Device for measuring rotations and associated method for measuring rotation

Abstract

The invention relates to a mechanical resonator (1) that comprises at least four masses (2a, 2b, 2c, 2d), control means that comprise means for measuring the relative displacement between each pair of masses and means for applying inter-mass forces for each pair of masses; and a module for regulating vibrations. The resonator (1) has cubic symmetry and the masses (2a, 2b, 2c, 2d) are interlocked with one another. The masses each have a ternary axis of symmetry oriented along a ternary axis of symmetry of a cube. The masses are interconnected by first springs (3) and / or are connected to an outer support of the resonator (1) by second springs (11).

Description

[0001] DESCRIPTION TITLE: Rotation measuring apparatus and associated rotation measuring method Technical field The invention relates to the field of inertial sensors, such as vibrating gyroscopic sensors or resonators, used in particular for measuring rotations. The invention also relates to a method for measuring rotations. Prior art Vibrating gyroscopic sensors are commonly used in many fields due to their robustness, low power consumption and speed of implementation. Such vibrating gyroscopic sensors comprise a resonator which can take various forms, such as a bell or a tuning fork. For example, US patent 4,644,793 describes a resonator structure composed of a cylindrical shell associated with a plate positioned on a plane of symmetry of the cylindrical shell and allowing a connection with a support. Furthermore, it is known, in particular from document US 9,631,929,resonators with two nested masses having a common center of gravity, in order to obtain a symmetrical and planar structure. Documents FR 2 692 349 and FR 2 705 147 disclose vibrating gyroscopes comprising four identical metal beams arranged on a common base using linear or planar vibration modes to measure a rotation around a single sensitive axis corresponding to the axis of the gyrometer. In addition, a gyrometer-type device capable of measuring the three components of the rotation speed is known from document US 5,625,145. Finally, document US 9,863,770 describes a gyroscope whose resonator comprises eight suspended masses connected together by springs. Such a configuration has several advantages, including the possibility of measuring rotations around three orthogonal axes, thus completely describing the rotational movement in three dimensions, an isotropic distribution of the moving masses relative to the centerof gravity leading to an overall cancellation of external forces during acceleration and also during rotation. Nevertheless, all eight masses have numerous degrees of freedom that can be excited, which creates a certain complexity in controlling the movements of the resonator, given the number of parasitic vibration modes. Statement of the invention In view of the above, the aim of the invention is to propose a compact, precise resonator with a high degree of symmetry capable of equipping a device for measuring rotations in a three-dimensional frame of reference. The subject of the invention is a mechanical resonator comprising at least four identical and rigid masses, capable of exhibiting translational vibration modes. The resonator comprises control means comprising measuring means capable of measuring a relative displacement between each pair of masses in at least two directions and application means capable ofapplying inter-mass forces for each pair of masses in at least two directions. The resonator further comprises a vibration control module receiving data from the measuring means and issuing instructions for controlling the application means according to the received data. The resonator has cubic symmetry and the masses are nested together and each have a ternary axis of symmetry oriented along a ternary axis of symmetry of a cube. The masses are connected to each other by first springs and / or are connected to an external support of the resonator by second springs. Such a resonator can advantageously equip a clock or a chronometer, since it would allow time measurement independent of the rotational and / or translational movements undergone by the resonator. Preferably, the masses each have a plane of symmetry. According to one characteristic, the masses each comprise two basesconnected by at least three rods. Advantageously, the first springs are positioned perpendicular to each other along the twelve edges of the cube. Preferably, the first springs are straight rods stressed axially and / or in bending. Preferably, the second springs are arranged at each end of the masses, in particular in symmetrical extension of the first springs. The symmetrical extension of the first springs by the second springs makes it possible to preserve the balance of the overall center of gravity of the masses. Preferably, the second springs are straight rods stressed axially and / or in bending. According to one characteristic, the second springs have an axial stiffness and / or a bending stiffness different from an axial stiffness and / or a bending stiffness of the first springs. Advantageously, the masses are each made of at least two assembled parts, in order to facilitate construction. According to acharacteristic, the control means are transducers, in particular electrostatic or piezoelectric transducers, making