MOON PHASE INDICATION MECHANISM

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 are useful for easily determining the moon's phase. The simplest moon phase display mechanisms include a pointer that indicates the different lunar phases (first quarter, full moon, last quarter, new moon). Other known moon phase display mechanisms include a disc bearing two representations of the moon, a portion of which is visible through a specially shaped aperture in the watch dial, 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; nevertheless, the way the Moon is represented bears only a distant relation to how the lunar orb appears in the sky. Another moon phase display mechanism uses a two-tone sphere that completes a full rotation with each lunar cycle. Such a moon phase display mechanism allows for a realistic representation of the Moon's face. However, because such a moon phase display mechanism uses a sphere to represent the different phases of the Moon, it is thick and takes up considerable space, making it difficult to integrate into a clockwork movement, especially in a wristwatch.

[0003] We also know from document WO91 / 11756 of a device for representing the moon, notably on the dial of a watch. Summary of the invention

[0004] The present invention aims to provide a moon phase display mechanism which provides a moon phase display that is in particular more faithful to reality and more easily understandable for the watch owner.

[0005] For this purpose, the present invention relates to a moon phase display mechanism powered by a clockwork movement, according to claim 1 of the patent.

[0006] Thanks to these features, the present invention provides a moon phase display mechanism that shows the different phases of the moon day after day in an original and easily understandable way for 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, making it much simpler for the user to determine which phase of the lunar cycle the moon is in. The moon phase display mechanism according to the invention is also thinner than those using a rotating sphere, and therefore easier to integrate into a watch movement, especially a wristwatch. Furthermore, regardless of the phase the moon is in, its representation is always visible to the watch owner.It should also be noted that the moon phase display mechanism according to the invention provides a realistic representation of the different phases of the Moon, formed by two surfaces of different colors separated by a terminator, that is, the curve that separates the illuminated part from the dark part of the Moon, whose profile is very realistic and faithful to what the user can see when observing the Moon in the sky. This is particularly true during the first and last quarter moon, when optical distortions are almost zero and the terminator thus appears perfectly straight.

[0007] According to another particular embodiment of the invention, the transparent support is in the form of a plano-concave lens delimited at the top, on the observer's side, by a flat surface which receives the representation of the Moon, and delimited at the bottom by a concave surface which is given a profile preferably but not necessarily aspherical, this plano-concave lens being combined with a shutter which is given a curved profile, preferably of the hyperbolic type.

[0008] Thanks to the combined use of a plano-concave lens, preferably aspherical, and a curved-profile shutter, preferably but not limited to hyperbolic, the observer sees a terminator—that is, the curve separating the illuminated and dark portions of the Moon—whose profile is highly realistic and faithful to what the user sees 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 housed in a smaller volume, such as that of a wristwatch case. For example, for a representation of the Moon of the same diameter, the moon phase display mechanism according to the invention is considered to be half the thickness of a moon phase display mechanism using a sphere.Similarly, 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. Brief description of the figures

[0009] Other features and advantages of the present invention will become clearer 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 purposes and not as a limitation, only in connection with the accompanying drawing in which: there figure 1 is a plan view of the moon phase display mechanism according to the invention; the figure 2 is a larger-scale detail view of the oblong hole into which the pin carried by the finger protrudes; the figure 3Ais a larger-scale detail view of the first rocker in its intermediate position A the figure 3B is a larger-scale detail view of the first rocker in its extreme position B, in which it rests against the apex of the finger profile; the figure 4A is a larger-scale detail view of the first rake in its C position, in which its feeler beak is at the top of the cam profile; the 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's notch; the figure 5 is a top view of the transparent support and sheet metal from which the aspheric plano-concave lens and shutter are obtained; the figure 6 is an elevation and cross-sectional view of the optical assembly formed by the aspheric plano-concave lens, the shutter, and the substrate; the figure 7is a schematic top view that illustrates the appearance of the representation of the Moon as it may be perceived by the observer when the shutter begins to enter the space separating the aspheric plano-concave lens from the substrate; the figure 8A is a schematic view of the moon phase display mechanism when it is in its extreme position E at the beginning of a lunar cycle; the 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

