Mechanism for displaying the phases of the moon

Abstract

The invention relates to a moon phase display mechanism powered by a clockwork movement, this moon phase display mechanism (1) comprising a transparent support (98) having an upper face (100) and a lower face (102) extending at a distance from the upper face (100), a representation (104) of the Moon being projected onto one of the upper (100) or lower (102) faces of this transparent support (98), a substrate (106) being disposed under the transparent support (98), at a distance from its lower face (102), the moon phase display mechanism (1) also comprising a shutter (94) which is driven by drive means (72) powered 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 during a lunar cycle, so as to reveal day after day to an observer the appearance of the Moon as it 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 returned by the drive means from its final position to its initial position at the end of the lunar cycle.

Description

Technical field of the invention

[0001] The present invention relates to a moon phase display mechanism. More specifically, 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

[0002] Timepieces, particularly wristwatches, equipped with a moon phase display mechanism have been known for a long time. These moon phase display mechanisms are, however, more decorative than they provide information allowing the watch owner to easily determine which quarter of the moon they are in. The simplest moon phase display mechanisms include a hand 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 that carries two representations of the Moon, part of this disc being visible through a suitably shaped opening in the watch dial and revealing successively 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; however, the way in which the Moon is represented bears only a distant relation to the way in which the lunar body appears in the sky. Yet another mechanism for displaying moon phases comprises a two-colored sphere that makes a complete rotation on itself during each lunar cycle. Such a moon phase display mechanism makes it possible to represent the face of the Moon in a realistic manner. 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 it into a watch movement, particularly in a wristwatch. Also known from WO91 / 11756 is a device for representing the moon, in particular on the dial of a watch. Summary of the invention

[0003] The present invention aims to provide a moon phase display mechanism which provides a moon phase display which is in particular more faithful to reality and more easily understandable for the owner of the watch.

[0004] 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.

[0005] Thanks to the combined use of a plano-concave lens, preferably aspherical, and a shutter with a curved profile, preferably but not limited to 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, the profile of which is very realistic and very faithful to what the user can see when observing the Moon in the sky. In addition, the moon phase display mechanism is more compact than a moon phase display mechanism using a sphere and can thus be housed in a smaller volume such as that of a case of a timepiece of the wristwatch type. As an example, it is considered 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.Likewise, it is understood that, since 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.

[0006] 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 fixedly coupled in translation.

[0007] Thanks to these characteristics, the present invention provides a moon phase display mechanism that allows the different aspects of the Moon to be displayed day after day in an original manner that is easily understood by the user. In particular, the representation of the Moon provided by the moon phase display mechanism according to the invention is very close to the actual appearance of the Moon in the sky, so that it is much simpler for the user to determine in which period of the lunar cycle the Moon is located. The moon phase display mechanism according to the invention is also less thick than those using a sphere rotating on itself, and therefore easier to integrate into a watch movement, particularly a wristwatch. In addition, regardless of the quarter 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 realistic representation of the different phases of the Moon, formed by two surfaces of different colors and separated by a terminator, that is to say the curve which separates the illuminated part from the dark part of the Moon, the profile of which 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 straight. Brief description of the figures

[0008] Other characteristics and advantages of the present invention will emerge more clearly from the following detailed description of an exemplary embodiment of a moon phase display mechanism according to the invention, this example being given purely for illustrative and non-limiting purposes only in conjunction with the appended drawing in which: there figure 1 is a plan view of the moon phase display mechanism according to the invention; figure 2 is a larger-scale detail view of the oblong hole into which the pin carried by the finger projects; Figure 3A is a larger scale detail view of the first rocker in its intermediate position A la Figure 3B is a larger-scale detail view of the first rocker in its extreme position B in which it rests against the top of the finger profile; Figure 4Ais a larger scale detail view of the first rake in its position C in which its feeler beak is at the top of the cam profile; Figure 4B is a larger-scale detail view of the first rake in its position D in which its feeler beak falls along the cam recess; the 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; the figure 6 is an elevational and sectional view of the optical assembly formed by the aspherical plano-concave lens, the shutter and the substrate; figure 7 is a schematic top view illustrating the appearance of the representation of the Moon as it can be perceived by the observer when the shutter begins to penetrate the space separating the aspherical plano-concave lens from the substrate; Figure 8Ais a schematic view of the moon phase display mechanism when it is in its extreme position E at the start of a lunar cycle; 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 curved profile shutter, preferably hyperbolic. Detailed description of an embodiment of the invention