it possible to measure deformations and / or to apply forces. Preferably, the transducers are arranged parallel to a first and / or a second bisector plane of the ternary symmetry axes of each pair of two masses and make it possible to measure a displacement and to apply forces along a normal respectively to the first and / or the second bisector plane of the ternary symmetry axes of each pair of two masses. According to a characteristic, the transducers are in the form of plates and are arranged on the rods of the masses, so that each plate placed on the rod of a mass corresponds to another associated plate which is parallel to it and arranged nearby on the rod of another mass. According to a characteristic, the control means are transducers of the microelectromechanical system (MEMS) type.Advantageously, the transducers are glued to the masses on the six faces of the cube and integrate the first springs, the second springs and means of attachment to a housing which envelops them, the transducers being capable of carrying out measurements of relative deformation between two masses and of applying inter-mass forces. According to another aspect, the subject of the invention is a rotation measuring apparatus as defined above, the resonator further comprising a rotation calculation module configured to calculate a rotation of the apparatus from data representative of amplitude and phases of vibrations coming from the vibration regulation module, the vibration regulation module being configured to generate translational vibration modes from three initial elementary vibration patterns, understood as bases of modal decomposition of any vibration, having the property of creating a zero global vibration at thefrequency of the natural modes. Such a resonator makes possible a physical memorization of the orientation in three dimensions in an inertial frame, independently of any external computer. Indeed, the memorization of the orientation in three dimensions in an inertial frame is materialized by the orientation of the vibration speeds of the different masses. Preferably, the vibration regulation module maintains a relative phase between a distribution of the patterns on three orthogonal axes, in particular the quaternary symmetry axes of the resonator, an amplitude of each of the patterns and a relative orientation of each of the patterns between them. Advantageously, the vibration regulation module positions at predetermined values, according to a temporal law, amplitudes, phases and orientations of each of said elementary patterns, the temporal law being capable of exploiting the symmetries of the defects of the resonator in order to average them. For example, thedefects of the resonator are identified using an angular reference external to the resonator, used continuously or punctually. According to another aspect, the invention relates to a method for measuring rotation of a rotation measuring apparatus as defined above. Said rotation measuring method comprises at least: − a step of measuring the relative displacements between the masses for each pair of masses; − a step of calculating the movement of each mass as a function of the measurements of the relative displacements; − a step of decomposing the calculated movements of each mass as a function of the initial elementary vibration patterns; and − a step of constructing a rotation matrix from the decomposition obtained, preferably taking into account the defects of the resonator by corrective terms. For example, the method comprises a step of providing rotation speed information from the forces calculated by the regulation modulevibrations. The method can in particular exclude forces resulting from monitoring predetermined values ​​according to the time law. For example, the method provides rotation information from the integral, carried out using rotation matrices or quaternions, of the rotation speed information. Brief description of the drawings Other objects, characteristics and advantages of the invention will appear on reading the following description, given solely by way of non-limiting example, and made with reference to the appended drawings in which: − [Fig 1] illustrates a general constitution of a resonator according to the invention; − [Fig 2] illustrates a mass of the resonator of [Fig 1] considered separately; − [Fig 3] illustrates ternary and quaternary axes of symmetry of a cube; − [Fig 4] illustrates a placement of control means arranged between two masses; − [Fig 5] is a perspective view of an embodiment of the resonator according to the invention; −[Fig 6] is a perspective view of the embodiment of [Fig 5] without representation of a mass; − [Fig 7] is a detail view of [Fig 6]; − [Fig 8], [Fig 10] and [Fig 11] are perspective views of another embodiment of the resonator according to the invention; − [Fig 9] shows MEMS structures used in the embodiment of the resonator shown in [Fig 8], [Fig 10] and [Fig 11]; − [Fig 12] illustrates vibration patterns of the masses; − [Fig 13] schematically illustrates a rotation measuring apparatus according to the invention; − [Fig 14] is a sectional view along a plane perpendicular to the ternary axis of symmetry of the rods of a mass of a resonator according to an exemplary embodiment of the invention; − [Fig 15] is a view similar to that of [Fig 14] according to another embodiment of the invention providing half-plays