[0010] The present invention proceeds from the general inventive idea of ​​transferring a representation of the Moon onto either the upper or lower face of a transparent support positioned above and at a distance from a substrate, with a shutter interposed 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 exhibit inverse 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 background are dark and the shutter is clear, it is understood that when the shutter is not in the space between the transparent support and the dark background, the representation of the Moon above the dark background is not perceptible to the observer. Then, as the clear shutter moves into the space between the transparent support and the dark background, the representation of the Moon gradually becomes perceptible to the user. The present invention thus provides a more compact mechanism than moon phase display mechanisms that include a sphere, and allows the moon phases to be displayed in an original and far more realistic manner than most prior art moon phase display devices.Consequently, the observer finds it much easier to determine which phase of the lunar cycle they are in. Furthermore, realism is further enhanced if, according to a specific embodiment 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 with a hyperbolic profile. This combination makes it possible to obtain a terminator whose profile closely resembles that observed in reality as the Moon waxes, becomes full, then wanes, and the lunar cycle begins anew.

[0011] Housed, for example, in a timepiece such as a wristwatch, the moon phase display mechanism 1 according to the invention is powered 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 whose pinion (not visible in the figures) drives a 24-hour wheel 2 which, as its name indicates, is arranged to complete one full rotation per day.

[0012] The 24-hour wheel 2 has a finger 4 on an axle 6, from which this finger 4 is mounted to rotate freely. To allow it to pivot relative to the 24-hour wheel 2, the finger 4 is mounted on the axle 6 with slight axial play thanks to a ring 8 engaged on this axle 6. Furthermore, the finger 4 is fitted with a pin 10 which protrudes into an oblong hole 12 formed in the thickness of the 24-hour wheel 2 and which limits the free rotation of the finger 4 relative to the 24-hour wheel 2 (see figure 2 ). It is therefore understood that when the pin 10 comes against an inner wall 14 of the oblong hole 12, it is driven in rotation by the wheel 24 hours 2 and in turn drives the finger 4 which also makes a complete turn in 24 hours.

[0013] The moon phase display mechanism 1 according to the invention also includes a first rocker 16 which is pivotally mounted about a pivot axis 18 and which is elastically applied against a first part 20a of a profile 20 of the finger 4 by an upper spring 22. The drawing also shows the presence of a star 24 whose position is indexed by a jumper 26 which is held elastically against a tooth 28 of this star 24 by a lower spring 30.

[0014] The 24-hour wheel 2 rotates clockwise, driving finger 4 with it. The first rocker 16 thus slides along the first part 20a of the profile 20 of 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 vertex 34 of the profile 20 of 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, finger 4 moves forward further, the first rocker 16 passes the extreme position Bin which it rests against the apex 34 of the profile 20 of the finger 4, and drives the star 24 by one step counterclockwise. This movement is made possible by the fact that when the first rocker 16 passes the apex 34 of the profile 20 of the finger 4, a lever effect occurs on the finger 4, causing it to pivot and the pin 10 to move concomitantly. The pin 10, bearing against one end of the oblong hole 12 in the thickness of the 24 o'clock wheel 2, moves to bear 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 beyond the apex 34 of this profile 20.It should be noted that at the very moment when the first rocker 16 causes the star 24 to advance by one step, 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 next hollow of this teeth 28. By falling back into the next 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.

[0015] According to a preferred but non-limiting embodiment of the moon phase display mechanism of the invention, it also includes 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 rocker 40 pivoted about an axis 42 and which includes an actuation means 44 such as a pin at an end opposite to the pivot axis 42. This second rocker 40 includes, for example, a folded area 46 against which a corrector (not visible in the drawing) presses when the corrector is actuated against the elastic restoring force of a spring by the owner of the wristwatch from outside the volume of the watch case.Under the effect of the corrector's action, 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 apex 34 of the profile 20 of the finger 4.

[0016] According to a preferred method given purely for illustrative and non-limiting purposes, one complete rotation of the star 24 corresponds to two successive lunar cycles, a lunar cycle being the time between two successive new moons, also called a lunar month. To this end, 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 gearbox 56, and 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 gearbox 56, the gear ratios of this kinematic chain being calculated so that the cam 52 completes one full rotation per lunar cycle.

