wheel 2, will move to abut against the opposite end of this oblong hole 12. Then, the first rocker 16 begins to slide again along a second part 20b of the profile 20 of the finger 4 which is located after the vertex 34 of this profile 20. It will be noted that at the very moment when the first rocker 16 causes the advance of a step of the star 24, the jumper 26 passes, against the restoring force of the lower spring 30, from a hollow between two consecutive teeth of the teeth 28 of the star 24 to the immediately following hollow of this toothing 28 . Falling back into the next hollow, the saltire 26 allows the star 24 to complete its advance of one step and once again ensures the precise positioning of this star 24.

According to a preferred but non-limiting mode of execution of the moon phase display mechanism according to the invention, it also comprises a manual device for correcting the moon phase display. Designated as a whole by the general numerical reference 38, this manual correction device comprises a second rocker 40 pivoted around an axis 42 and which comprises an actuating means 44 such as a pin at an end opposite the axis pivot 42. This second rocker 40 comprises for example a folded zone 46 against which a corrector (not visible in the drawing) rests when the latter is actuated against the elastic return force of a spring by the owner of the wristwatch from outside the volume of the watch case. Under the effect of actuation of the corrector, the second rocker 40 pivots around its axis 42 and in turn controls the pivoting of the first rocker 16 so as to cause the star 24 to advance by one step. This advance of the star 24 takes place under the same conditions as those described above when the first rocker exceeds the vertex 34 of the profile 20 of the finger 4.

According to a preferred mode given for purely illustrative and non-limiting purposes only, a complete revolution of the star 24 corresponds to two successive lunar cycles, a lunar cycle corresponding to the time which elapses between two new successive Moons and which is also called month lunar. For this purpose, the moon phase display mechanism according to the invention is completed by a first pinion 50 mounted coaxially and fixed in rotation on the star 24, by a return 56 as well as by a cam 52 on the the axis of rotation of which is fixed fixed a second pinion 54. The first pinion 50 drives the second pinion 54 via the gearbox 56, the tooth ratios of this kinematic chain being calculated so that the cam 52 makes one revolution complete per lunar cycle.

The cam 52 has a spiral profile 58 provided with a substantially rectilinear recess 60. A first rake 62 equipped with a toothed sector 64 is also provided with a feeler tip 66 by which it permanently follows the profile 58 of the cam 52. Shortly before the start of a new lunar cycle, for example at around midnight, the feeler tip 66 of the first rake 62 is located at the top of the profile 58 of the cam 52 (position C - Figure 4A ), then falls along the recess 60 of the cam 52 (position D - figure 4B ). During this movement, the first rake 62 which, through its toothed sector 64, is in permanent engagement with a third pinion 68, causes this third pinion 68 to rotate clockwise by an amount corresponding to the fall of the feeler tip 66 along the recess 60.

By rotating, the third pinion 68 rotates a wheel 70 with which it forms a mobile 69. In other words, the third pinion 68 is mounted on the wheel 70 coaxially and fixed in rotation relative to this wheel 70. Consequently, the wheel 70 transmits its rotational movement to drive means 72 of the moon phase display mechanism 1 which comprise a lower wheel 74 and an upper wheel 78 mounted free to rotate on an axis of rotation 76. The lower wheel 74 meshes with a rectilinear rack 80 which in turn meshes with the upper wheel 78.