between rods; − [Fig 16] illustrates an alternative orientation of the mass relative to the orientation of the mass of [Fig14] and [Fig 15]; − [Fig 17] illustrates rods having the shape of an equilateral triangle of reduced dimension according to another embodiment of the invention; and − [Fig 18] and [Fig 19] respectively illustrate rods having diamond and hexagonal shapes, according to two other embodiments of the invention. Detailed description of at least one embodiment Figures 1 to 3 respectively illustrate a general constitution of a resonator 1 of a rotation measuring device according to the invention, a mass of the resonator 1 considered separately and ternary and quaternary axes of symmetry of a cube. The invention finds an interesting application in the field of fixed-frequency vibrating resonators, for example made of quartz, in particular for time measuring devices. The invention also finds a useful application in any technical field where it is necessary to measure rotations along one or more axes, in relation to a spaceinertial, including, in particular, aiming and stabilization systems and inertial units. According to an embodiment illustrated in Figure 1, the resonator 1 comprises four identical, rigid, nested masses 2a, 2b, 2c, 2d connected to each other by first springs 3. Each mass 2a, 2b, 2c, 2d has a ternary axis of symmetry 5, as shown in Figure 2. Thus, the mass is invariant during a rotation of 120° around the ternary axis of symmetry 5. Preferably, each mass 2a, 2b, 2c, 2d also has a plane of symmetry 4. In addition, each mass 2a, 2b, 2c, 2d comprises two bases 6 connected by at least three rods 7. For example, the bases 6 may be in the form of a disc of circular or polygonal section. According to another embodiment, as illustrated in Figure 6, the bases 6 can have more complex shapes of the chamfered cube type. The ternary symmetry axes 5 of the masses 2a, 2b, 2c, 2d are orientedalong the four axes of ternary symmetry 8, or of order three, of a cube 9, as illustrated in figure 3, having twelve edges 10. The four axes of ternary symmetry 8 of the cube 9 are concurrent with the center of symmetry O of the cube 9. Axes X, Y and Z, forming an orthonormal reference frame centered on the center of symmetry O, constitute axes of quaternary symmetry, or of order four, of the cube 9. These axes X, Y and Z also constitute normals to the first bisector planes of the axes of ternary symmetry. Straight lines, passing through the center of symmetry O and having as direction vectors ( 1 , 1 ,0), (0, 1 1 √2 √2 √2, √2), ( 1 √2.0, 1 √2), in the X, Y and Z reference system, constitute normals to the second bisector planes of the ternary symmetry axes. According to one embodiment, the first springs 3 are rectilinear rods stressed axially and in bending. The first springs 3 are arranged perpendicular to each other along the twelve edges 10 of the cube 9. The first springs 3 make it possible to create, in the absence of vibration, an equilibrium for which the centers of the masses 2a, 2b, 2c, 2d are positioned at the center of symmetry O of the cube 9. In vibration, the centers of gravity of the masses 2a, 2b, 2c, 2d have a relative movement, while maintaining an overall center of gravity of the masses 2a, 2b, 2c, 2d, constant and coincident with the center of symmetry O of the cube 9. It should be noted that the relative movement of the centers of gravity of the masses 2a, 2b, 2c, 2d is small in comparison with the dimensions of the resonator 1.The relative movement of the centers of gravity of the masses 2a, 2b, 2c, 2d can be about 1 μm relative to a length of about 1 cm of the edge 10 of the cube 9. In such a configuration, the hypothesis of small displacements is applicable and it is thus possible to neglect the changes in geometry to write equations describing an operation of the system. The resonator 1 is connected to an external support, not shown in the figures, by means of second springs 11, in particular identical in shape to the first springs 3. Thus, the second springs 11 are of the rectilinear rod type arranged at each end of the masses 2a, 2b, 2c, 2d, preferably in symmetrical extension of the first springs 3. According to one embodiment, the second springs 11 more particularly connect the base 6 to the external support. More particularly, the second springs 11 are three in number for each base.Thus configured, the twenty-four second springs 11 may have a section and / or a stiffness different from that of the first springs 3 connecting the masses 2a, 2b, 2c, 2d to each other. The resonator 1 thus has cubic symmetry. In order to allow the masses 2a, 2b, 2c, 2d to be nested, they may be made in at least two assembled parts. Alternatively, the masses 2a, 2b, 2c, 2d may be made by additive manufacturing methods allowing the manufacture of nested parts. The resonator 1 is equipped with control means 12, 13, 14 comprising: - measuring means 19, capable of measuring a relative displacement between each pair of masses in at least two directions, and - application means 20, capable of applying inter-mass forces for each pair of masses in at least two directions. The overall resultant of the applied forces is zero.According to a particular embodiment, the resonator 1 is equipped with control means 12, 13, 14 configured to operate successively as means 19 for measuring the relative displacement between each pair of masses and