[0017] The cam 52 has a spiral profile 58 with a substantially straight step 60. A first rake 62 with a toothed sector 64 is also equipped with a feeler beak 66 by which it continuously 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 rake 62 is at the apex of the profile 58 of the cam 52 (position C - figure 4A ), then falls along the 60th notch of the cam 52 (position D - figure 4B ). During this movement, the first rake 62, which, by its toothed sector 64, is in permanent contact with a third pinion 68, rotates this third pinion 68 clockwise by an amount corresponding to the fall of the feeler beak 66 along the notch 60.

[0018] As it rotates, the third pinion 68 turns a wheel 70, with which it forms a moving part 69. In other words, the third pinion 68 is mounted coaxially on the wheel 70 and is fixed in rotation relative to this wheel 70. Consequently, the wheel 70 transmits its rotational motion to drive means 72 of the moon phase display mechanism 1, which include a lower wheel 74 and an upper wheel 78 mounted freely to rotate on a rotation axis 76. The lower wheel 74 meshes with a straight rack 80, which in turn meshes with the upper wheel 78.

[0019] 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 straight rack 80 in translation and pushes it into a first extreme position E illustrated at the figure 8Awhich corresponds to the beginning of a new lunar cycle. Subsequently, when, after having fallen along the notch 60 of the cam 52 at the beginning of the lunar cycle, the feeler 66 begins to follow the profile 58 of the cam 52 again, the feeler 66 is progressively pushed back clockwise to 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 right to left in the drawing from its first extreme position E which corresponds to the beginning of a new lunar cycle until its second extreme position F illustrated at 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 be at the top of the notch 60 of the cam 52 and, at the beginning of a new lunar cycle, the feeler beak 66 will fall along the notch 60, which will cause the straight rack 80 to return to its initial position.

[0020] The moon phase display mechanism according to the invention is complemented by a device that allows for the compensation of play and returns 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 one side with the teeth of the straight rack 80, and on the other side with an intermediate wheel 82 of an intermediate moving part 84 which also includes an intermediate pinion 86. This intermediate pinion 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 backlash in the kinematic chain extending between the first rake 62 and the second rake 90 is taken up, so that the positioning of the straight rack 80 is always precise.

[0021] According to the invention, the moon phase display mechanism 1 comprises a straight rack 80 to which a shutter 94 is fixedly coupled in translation. The moon phase display mechanism 1 also comprises, on the observer's side 96, a transparent support 98 having an upper face 100 extending 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, with respect to the observer 96, disposed below the transparent support 98, at a distance from the latter.The shutter 94 is mounted on the straight rack 80 so as to be able to progressively penetrate the space which separates the transparent support 98 from the substrate 106 when the straight rack 80 is driven by the lower wheel 74. The shutter 94 and the substrate 106 have reversed contrasts: either the shutter 94 is clear 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, as an example 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 clear, reflective shutter 94 enters the space between the transparent support 98 and the dark substrate 106, the representation 104 of the Moon gradually becomes perceptible to the user. More precisely, when the shutter 94 begins to enter the space between the transparent support 98 and the dark substrate 106, the observer 96 gradually sees the first quarter 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 complete representation 104 of the Moon: this is the full moon.Then, the shutter 94 continues its rectilinear movement in the same direction and begins to move out of the gap between the transparent support 98 and the dark substrate 106, so that the observer 96 gradually sees the last quarter moon appear. This corresponds to the moment when the shutter 94 leaves the same surface uncovered as it did masked. Finally, when the shutter 94 has completely moved out of the gap between the transparent support 98 and the dark substrate 106, the observer 96 no longer sees the representation 104 of the Moon (assuming the substrate 106 is the same color as the representation 104 of the Moon) and therefore knows that the lunar cycle is over and a new lunar cycle is about to begin. Thus, thanks to the invention, the observer 96 has an easily understandable representation of the different phases of the Moon: new moon, first quarter moon, full moon, last quarter moon, and then new moon again.

[0022] According to a particular embodiment of the invention, the transparent support 98 is in the form of a plano-concave lens 108, delimited at the top, on the observer's side 96, by a flat surface 110 which receives the representation 104 of the Moon, and delimited at the bottom by a concave surface 112 which is preferably given an aspheric profile. This aspheric plano-concave lens 108 is combined with a shutter 94 folded at its center to give it a curved profile, preferably, but not necessarily, hyperbolic. This produces an image of the Moon whose terminator, that is, the curve separating the dark part from the illuminated part of the Moon, closely approximates the actual appearance of the Moon in the sky.