[0009] The present invention proceeds from the general inventive idea which consists of transferring a representation of the Moon onto one or the other of the two upper and lower faces of a transparent support which is arranged 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 represented in a color similar to that of the substrate, while the shutter and the substrate have inverted contrasts: if the substrate is light, then the shutter will be dark and, conversely, if the substrate is dark, the shutter will be light.Assuming, for illustrative purposes only, that the representation of the Moon and the substrate are dark and that the shutter is clear, 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 that is above the dark substrate is not perceptible to the observer. Then, as the clear shutter penetrates the space between the transparent support and the dark substrate, the representation of the Moon gradually becomes perceptible to the user. The present invention thus provides a mechanism that is more compact than moon phase display mechanisms that include a sphere and that allows the moon phases to be displayed in a novel and much more realistic manner than most prior art moon phase display devices.Consequently, it is much easier for the observer to understand which period of the lunar cycle he is in. Furthermore, realism is further increased if, in accordance with a special embodiment of the invention, the transparent support is given a preferably but not necessarily aspherical plano-concave profile and such a transparent support is combined with a curved shutter, preferably with a hyperbolic profile. Such a combination makes it possible to obtain a terminator whose profile is very faithful to that observed in reality as the Moon waxes, becomes full, then wanes and the lunar cycle resumes.

[0010] 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 operation depends on the division of time. More precisely, the clockwork movement comprises a timer wheel set, a pinion of which (not visible in the figures) drives a 24-hour wheel 2 which, as its name indicates, is arranged so as to make one complete revolution per day.

[0011] The 24-hour wheel 2 carries a finger 4 on an axle 6 of which this finger 4 is mounted free to rotate. In order to be able to pivot relative to the 24-hour wheel 2, the finger 4 is mounted on the axle 6 with a slight axial clearance thanks to a ring 8 engaged on this axle 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 ). It is therefore understood that when the pin 10 comes into contact with an inner wall 14 of the oblong hole 12, it is driven in rotation by the 24-hour wheel 2 and in turn drives the finger 4 which also makes a complete turn in 24 hours.

[0012] The moon phase display mechanism 1 according to the invention also comprises a first lever 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. Also noted in the drawing is 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.

[0013] The 24-hour wheel 2 rotates clockwise, carrying with it the finger 4. The first lever 16 thus slides along the first part 20a of the profile 20 of the finger 4 and, after passing through an intermediate position A ( Figure 3A ), finds himself in an extreme position B ( Figure 3B) in which it is supported by a foot 32 against a summit 34 of the profile 20 of the finger 4. Furthermore, the first rocker 16 engages by a beak 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 Bin which it is supported against the top 34 of the profile 20 of the finger 4, and drives the star 24 one step in the counterclockwise direction. This movement is allowed by the fact that at the moment when the first rocker 16 passes the top 34 of the profile 20 of the finger 4, a lever effect is produced on the finger 4 which causes the pivoting of this finger 4 and the concomitant movement of the pin 10 which, in abutment against one end of the oblong hole 12 made in the thickness of the 24-hour wheel 2, will move to come into abutment 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 top 34 of this profile 20.It will be noted that at the very moment when the first lever 16 causes the star 24 to advance by one step, the jumper 26 passes, against the return force of the lower spring 30, from a hollow between two consecutive teeth of the toothing 28 of the star 24 to the immediately following hollow of this toothing 28. By falling back into the following hollow, the jumper 26 allows the star 24 to complete its advance by one step and again ensures the precise positioning of this star 24.