as means 20 for applying inter-mass forces for each pair of masses. Alternatively, the resonator 1 may be equipped with control means 19 dedicated to measuring the relative displacement between each pair of masses and control means 20 dedicated to applying inter-mass forces for each pair of masses. The control means 12, 13, 14 may be electrostatic, piezoelectric or microelectromechanical system type transducers, also designated by the acronym MEMS for “MicroElectroMechanical Systems” in English.For example, in the case of electrostatic transducers, each pair of masses is equipped with two pairs of electrodes 12, as control means 12, making it possible to measure the displacement and to apply electrostatic forces along the normal to the first bisector plane of the two masses. Figure 4 illustrates a placement of control means 12, as electrodes 12, arranged between two masses 2a and 2b forming an angle of value equal to cos. −1 ( −1� 3), or approximately 109°28'. The electrodes 12 may be plate-shaped and are arranged parallel to the first and / or second bisector plane of the ternary symmetry axes 5 of the two masses and make it possible to measure the displacement and to apply electrostatic forces along the normal respectively to the first and / or second bisector plane of the ternary symmetry axes 5 of the two masses. Alternatively, the electrodes 12 may be replaced by piezoelectric elements positioned on the first springs 13 and making it possible to measure their deformations and / or to apply forces. Figures 5 to 7 illustrate another illustrated embodiment, in which, respectively, Figure 5 is a perspective view of the resonator 1, Figure 6 a perspective view of the resonator 1 of Figure 1 in which a mass is not shown and Figure 7 a detail view of Figure 6.In the embodiment illustrated in Figures 5 to 7, electrostatic type transducers, in the form of plates, are placed on the rods 7 of the masses 2a, 2b, 2c, 2d. In Figure 6, the mass 2a is not shown for the sake of clarity. The plates are placed on the rods 7 of the masses 2a, 2b, 2c, 2d so that each plate placed on the rod 7 of a mass corresponds to another associated plate, which is parallel to it, and arranged nearby on the rod 7 of another mass. According to the example presented, Figure 7 illustrates pairs of plates 13ca and 13ac, 13ba and 13ab, 13da and 13ad. According to the notation used, the first index indicates the mass on which the plate is arranged, the second index corresponds to the mass on which the associated plate is arranged. Thus, plate 13ca is arranged on a rod 7 of mass 2c and is associated with plate 13ac which is arranged nearby on rod 7 of mass 2a.Figures 8, 10 and 11 are perspective views of another embodiment of the resonator 1 according to the invention. In such another embodiment, the transducers comprise six MEMS-type planar structures 14 bonded to the masses 2a, 2b, 2c, 2d on the six faces of the cube 9. In Figures 8 and 9, only three of the six structures 14 are shown to facilitate understanding. The references a, b, c, d in Figure 9 indicate the bonding zones corresponding to the masses 2a, 2b, 2c, 2d, respectively. The MEMS structures 14 integrate the first springs 3, the second springs 11 and means for fixing to a housing 15 which envelops them. The MEMS structures 14 are capable of performing relative deformation measurements between two masses 2a, 2b, 2c, 2d and of applying inter-mass forces. In all embodiments, the resonator 1 has cubic symmetry.In the embodiments presented, the resonator 1 comprises four masses 2a, 2b, 2c, 2d. However, the invention is not limited to the embodiments described and it is possible in particular to vary the number N of masses that the resonator 1 comprises provided that the constraints related to the symmetry of the resonator are respected and without departing from the scope of the invention. Indeed, the number N of masses that the resonator 1 comprises could exceed four, if the arrangement of these N masses respects the same symmetry constraints along the N axes of symmetry associated with each of the N masses, as for the embodiments described above. Alternatively, the presence of the second springs 11 could make it possible to dispense with the first springs 3.In such a configuration, the masses 2a, 2b, 2c, 2d then vibrate relative to the housing 15 operating as a neutral point and the measurement of the displacements and the application of the forces can be carried out relative to the housing 15. The cubic symmetry implies that, for each of the masses 2a, 2b, 2c, 2d taken individually, a stiffness of the translational links is identical in all directions. Under the effect of the rotations, assuming zero damping, the initial translational vibrations of each of the masses propagate on the three axes of quaternary symmetry X, Y and Z according to the following relation: �. where ^^^^, ^^^^, ^^^^ are respectively the positions of each mass along the X, Y, Z axes of quaternary symmetry of the resonator, ^^^^, ^^̇^^, ^^^^ are respectively the velocities of each mass along the X, Y, Z axes of quaternary symmetry of the resonator, ^^̈^^, ^^̈^^, ^^̈^^ are respectively the accelerations of each mass along the X, Y, Z axes of quaternary symmetry of the resonator, ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ are respectively the rotation speeds of the resonator, in an inertial space, according to the X, Y, Z