According to the invention, the lower wheel 74 is responsible for controlling the moon phase display mechanism 1. For this purpose, by pivoting, the lower wheel 74 drives the rectilinear rack 80 in translation and pushes it back into a first extreme position E illustrated in Figure 8A which corresponds to the start of a new lunar cycle. Subsequently, when, after having fallen along the recess 60 of the cam 52 at the start of the lunar cycle, the feeler tip 66 begins to follow the profile 58 of the cam 52 again, the feeler tip 66 is gradually pushed back into the clockwise towards a second extreme position F (see Figure 8B ), so that the third pinion 68, and therefore the wheel 70, rotate counterclockwise. Consequently, the lower wheel 74 turns clockwise and drives the rectilinear rack 80 in translation from the right to the left of the drawing from its first extreme position E which corresponds to the start of a new lunar cycle up to its second position extreme E illustrated in Figure 8B which corresponds to the end of the lunar cycle. Once the feeler tip 66 has traveled the entire length of the profile 58 of the cam 52, it will again find itself at the top of the recess 60 of the cam 52 and, at the start of a new lunar cycle, the feeler tip 66 will fall along the recess 60, which will cause the rectilinear rack 80 to return to its initial position.

The moon phase display mechanism according to the invention is supplemented by a device which makes it possible to compensate for the gaps and return this moon phase display mechanism to its extreme position E at the end of a lunar cycle. This device consists of the upper wheel 78 engaged on the one hand with the teeth of the rectilinear rack 80, and on the other hand with an intermediate wheel 82 of an intermediate mobile 84 which also includes an intermediate pinion 86. This pinion intermediate 86 meshes with a toothed sector 88 of a second rake 90 which is elastically constrained by the restoring force of a fourth spring 92. Thanks to this arrangement, all the play in the kinematic chain which extends between the first rake 62 and the second rake 90, so that the positioning of the rectilinear rack 80 is always precise.

According to the invention, the moon phase display mechanism 1 comprises the rectilinear rack 80 with which a shutter 94 is coupled in a fixed manner in translation. The moon phase display mechanism 1 also comprises, on the side of an observer 96, a transparent support 98 provided with an upper face 100 which extends parallel to and at a distance from a lower face 102. A representation 104 of the Moon, for example in the form of a decal, is transferred to the upper face 100 of the transparent support 98. This representation 104 of the Moon could also be transferred to the lower face 102 of the transparent support 98. A substrate 106 is, relative to the observer 96, placed under the transparent support 98, at a distance from this last. The shutter 94 is mounted on the rectilinear rack 80 so as to be able to gradually penetrate into the space which separates the transparent support 98 from the substrate 106 when the rectilinear rack 80 is driven by the lower wheel 74. The shutter 94 and the substrate 106 has inverted contrasts: either the shutter 94 is light and the substrate 106 as well as the representation 104 of the Moon are dark, or the shutter 94 is dark and the substrate 106 as well as the representation 104 of the Moon are clear. Assuming, by way of example only, that the representation 104 of the Moon and the substrate 106 are dark and that the shutter 94 is light and reflective, it is understood that when the shutter 94 is not in space located between the transparent support 98 and the dark substrate 106, the representation 104 of the Moon is above the dark substrate 106 and is therefore not perceptible by the observer 96. Then, as the clear and reflective shutter 94 enters the space which separates the transparent support 98 from the dark substrate 106, the representation 104 of the Moon gradually becomes perceptible by the user. More precisely, when the shutter 94 begins to penetrate the space between the transparent support 98 and the dark substrate 106, the observer 96 gradually sees the first quarter of the moon appear. Then, when the reflective shutter 94 is completely between the transparent support 98 and the dark substrate 106, the observer 96 sees the representation 104 of the Moon in full: it is the full moon. Then, the shutter 94 continues its rectilinear movement in the same direction and begins to leave the space between the transparent support 98 and the dark substrate 106, so that the observer 96 sees the last quarter of the moon gradually appear, situation which corresponds to the moment when the shutter 94 leaves the same surface free as masked. Finally, when the shutter 94 is completely out of the space between the transparent support 98 and the dark substrate 106, the observer 96 again no longer sees the representation 104 of the Moon (in the hypothesis where the substrate 106 is of the same color as representation 104 of the Moon) and therefore knows that the lunar cycle has ended and that a new lunar cycle will begin. Thus, thanks to the invention, the observer 96 has an easily intelligible representation of the different phases of the Moon: new moon, first quarter moon, full moon, last quarter moon then new moon again.