[0014] According to a preferred but non-limiting embodiment of the moon phase display mechanism according to the invention, the latter also comprises a manual device for correcting the moon phase display. Designated as a whole by the general reference numeral 38, this manual correction device comprises a second lever 40 pivoted about an axis 42 and which comprises an actuating means 44 such as a pin at an end opposite the pivot axis 42. This second lever 40 comprises, for example, a folded zone 46 against which a corrector (not visible in the drawing) presses 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 the 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 passes the top 34 of the profile 20 of the finger 4.

[0015] According to a preferred embodiment given purely for 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 successive new Moons and which is also called a lunar month. 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 axis of rotation of which a second pinion 54 is fixedly mounted. The first pinion 50 drives the second pinion 54 via the return 56, the tooth ratios of this kinematic chain being calculated so that the cam 52 makes a complete revolution per lunar cycle.

[0016] The cam 52 has a spiral profile 58 with a substantially rectilinear step 60. A first rack 62 with a toothed sector 64 is also provided with a feeler beak 66 by which it permanently follows the profile 58 of the cam 52. Shortly before the start of a new lunar cycle, for example around midnight, the feeler beak 66 of the first rack 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, by its toothed sector 64, is in permanent engagement with a third pinion 68, turns this third pinion 68 clockwise by an amount corresponding to the fall of the feeler beak 66 along the step 60.

[0017] By rotating, the third pinion 68 turns a wheel 70 with which it forms a mobile 69. In other words, the third pinion 68 is mounted on the wheel 70 in a coaxial manner 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 freely in rotation on a rotation axis 76. The lower wheel 74 meshes with a rectilinear rack 80 which in turn meshes with the upper wheel 78.

[0018] According to the invention, the lower wheel 74 is responsible for controlling the moon phase display mechanism 1. To this end, by pivoting, the lower wheel 74 drives the rectilinear rack 80 in translation and pushes it into a first extreme position E illustrated in the Figure 8Awhich corresponds to the beginning of a new lunar cycle. Subsequently, when, after having fallen along the step 60 of the cam 52 at the beginning of the lunar cycle, the feeler beak 66 begins to follow the profile 58 of the cam 52 again, the feeler beak 66 is gradually pushed back in a clockwise direction towards a second extreme position F (see Figure 8B ), so that the third pinion 68, and therefore the wheel 70, rotates counterclockwise. Consequently, the lower wheel 74 rotates clockwise and drives the straight rack 80 in translation from the right to the left of the drawing from its first extreme position E which corresponds to the beginning of a new lunar cycle up to its second extreme position F illustrated in the Figure 8Bwhich corresponds to the end of the lunar cycle. Once the feeler beak 66 has traveled the entire length of the profile 58 of the cam 52, it will again find itself at the top of the step 60 of the cam 52 and, at the start of a new lunar cycle, the feeler beak 66 will fall along the step 60, which will cause the rectilinear rack 80 to return to its initial position.

[0019] The moon phase display mechanism according to the invention is completed by a device which makes it possible to take up the play and return this moon phase display mechanism to its extreme position Eat the end of a lunar cycle. This device consists of the upper wheel 78 meshing 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 comprises an intermediate pinion 86. This intermediate pinion 86 meshes with a toothed sector 88 of a second rack 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 rack 62 and the second rack 90 is taken up, so that the positioning of the rectilinear rack 80 is always precise.