[0023] To determine the geometric dimensions of the aspheric plano-concave lens 108 and the hyperbolic profile shutter 94, computer-aided optical system design software such as that marketed under the LightTools brand is used, version 8 of which was published in 2019 and was used for the purposes of the present invention.

[0024] 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 that can be adjusted to obtain a realistic representation of the phases of the Moon are: the material in which the plano-concave aspheric lens 108 will be made and therefore the refractive index of the latter; the profile of the concave aspheric surface 112 of the plano-concave aspheric lens 108 and therefore its conicity constant; the dimensions of the shutter 94; the distance which separates the apex of the arch formed by the concave aspheric surface 112 and the shutter 94; the curved profile, preferably hyperbolic, of the shutter 94 and therefore its conicity constant.

[0025] As a preferred example only, the aspheric plano-concave lens 108 is made of a transparent material with a refractive index 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 refractive index of the material from which the lens is made, the closer the lens must be to the shutter 94 so that the latter is not visible to the observer through the lens. It is easy to understand that this is advantageous from a space-saving point of view when integrating a moon phase display device according to the present invention into a timepiece such as a wristwatch. On the other hand, the higher the refractive index, the more expensive and difficult the corresponding material is to machine.Furthermore, it was observed that when the lens becomes too close to the shutter 94, the image of the lens's peripheral edge eventually appears, forming an opaline to milky halo around the representation 104 of the Moon, which is unacceptable. Similarly, it was found that by selecting excessively low refractive index values, the image of the curved, preferably hyperbolic, shutter 94, which gradually obscured the representation of the Moon, was neither aesthetically pleasing nor truly realistic compared to the actual representation of the Moon. Therefore, a value in the range of 1.60 to 1.85, and preferably equal to or nearly equal to 1, is recommended.The optical refractive index 78 of the material in which the aspheric plano-concave lens 108 is made has emerged as an optimum, providing the best compromise between the optical refractive index of the material in which the aspheric plano-concave lens 108 is made and the distance separating the aspheric concave surface 112 of the aspheric plano-concave lens 108 and the shutter 94. This allows for a moon phase display mechanism whose size is compatible with the dimensions of the timepiece in which it is intended to be housed, while also providing a terminator with a suitable profile. An example of a material well-suited to the needs of the present invention is the glass produced and marketed by Schott under the reference N-SF 11.

[0026] The dimensions of a block of transparent or at least translucent material, such as a glass or polymer cylinder like polycarbonate, from which the aspheric plano-concave lens 108 is obtained, are then entered into the computer-aided design software. In this case, the aspheric plano-concave lens 108 is obtained by machining a cylindrical glass block with a 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 ).

[0027] Regarding the hyperbolic profile shutter 94, it is obtained from a rectangular sheet of metal whose thickness e is preferably, but not exclusively, between 0.08 mm and 0.2 mm, and whose length l the side extending parallel to the direction of movement of the shutter 94 is chosen to be between 7 mm and 8 mm, while the width LThe side extending perpendicularly to the direction of movement of this shutter 94 is chosen to be between 9 mm and 10 mm. This sheet metal has a fold 114 in its center, extending 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 should be noted that it is not necessary for the shutter 94 to maintain its hyperbolic profile to its extremities because, in these areas, the optical distortion effect is produced primarily by the aspheric plano-concave lens 108. These flat edges 116 therefore serve only to completely obstruct the field of vision provided by the aspheric plano-concave lens 108 and, due to their flatness, these edges 116 allow for a reduction in the size of the moon phase display mechanism.

[0028] The profile of the aspheric concave surface 112 of the aspheric 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 plano-concave aspheric lens 108, the distance r corresponds to the distance separating each point from the central axis of symmetry S from the point of the aspheric 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 of 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 Or k = − e 2

[0029] As seen on the figure 6 , the origin of the function z(r) corresponds to the point Owhich is located at the top of the vault formed by the aspheric concave surface 112. The value of the function z(r) corresponds, at each point of the vault formed by the aspheric concave surface 112, to the height of that point considered from the base of the aspheric plano-concave lens 108.