According to a particular mode of execution of the invention, the transparent support 98 is in the form of a lens 108 of plano-concave shape delimited upwards, on the side of the observer 96, by a flat surface 110 which receives the representation 104 of the Moon, and delimited downwards by a concave surface 112 which is given a preferably aspherical profile. This aspherical plano-concave lens 108 is combined with a shutter 94 folded in its center to give it a curved profile, preferably but not necessarily hyperbolic. We thus obtain an image of the Moon whose terminator, that is to say the curve which separates the dark part from the illuminated part of the Moon, comes as close as possible to the real appearance of the Moon in the sky.

To determine the geometric dimensions of the aspherical plano-concave lens 108 and the shutter 94 with hyperbolic profile, computer-aided optical system design software is used such as that marketed under the brand LightTools, version 8 of which has been published in 2019 was used for the purposes of the present invention.

• le matériau dans lequel va être réalisée la lentille plan-concave asphérique 108 et donc l'indice de réfraction de cette dernière ;
• le profil de la surface concave asphérique 112 de la lentille plan-concave asphérique 108 et donc sa constante de conicité ;
• les dimensions de l'obturateur 94 ;
• la distance qui sépare le sommet de la voûte formée par la surface concave asphérique 112 et l'obturateur 94 ;
• le profil courbe, de préférence hyperbolique, de l'obturateur 94 et donc sa constante de conicité.

Once the dimensions of the representation 104 of the Moon that we want to be able to display by means of the moon phase display mechanism according to the invention have been defined, the main parameters on which it is possible to act to obtain a representation realistic phases of the Moon are:

• the material in which the aspherical plano-concave lens 108 will be made and therefore the refractive index of the latter;
• the profile of the aspherical concave surface 112 of the aspherical plano-concave lens 108 and therefore its conicity constant;
• the dimensions of the shutter 94;
• the distance which separates the top of the vault formed by the aspherical concave surface 112 and the shutter 94;
• the curved profile, preferably hyperbolic, of the shutter 94 and therefore its conicity constant.

As a preferred example only, the aspherical plano-concave lens 108 is made of a transparent material whose refractive index is preferably between 1.60 and 1.85, with an optimal value around 1.78. This value was chosen after numerous tests which made it possible to note that, the higher the value of the refractive index of the material in which the lens is made, the closer it was necessary to bring the lens closer to the shutter 94 so that this latter is not visible to the observer through this lens. It is easy to understand that this is favorable from the point of view of space requirements in the case where it is desired to integrate a moon phase display device conforming to the present invention in a timepiece of the wristwatch type. On the other hand, the higher the refractive index, the more expensive and difficult the corresponding material is to machine. Furthermore, we realized that when the lens becomes too close to the shutter 94, we end up seeing the image of the peripheral edge of the lens which forms an opaline to lactescent crown around the representation 104 of the Moon , which is not acceptable. Likewise, it was noted that by selecting refractive index values that were too low, the image of the shutter 94 with a curved and preferably hyperbolic profile which gradually came to cover the representation of the Moon was not very aesthetic. , nor really realistic compared to the true representation of the Moon. This is why a value of around 1.60 to 1.85 and preferably equal to or substantially equal to 1.78 for the optical refractive index of the material in which the aspherical plano-concave lens 108 is made appeared to be an optimum making it possible to provide the best compromise between optical refraction index of the material in which is made the aspherical plane-concave lens 108 and the distance separating the aspherical concave surface 112 from the aspherical plane-concave lens 108 and the shutter 94, and thus obtain a moon phase display mechanism whose size is compatible with the dimensions of the timepiece in which this mechanism is intended to be housed while providing a terminator whose profile is suitable. An example of a material which is well suited for the purposes of the present invention is the glass produced and marketed by Schott under the reference N-SF 11.