[0020] According to the invention, the moon phase display mechanism 1 comprises the rectilinear rack 80 with which a shutter 94 is fixedly coupled 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 onto the upper face 100 of the transparent support 98. This representation 104 of the Moon could also be transferred onto the lower face 102 of the transparent support 98. A substrate 106 is, relative to the observer 96, arranged under the transparent support 98, at a distance from the latter.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 have reversed 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 light. Assuming, for example purposes only, that the representation 104 of the Moon and the substrate 106 are dark and that the shutter 94 is clear and reflective, it is understood that when the shutter 94 is not in the space 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 to the observer 96.Then, as the light and reflective shutter 94 penetrates the space separating the transparent support 98 from the dark substrate 106, the representation 104 of the Moon gradually becomes perceptible to 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: this is the full moon.Then, the shutter 94 continues its rectilinear movement in the same direction and begins to move out of the space between the transparent support 98 and the dark substrate 106, so that the observer 96 gradually sees the last quarter of the moon appear, a 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 no longer sees the representation 104 of the Moon (assuming that the substrate 106 is the same color as the representation 104 of the Moon) and therefore knows that the lunar cycle is over and that a new lunar cycle is about to 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 and then new moon again.

[0021] According to a particular embodiment 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 to which a preferably aspherical profile is given. 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. An image of the Moon is thus obtained 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.

[0022] To determine the geometric dimensions of the aspherical plano-concave lens 108 and the hyperbolic profile shutter 94, computer-aided optical system design software such as that marketed under the brand name LightTools, version 8 of which was published in 2019, was used for the purposes of the present invention.

[0023] Once the dimensions of the representation 104 of the Moon that one wishes 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 realistic representation of the phases of the Moon are: the material from 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.

[0024] 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 in the vicinity of 1.78. This value was chosen after numerous tests which showed that, the higher the value of the refractive index of the material from which the lens is made, the closer the lens had to be placed to the shutter 94 so that the latter was not visible to the observer through this lens. It is easily understood 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 according to the present invention into a timepiece of the wristwatch type. On the other hand, the higher the refractive index, the more expensive and difficult to machine the corresponding material is.Furthermore, it was found that when the lens gets too close to the shutter 94, we end up seeing the image of the peripheral edge of the lens which forms an opaline to milky crown around the representation 104 of the Moon, which is not acceptable. Similarly, it was found that by selecting refractive index values ​​which are 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 the order of 1.60 to 1.85 and preferably equal or substantially equal to 1.78 for the optical refractive index of the material from which the aspherical plano-concave lens 108 is made appeared to be an optimum making it possible to provide the best compromise between the optical refractive index of the material from which the aspherical plano-concave lens 108 is made and the distance separating the aspherical concave surface 112 of the aspherical plano-concave lens 108 and the shutter 94, and thus to 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.

[0025] The dimensions of a block of transparent or at least translucent material such as a cylinder of glass or polymer such as polycarbonate are then entered into the computer-aided design software, from which the aspherical plano-concave lens 108 is obtained. In this case, the aspherical plano-concave lens 108 is obtained by machining a cylindrical glass block 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 ).

[0026] As regards the shutter 94 with hyperbolic profile, this is obtained from a rectangular sheet of which the thickness e is preferably but not limited to between 0.08 mm and 0.2 mm, and the length Iof the 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 9 mm and 10 mm. 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. It will be noted in fact that it is not necessary for the shutter 94 to retain its hyperbolic profile 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 have the sole 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 size of the moon phase display mechanism.

[0027] 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 from the central axis of symmetry S from the point of the aspherical concave surface 112 which is opposite (see figure 6 ). Similarly, the hyperbolic profile of the shutter 94 is determined by the distance r' which separates each point from the plane of symmetry S' of this shutter 94 of the surface of the latter. These distances r , r'are determined using the same relationship below: z r = r 2 R 1 + 1 − 1 + k r 2 R 2 + ∑ n = 1 N A n ⋅ r n where k = -e 2<

[0028] As visible on the figure 6 , the origin of the function z(r) corresponds to the point O which is located 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, to the height of this point considered from the base of the aspherical plano-concave lens 108.

[0029] 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.