[0030] The values ​​of the constants R And k which characterize the aspheric plano-concave lens 108, as well as those of the constants R' And k' The characteristics of shutter 94 will be determined by successive iterations as described below. As for the coefficients A n These are coefficients of a polynomial sum whose values ​​will also be determined by iterations.

[0031] Regarding the aspheric plano-concave lens 108, the constant R corresponds to the radius of curvature of the aspheric concave surface 112 at point Owhich is located at the apex of the vault formed by this aspheric concave surface 112. So that the terminator T which is the dividing line between the dark and illuminated parts of the Moon, appears straight in the middle of the lunar cycle; it is necessary that in the vicinity of the point O the aspheric concave surface 112 is practically flat. To this end, a value for the radius of curvature is initially entered into the computer-aided design software R very large, on the order of several thousand millimeters. As for the constant "k," which is called the "conic constant," it is a quantity that describes conic sections. By conic section, we mean a plane curve defined by the intersection of a right circular cone with a plane. When the cutting plane does not pass through the vertex of the cone, its intersection with the cone corresponds to one of the following plane curves: ellipse, parabola, or hyperbola.

[0032] 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 that uniquely characterizes the shape of that conic section; it can be interpreted as a measure of how far 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.

[0033] The conic constant k appears in the equation y 2 − 2 Rx + k + 1 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 we are considering, 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.

[0034] Therefore, for the aspheric plano-concave lens 108, the simulation begins with a value of the conic constant k zero and a value of the radius of curvature R very large.

[0035] 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 aspheric plano-concave lens 108 and, as such, its geometric characteristics can be determined by computer-aided optical system design software such as LightTools.

[0036] Finally, the aspheric plano-concave lens 108 is considered to be of even order, so we begin by arbitrarily choosing values ​​for the coefficients A4, A6, and A8. In choosing the initial values ​​for these coefficients, a person skilled in the art is guided by the knowledge that these values ​​are very small and decrease steadily as the index n increases. We therefore decide to stop at the coefficient A 8 because the contribution of higher-order coefficients to the improvement of the resulting aspect of the terminator Tis negligible. Regarding the coefficient A 2 This one is ignored because the first term of the expression z(r) already contains the square of the variable r .

[0037] Using computer-aided design software, a representation 118 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. figure 9I corresponds to the last quarter moon and the figure 9L We are at the new moon. To perform 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 aspheric plano-concave lens 108, while the parameter values ​​remain unchanged A' n as well as the conic constant k' and the radius of curvature R' which characterize shutter 94, and the resulting appearance of the terminator is observed on the computer screen T We repeat the experiment, this time keeping the parameter values ​​constant. A n , k And R which characterize the aspheric plano-concave lens 108, and by varying the values ​​of the parameters A' n as well as k ' And R' which characterize shutter 94, and the resulting appearance of the terminator is observed on the computer screen Tusing the "Photorealistic Rendering" function of the LightTools software. This function allows visualization of the entire device formed by the aspheric 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 satisfactory. This process is repeated step by step until a terminator profile 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 that is left to the judgment of each individual.

[0038] It should be noted that for the dimensional characteristics of the aspheric plano-concave lens 108 and the shutter 94 mentioned above, the most satisfactory results regarding the visual appearance of the terminator Twere obtained for the values ​​k = -1 and R = 20840 mm and A4 = 3.769 x 10⁻³, A6 = 2.9534 x 10⁻⁵ and A8 = -1.407 x 10⁻⁷ for the aspheric plano-concave lens 108, and for the values ​​k' = -4.922 and R' = 2.556 mm and A4 = 1.654 x 10⁻⁵, A6 = -1.511 x 10⁻⁶ and A8 = 4.686 x 10⁻⁸ for the shutter 94. It should be noted that the value of the taper constant k for the aspheric plano-concave lens 108 is -1, which corresponds to a parabolic profile. As for the value of the taper constant... k' which characterizes the profile of the 98 shutter, this is less than -1, which corresponds to a hyperbolic profile.

[0039] Thus, the point O which is located at the top of the vault formed by the aspheric 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 pointO The thickness of the 108 aspheric plano-concave lens is 0.22 mm. This is the minimum thickness of the 108 aspheric plano-concave lens.