We then introduce into the computer-aided design software the dimensions of a block of transparent or at least translucent material such as a glass cylinder or a polymer such as polycarbonate from which the aspherical plano-concave lens 108 is obtained. . In the present case, the aspherical plano-concave lens 108 is obtained by machining a block of cylindrical glass whose diameter D is between 6 mm and 7 mm and whose height H is between 0.9 mm and 1.1 mm (see Figure 5 ).

With regard to the shutter 94 with a hyperbolic profile, this is obtained from a rectangular-shaped sheet whose thickness e is preferably but not limited to between 0.08 mm and 0.2 mm, and whose length l of side which extends parallel to the direction of movement of the shutter 94 is chosen to be between 7 mm and 8 mm, while the width L of the side which extends perpendicular to the direction of movement of this shutter 94 is chosen to be between between 9mm and 10mm. This sheet is provided in its center with a fold 114 which extends in a direction parallel to the direction of movement of the shutter 94 and preferably has flat edges 116 parallel to the fold 114. note in fact that it is not necessary for the shutter 94 to retain its hyperbolic profile up to its ends because, in these zones, the optical distortion effect is produced essentially by the aspherical plano-concave lens 108. These flat edges 116 therefore only have the function of completely obstructing the field of vision provided by the aspherical plano-concave lens 108 and, due to their flatness, these edges 116 make it possible to reduce the bulk of the phase display mechanism of moon.

où k = -e² The profile of the aspherical concave surface 112 of the aspherical plano-concave lens 108 is determined by the values of the distances r and z(r). If we call S the central axis of symmetry of the aspherical plano-concave lens 108, the distance r corresponds to the distance which separates each point of the central axis of symmetry S from the point of the aspherical concave surface 112 which is located opposite (see Figure 6 ). Likewise, the hyperbolic profile of the shutter 94 is determined by the distance r' which separates each point of the plane of symmetry S' of this shutter 94 from the surface of the latter. These distances r , r' are determined using the same relationship below: $$z\left(r\right)=\frac{\frac{r^2}{R}}{1+\sqrt{1-\left(1+k\right)\frac{r^2}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}}}+{\displaystyle \sum _{\mathrm{not}=1}^{\mathrm{NOT}}{\mathrm{HAS}}_{\mathrm{not}}\cdot r^{\mathrm{not}}}$$

where k = -e ²

As visible on the Figure 6 , the origin of the function z(r) corresponds to the point O which is at the top of the vault formed by the aspherical concave surface 112. The value of the function z(r) corresponds, at each point of the vault formed by the aspherical concave surface 112, at the height of this point considered from the base of the aspherical plane-concave lens 108.

The values of the constants R and k which characterize the aspherical plano-concave lens 108, as well as those of the constants R' and k' which characterize the shutter 94 will be determined by successive iterations in the manner described below. As for the coefficients A _n , these are coefficients of a polynomial sum whose values will also be determined by iterations.

As for the aspherical plano-concave lens 108, the constant R corresponds to the radius of curvature of the aspherical concave surface 112 at point O which is at the top of the vault formed by this aspherical concave surface 112. So that the terminator T which is the dividing line between the dark part and the illuminated part of the Moon appears rectilinear in the middle of the lunar cycle, it is necessary that in the vicinity of point O the concave aspherical surface 112 is practically flat. For this purpose, a very large value of the radius of curvature R , of the order of several thousand millimeters, is initially introduced into the computer-aided design software. As for the constant “k” which is called “conic constant”, it is a quantity which describes the conic sections. By conical section, we mean a plane curve defined by the intersection of a cone of revolution with a plane. When the cutting plane does not pass through the vertex of the cone, its intersection with this cone corresponds to one of the following plane curves: ellipse, parabola or hyperbola.