[0030] As for the aspherical plano-concave lens 108, the constant R corresponds to the radius of curvature of the aspherical concave surface 112 at the point O which is located at the top of the vault formed by this aspherical concave surface 112. In order for the terminator T which is the demarcation line between the dark part and the illuminated part of the Moon to appear rectilinear in the middle of the lunar cycle, it is necessary that in the vicinity of the point O the aspherical concave surface 112 is practically flat. For this purpose, a value of the radius of curvature is initially entered into the computer-aided design software Rvery large, of the order of several thousand millimeters. As for the constant "k" which is called "conic constant", it is a quantity which describes conic sections. By conic 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.

[0031] We note that k = -e 2< with ewhich corresponds to the eccentricity of the conic section. The eccentricity of a conic section is a positive real number that characterizes only the shape of that 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.

[0032] The conic constant k is involved in the equation y 2 − 2 Rx + k + 1 x 2 = 0 which describes a conic 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, we initially indicated to the computer-aided design software that the conicity constant was zero (k = 0), in other words that we were dealing with a circle.

[0033] Therefore, for the aspherical plano-concave lens 108, we start the simulation with a value of the conic constant k of zero and a value of the radius of curvature R very large.

[0034] The same applies to shutter 94 for which the simulation begins with a value of the conical constant k' zero and a value of the radius of curvature R'very large. It is important to note that the shutter 94 can be considered as the object whose image is perceived through the plano-concave aspheric lens 108 and, as such, its geometric characteristics can be determined by computer-aided optical systems design software such as LightTools.

[0035] Finally, the aspherical plano-concave lens 108 is considered to be of even order, so that one begins 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 as the index n increases. We decide to stop at the coefficient A 8 because the contribution of higher order coefficients on the improvement of the resulting aspect of the terminatorT is negligible. As for the coefficient A 2 , this is ignored because the first term of the expression z(r) already contains the square of the variable r .

[0036] Using computer-aided design software, a 118 representation of the Moon and its terminator is simulated T for several shutter positions 94 (see figures 7 And 9A to 9L ). To the Figure 9A , we are at the beginning of a lunar cycle. At the Figure 9C , the Moon is in its first quarter. At the Figure 9F , we are in the middle of the lunar cycle and the Moon is full. The 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, by varying the values ​​of the parameters A n as well as the conic constant k and the radius of curvature Rwhich characterize the aspherical plano-concave lens 108, while the values ​​of the parameters are kept unchanged A' n as well as the conic 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 the values ​​of the parameters constant. 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 Tusing the "Photorealistic Rendering" function of the LighTools software. This function allows you 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 thus possible to verify that the desired optical effect is suitable. This is done step by step until a profile of the terminator is obtained T that one considers faithful to its real appearance and with which one is satisfied. Of course, this is a purely subjective criterion which is left to the appreciation of each individual.

[0037] 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 Twere 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 respect 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 respect to the shutter 94. It will be observed that as regards 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.

[0038] So 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. Therefore, we deduce that at this point O , the thickness of the 108 aspherical plano-concave lens is 0.22 mm. This is the minimum thickness of the 108 aspherical plano-concave lens.

[0039] It goes without saying that the present invention is not limited to the embodiment which has just been described and that various simple modifications and variants can be envisaged by those skilled in the art without departing from the scope of the invention as defined by the appended claims. It will be noted 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 will also be noted that in order to avoid light reflection phenomena, the surface of the shutter can advantageously have a roughness. Still with the same aim of limiting light reflections as much as possible, the plano-concave lens can be subjected to an anti-reflection treatment and its edges can be metallized. According to a particular embodiment of the invention not shown in the drawing, it may be provided to provide the cam 52 with two recesses 60.Since star 24 makes a complete revolution in two lunar cycles, it is then possible to put star 24 in direct engagement with cam 52, and thus to save on pinions 50 and 54 and idler 56. Nomenclature