[0040] It is understood that the present invention is not limited to the embodiment just described and that various simple modifications and variations can be envisaged by those skilled in the art without departing from the scope of the invention as defined by the appended claims. It should be noted in particular that, in the case where the shutter is clear, it can be coated 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 be roughened. Also with the aim of minimizing light reflections, the plano-concave lens can be treated with an anti-reflective coating and its edges can be metallized. According to a particular embodiment of the invention not shown in the drawing, the cam 52 can be provided with two notches 60.Since the star 24 makes a complete revolution in two lunar cycles, it is then possible to put the star 24 in direct contact with the cam 52, and thus save the pinions 50 and 54 and the linkage 56. Nomenclature

[0041] 1. Moon phase display mechanism 2. 24-hour wheel 4. Finger 6. Axle 8. Bushing 10. Pin 12. Oblong hole 14. Inner wall 16. First rocker arm 18. Pivot axle 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 rocker arm 42. Pivot axle 44. Actuating means 46. Bent area 50. First pinion 52. Cam 54. Second pinion 56. Gear 58. Profile 60. Step 62. First rake 64. Toothed sector 66. Feeler beak 68. Third pinion 69. Moving part 70. Wheel 72. Drive means 74. Lower wheel 76. Rotation axis 78. Upper wheel 80. Straight rack 82. Intermediate wheel 84. Intermediate moving part 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.Plano-concave aspheric lens 110. Plane surface 112. Concave aspheric surface 114. Fold 116. Flat edges 118. Representation of the Moon.

Claims

1. A moon phase display mechanism intended to be moved by a horological 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 disposed 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) as well as drive means (72) intended to be moved by the horological movement, and arranged to drive the shutter (94) in displacement between the transparent support (98) and the substrate (106), the shutter (94) and the substrate (106) having display contrasts which are inverted relative to each other, the shutter (94) being displaced 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 (96) the 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, a mechanism characterised in that t The drive means (72) comprise a rectilinear rack (80) with which the shutter (94) is fixedly coupled in translation.

2. The display mechanism according to claim 1, characterised in that it comprises a clearance take-up device, an upper wheel (78) of which comprises an axis of rotation (76) on which a lower wheel (74) of the drive means (72) is mounted free in rotation, this lower wheel (74) meshing with the rectilinear rack (80).

3. The display mechanism according to one of claims 1 and 3, characterised in that it comprises a cam (52) which is intended to be kinematically driven by a motion-work mobile of the horological movement, this cam (52) performing a complete revolution on itself in an integer number of times a lunar cycle, the display mechanism comprising a first rack (62) which permanently follows a profile (58) of the cam (52), this first rack (62) being provided with a toothed sector (64) by which it meshes with the drive means (72) of the moon phase display mechanism (1).

4. The display mechanism according to claim 3, 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 step (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 step (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) of the moon phase display mechanism (1).

5. The moon phase display mechanism according to one of claims 3 and 4 when these depend on claim 3., characterised in that the upper wheel (78) is engaged, 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 comprises an intermediate pinion (86), this intermediate pinion (86) meshing with a toothed sector (88) of a second rack (90) which is elastically constrained by the return force of a fourth spring (92).

6. The moon phase display mechanism according to one of claims 1 to 5, characterised in that the transparent support (98) is in the form of a lens (108) of plano-concave shape delimited upwardly, on the side of the observer (96), by a planar surface (110) on which the representation (104) of the Moon is transferred, and delimited downwardly by a concave surface (112) which has a curved profile, the optical features of this aspherical plano-concave lens (108) being combined with the geometric features of the shutter (94) which has a curved profile.

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

9. The moon phase display mechanism according to one of claims 7 and 8, characterised in that the plano-concave lens (108) is made of glass or polymer.

10. The moon phase display mechanism according to one of claims 6 to 9, characterised in that the concave surface (112) is curved.

11. The moon phase display mechanism according to claim 10, characterised in that the concave surface (112) has an aspherical profile.

12. The moon phase display mechanism according to one of claims 10 and 11, characterised in that the shutter (94) has a hyperbolic profile.

13. Moon phase display mechanism according to claim 12, characterised in that the shutter (94) has a hyperbolic profile.