We note that k = -e ² with e which corresponds to the eccentricity of the conic section. The eccentricity of a conic section is a positive real number which only characterizes the shape of this conic section; The eccentricity of a conic section can be interpreted as a measure of the amount by which a conic section deviates from a circle. Thus, the eccentricity of a circle is zero. The eccentricity of an ellipse that is not a circle is strictly between zero and one. The eccentricity of a parabola is equal to 1 and the eccentricity of a hyperbola is greater than 1.

qui décrit une section conique dont l'apex est à l'origine et dont la tangente s'étend selon l'axe « y » et où R est le rayon de courbure pour x = 0. Cette formule est utilisée en optique géométrique pour décrire la surface optique d'une lentille. Dans le cas qui nous intéresse, on a initialement indiqué au logiciel de conception assistée par ordinateur que la constante de conicité était nulle (k = 0), autrement dit que l'on avait affaire à un cercle.The conic constant k occurs in the equation $${\mathrm{y}}^{}$$$${\mathrm{}}^2-2\mathrm{Rx}+\left(\mathrm{k}+1\right){\mathrm{x}}^2=0$$

which describes a conical section whose apex is at the origin and whose tangent extends along the "y" axis and where R is the radius of curvature for x = 0. This formula is used in geometric optics to describe the optical surface of a lens. In the case that interests us, the computer-aided design software was initially told that the conicity constant was zero (k = 0), in other words that we were dealing with a circle.

Consequently, with regard to the aspherical plano-concave lens 108, the simulation begins with a zero value of the conical constant k and a very large value of the radius of curvature R.

It is the same with regard to the shutter 94 for which the simulation begins with a zero value of the conical constant k' and a very large value of the radius of curvature R' . It is important to note that the shutter 94 can be considered as the object whose image is perceived through the aspherical plano-concave lens 108 and, as such, its geometric characteristics can be determined by software. computer-aided design of optical systems such as LightTools.

Finally, we consider that the aspherical plano-concave lens 108 is of even order, so that we start by arbitrarily choosing values for the coefficients A ₄ , A ₆ and A ₈ . In the initial choice of the values of the coefficients A ₄ , A ₆ and A ₈ , the person skilled in the art is guided by the fact that he knows that the values of these coefficients are very low and that they continue to decrease over time. as the index n increases. We also decide to stop at the coefficient A ₈ because the contribution of the higher order coefficients to the improvement of the resulting appearance of the terminator T is negligible. Concerning the coefficient A ₂ , this is ignored because the first term of the expression z(r) already contains the square of the variable r .

Using computer-aided design software, a representation 118 of the Moon and its terminator T is simulated for several positions of the shutter 94 (see figures 7 And 9A to 9L ). To the Figure 9A , we are at the start of a lunar cycle. To the Figure 9C , the Moon is in its first quarter. To the figure 9F , we are in the middle of the lunar cycle and the Moon is full. There Figure 9I corresponds to the last quarter of the Moon and the figure 9L We are at the new Moon. To carry out the simulations, we begin, for example, to vary the values of the parameters A _n as well as the conical constant k and the radius of curvature R which characterize the aspherical plano-concave lens 108, while we keep unchanged the values of the parameters A' _n as well as the conical constant k' and the radius of curvature R' which characterize the shutter 94, and we observe on the computer screen the resulting appearance of the terminator T. We repeat the experiment, this time keeping constant the values of the parameters A _n , k and R which characterize the aspherical plano-concave lens 108, and by varying the values of the parameters A' _n as well as k ' and R ' which characterize the shutter 94, and we observe on the computer screen the resulting appearance of the terminator T by means of the "Photorealistic Rendering" function of the LightTools software. This function makes it possible to visualize the entire device formed by the aspherical plano-concave lens, the hyperbolic shutter and the substrate as if this device were photographed at the desired angles and distances. Thanks to the “Photorealistic Rendering” function, it is possible to verify that the desired optical effect is suitable. We proceed in this way step by step until we obtain a profile of the terminator T which we consider faithful to its real appearance and with which we are satisfied. Of course, this is a purely subjective criterion which is left to everyone's discretion.