[0040] 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 lever 18. Pivot shaft 20. Profile 22. Upper spring 24. Star 26. Jumper 28. Teeth 30. Lower spring 32. Foot 34. Top 36. Beak 38. Manual correction device 40. Second lever 42. Pivot shaft 44. Actuating means 46. Folded area 50. First pinion 52. Cam 54. Second pinion 56. Intermediate wheel 58. Profile 60. Offset 62. First rack 64. Toothed sector 66. Feeler beak 68. Third pinion 69. Mobile 70. Wheel 72. Drive means 74. Lower wheel 76. Axis of rotation 78. Upper wheel 80. Rectilinear rack 82. Intermediate wheel 84. Intermediate mobile 86. Intermediate pinion 88. Toothed sector 90. Second rake 92. Fourth spring 94. Shutter 96. Observer 98. Transparent support 100. Upper face 102. Lower face 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

1. A moon phase display mechanism driven by a horology 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 away 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 deposited 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) driven by drive means (72) moved by the horology movement and arranged to move between the transparent support (98) and the substrate (106), the shutter (94) and the substrate (106) having contrasting displays which are reversed relative to each other, the shutter (94) being moved from an initial position to a final position over the course of a lunar cycle so as to reveal to an observer (96) the daily aspect of the Moon which changes 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 returned by the drive means from its final position to its initial position at the end of the lunar cycle, characterised in that the transparent support (98) is in the form of a plano-concave lens (108) delimited towards the top, on the side of the observer (96), by a flat surface (110) on which a representation (104) of the Moon has been transferred, and delimited towards the bottom by a concave surface (112) with a curved profile, this aspherical plano-concave lens (108) being combined with the shutter (94) which has a curved profile.

2. The display mechanism according to claim 1, characterised in that the drive means (72) comprise a rectilinear rack (80) with which the shutter (94) is fixedly coupled in translation.

3. The display mechanism according to claim 2, characterised in that the drive means (72) comprise a lower wheel (74) and an upper wheel (78) on an axis of rotation (76) from which the lower wheel (74) is mounted so as to rotate freely and meshes with the rectilinear rack (80).

4. A horology movement comprising a display mechanism according to any of claims 2 or 3, characterised in that the horology movement comprises a motion work that 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) that is permanently followed by a first rack (62), this first rack (62) being provided with a toothed sector (64) by which it meshes with the drive means (72) on the moon phase display mechanism (1).

5. The horology movement according to claim 4, characterised in that the first rack (62) is provided with a feeler beak (66) by which it permanently follows the cam (52) profile (58), this profile (58) being shaped as a snail and being provided with at least one substantially rectilinear indent (60) so that, shortly before the start of a new lunar cycle, the feeler beak (66) is at the top of the cam (52) profile (58), then falls along the indent (60), the first rack (62) driving during this movement by its toothed sector (64) a pinion (68) which is kinematically connected to the drive means (72) on the moon phase display mechanism (1).

6. The horology movement according to any of claims 4 or 5 when they are dependent on claim 3, characterised in that it is supplemented by a slack adjuster device consisting of the upper wheel (78) engaged, on one hand, with the rectilinear rack (80), and on the other hand, with an intermediate wheel (82) on an intermediate mobile (84) which also comprises an intermediate pinion (86), this intermediate pinion (86) meshing with a toothed sector (88) on a second rack (90) which is elastically restrained by the return force of a fourth spring (92).

7. The moon phase display mechanism according to any of claims 1 to 3 or horology movement according to any of claims 4 to 6, characterised in that the optical refractive index of the material from which the plano-concave lens (108) is made is comprised between 1.60 and 1.85.

8. The moon phase display mechanism or horology movement according to claim 7, characterised in that the optical refractive index is equal or substantially equal to 1.78.

9. The moon phase display mechanism according to any of claims 1 to 3, 7 or 8, or horology movement according to any of claims 4 to 8, characterised in that the plano-concave lens (108) is made of glass or of polymer.

10. The moon phase display mechanism according to any of claims 1 to 3, 7 to 9, or horology movement according to any of claims 4 to 9, characterised in that the concave surface (112) has an aspherical profile.

11. The moon phase display mechanism according to the preceding claim, characterised in that the shutter (94) has a hyperbolic profile.

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