It will be noted that for the dimensional characteristics of the aspherical plano-concave lens 108 and the shutter 94 mentioned above, the most satisfactory results as to the visual appearance of the terminator T were obtained for the values k = -1 and R = 20840 mm and A ₄ = 3.769.10 ^-3 , A ₆ = 2.9534.10 ^-5 and A ₈ = -1.407.10 ^-7 with regard to the aspherical plano-concave lens 108, and for the values k '= -4.922 and R' = 2.556 mm and A ₄ = 1.654.10 ^-5 , A ₆ = -1.511.10 ^-6 and A ₈ = 4.686.10 ^-8 with regard to shutter 94. It will be observed that As for the value of the conicity constant k, the value retained for the aspherical plano-concave lens 108 is equal to -1, which corresponds to a parabolic profile. As for the value of the conicity constant k' which characterizes the profile of the shutter 98, this is less than -1, which corresponds to a hyperbolic profile.

Thus, the point O which is located at the top of the vault formed by the aspherical concave surface 112 is at a distance P equal to 0.78 mm relative to the base of the cylindrical glass block. Consequently, we deduce that at this point O, the thickness of the aspherical plano-concave lens 108 is 0.22 mm. This is the minimum thickness of the aspherical plano-concave lens 108.

It goes without saying that the present invention is not limited to the embodiment which has just been described and that various modifications and simple variants can be envisaged by those skilled in the art without departing from the scope of the invention as defined. by the appended claims. Note in particular that, in the case where the shutter is clear, it can be covered with a layer of phosphorescent material such as that marketed under the registered trademark Super-LumiNova ^® . It should also be noted that in order to avoid light reflection phenomena, the surface of the shutter can advantageously have roughness. Still with the same aim of limiting light reflections as much as possible, the plano-concave lens can be subject to anti-reflective treatment and its edges can be metallized. According to a particular mode of the invention not shown in the drawing, it can be planned to provide the cam 52 with two recesses 60. Given that the star 24 makes a complete revolution in two lunar cycles, it is then possible to put the star 24 in direct connection with cam 52, and thus saving pinions 50 and 54 and return 56.

Nomenclature

• 1. Moon phase display mechanism
• 2. 24 hour wheel
• 4. Finger
• 6. Axis
• 8. Ring
• 10. Pin
• 12. Oblong hole
• 14. Inner wall
• 16. First seesaw
• 18. Pivot axis
• 20. Profile
• 22. Upper spring
• 24. Star
• 26. Long necklace
• 28. Teeth
• 30. Lower spring
• 32. Foot
• 34. Summit
• 36. Beak
• 38. Manual correction device
• 40. Second seesaw
• 42. Pivot axis
• 44. Means of actuation
• 46. Bent area
• 50. First gear
• 52. Cam
• 54. Second gear
• 56. Reference
• 58. Profile
• 60. Unhook
• 62. First rake
• 64. Toothed sector
• 66. Feeling tip
• 68. Third gear
• 69. Mobile
• 70. Wheel
• 72. Means of training
• 74. Lower wheel
• 76. Axis of rotation
• 78. Upper wheel
• 80. Rectilinear rack
• 82. Intermediate wheel
• 84. Intermediate mobile
• 86. Intermediate gear
• 88. Toothed sector
• 90. Second rake
• 92. Fourth spring
• 94. Shutter
• 96. Observer
• 98. Transparent support
• 100. Upper side
• 102. Underside
• 104. Representation of the Moon
• 106. Substrate
• 108. Aspherical plano-concave lens
• 110. Flat surface
• 112. Aspherical concave surface
• 114. Fold
• 116. Flat edges
• 118. Representation of the Moon

Claims (13)

Moon phase display mechanism driven by a clockwork movement, this moon phase display mechanism (1) comprising a transparent support (98) provided with an upper face (100) and a lower face (102) which extends at a distance from the upper face (100), a representation (104) of the Moon being transferred to one of the upper (100) or lower (102) faces of this transparent support (98), a substrate (106) being arranged under the transparent support (98), at a distance from the lower face (102) of the latter, the moon phase display mechanism (1) also comprising a shutter (94) which is driven by drive means (72) driven by the clockwork movement and which is arranged to move between the transparent support (98) and the substrate (106), the shutter (94) and the substrate (106) having display contrasts reversed relative to each other, the shutter (94) being moved from an initial position to a final position for a duration of a lunar cycle, so as to reveal day after day at an observer (96) the aspect of the Moon which passes from the new moon to the first quarter moon, then from the first quarter moon to the full moon, then to the last quarter moon and finally to the new moon, the shutter (94) being recalled by the drive means from its final position to its initial position at the end of the lunar cycle, mechanism in which the transparent support (98) is in the form of a lens (108) of planar shape -concave delimited upwards, on the side of the observer (96), by a flat surface (110) on which is transferred the representation (104) of the Moon, and delimited downwards by a concave surface (112) which has a curved profile, this aspherical plano-concave lens (108) being combined with the shutter (94) which has a curved profile. Display mechanism according to claim 1, characterized in that the drive means (72) comprise a rack rectilinear (80) with which the shutter (94) is coupled in a fixed manner in translation. Display mechanism according to claim 2, characterized in that the drive means (72) comprise a lower wheel (74) and an upper wheel (78) on an axis of rotation (76) of which is mounted free to rotate the lower wheel (74) which meshes with the rectilinear rack (80). Display mechanism according to one of claims 2 or 3, characterized in that the clockwork movement comprises a timer mobile which kinematically drives a cam (52) which makes a complete revolution on itself in an integer number of times a lunar cycle, this cam (52) having a profile (58) permanently followed by a first rake (62), this first rake (62) being provided with a toothed sector (64) by which it meshes with the means drive (72) of the moon phase display mechanism (1). Display mechanism according to claim 4, characterized in that the first rake (62) is provided with a feeler tip (66) by which it permanently follows the profile (58) of the cam (52), this profile ( 58) being shaped like a spiral and being provided with at least one substantially rectilinear recess (60) so that, shortly before the start of a new lunar cycle, the feeler tip (66) is at the top of the profile ( 58) of the cam (52), then falls along the recess (60), the first rake (62) driving during this movement by its toothed sector (64) a pinion (68) which is kinematically connected to the means of drive (72) of the moon phase display mechanism (1). Moon phase display mechanism according to one of claims 4 or 5, characterized in that it is supplemented by a backlash compensation device which consists of the upper wheel (78) in engagement, on the one hand with the rectilinear rack (80), and on the other hand with an intermediate wheel (82) of an intermediate mobile (84) which also includes a intermediate pinion (86), this intermediate pinion (86) meshing with a toothed sector (88) of a second rake (90) which is elastically constrained by the return force of a fourth spring (92). Moon phase display mechanism according to one of claims 1 to 6, characterized in that the optical refractive index of the material in which the plano-concave lens (108) is made is between 1.60 and 1.85. Moon phase display mechanism according to claim 7, characterized in that the optical refractive index is equal to or substantially equal to 1.78. Moon phase display mechanism according to one of claims 1 to 8, characterized in that the plano-concave lens (108) is made of glass or polymer. Moon phase display mechanism according to one of claims 1 to 9, characterized in that the concave surface (112) is curved. Moon phase display mechanism according to claim 10, characterized in that the concave surface (112) has an aspherical profile. Moon phase display mechanism according to one of claims 10 or 11, characterized in that the shutter (94) has a curved profile. Moon phase display mechanism according to claim 12, characterized in that the shutter (94) has a hyperbolic profile.

Images