axes of quaternary symmetry of the resonator, and ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ are respectively the resonance pulsations along the X, Y, Z axes of quaternary symmetry of the resonator corresponding to the triplet of degenerate modes corresponding to the type of vibration pattern considered (see below) with, in the case of perfect cubic symmetry, ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^. Eq.1 is the consequence of maintaining, in an isotropic medium, the vibration direction in an inertial frame or, in other words, the consequence of the Coriolis forces in the frame of resonator 1. In the case of perfect cubic symmetry, when resonator 1 is subjected to rotation, an orientation of the vibration of each of the masses 2a, 2b, 2c, 2d remains fixed in an inertial space. Such orientations can then be used as an orientation reference. If the cubic symmetry is not perfect and the damping is not zero, equation Eq. 1 must be completed by error terms and it is necessary to apply forces in order to compensate for losses and differences between the pulsations ^^^^ ^^^^ , ^^^^ ^^^^ , and ^^^^ ^^^^The system has (N–1)*6 degrees of freedom, where N is the number of masses in the system. Thus, for resonator 1 with four masses 2a, 2b, 2c, 2d, there are theoretically eighteen balanced degrees of freedom: nine translational vibration modes and nine rotational vibration modes. The distribution of rotational vibration modes can be complex because they cannot be grouped into triplets at the same frequency. Indeed, given the shape of masses 2a, 2b, 2c, 2d, their moment of inertia is not equal along the three axes of space. On the other hand, for translational vibration modes, cubic symmetry ensures isotropic behavior along the three dimensions of space. Figure 12 shows the translational vibration patterns of masses 2a, 2b, 2c, 2d.A vibration pattern corresponds to a modal decomposition basis of any translational vibration, which has the property of creating a global vibration of the system, of four masses 2a, 2b, 2c, 2d in the present case, zero at the frequency of the eigenmodes. There are, for the system of four masses 2a, 2b, 2c, 2d, a total of nine translational vibration modes including - three first degenerate modes, that is to say of the same frequency ^^^^. ^^^^ , concerning a three-dimensional pattern, - three second degenerate modes, of frequency ^^^^ ^^^^ , concerning a plane pattern, - three third degenerate modes, of frequency ^^^^ ^^^^ , concerning a linear pattern. The six degenerate modes of the plane and linear patterns are generally of almost identical frequency ^^^^ ^^^^ ≈ ^^^^ ^^^^The resonator is used with only one type of these patterns, either linear, planar, or three-dimensional. In the linear pattern, the translations are carried out along the same straight line, with two masses, corresponding to 2a and 2c, in one direction and two other masses, corresponding to 2b and 2d, in the other direction. At initialization, this straight line can be arbitrarily positioned along the X axis of quaternary symmetry. In the planar pattern, two masses, corresponding to 2a, 2b, are in translation in opposite directions to each other along a first straight line and two other masses, corresponding to 2c and 2d, are in translation in opposite directions to each other along a second straight line intersecting and perpendicular to the first straight line. At initialization, these straight lines can be chosen arbitrarily according to the bisectors of the X and Y axes of quaternary symmetry.In the three-dimensional pattern, at initialization, the translations of each of the masses 2a, 2b, 2c and 2d are carried out arbitrarily along their ternary symmetry axis 5 which coincides by construction with one of the four ternary symmetry axes 8 of the cube 9. Consequently, during the rotations of the resonator, the vibration axes of each of the patterns evolve according to equation Eq.1 while maintaining their relative orientations. The total rotation, from initialization to the current moment, can be represented by a following rotation matrix: 0sin ^^^^ cos ^^^^ −sin ^^^^ 0. 1 0 sin ^^^^ cos ^^^^ 0� 0 cos ^^^^ 0 0 1where: ^^^^ is an angle of rotation around the X axis of quaternary symmetry of the resonator, ^^^^ is an angle of rotation around the Y axis of quaternary symmetry of the resonator, and ^^^^ is an angle of rotation around the Z axis of quaternary symmetry of the resonator. In the case of the linear pattern, the vibrations of the positions of each of the masses 2a, 2b, 2c, 2d, can therefore be described, up to a permutation of masses, by the following relations, describing the vibrations of the four masses 2a, 2b, 2c, 2d in a single direction: where ^^^^ ^^^^ , …, ^^^^ ^^^^ are the coordinates of the masses 2a, 2b, 2c, 2d, ^^^^ ^^^^ is the pulsation corresponding, in the case of perfect cubic symmetry, to the linear pattern, ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^ , t is time, and ^^^^ ^^^^is the amplitude of the vibration initially positioned along the x axis. In the case of the plane pattern, the vibrations of the positions of each of the masses 2a, 2b, 2c, 2d, can therefore be described, up to a permutation of masses, by the following relations, describing the vibrations of the four masses 2a, 2b, 2c, 2d along two orthogonal directions: where ^^^^ ^^^^ , …, ^^^^ ^^^^ are the coordinates of the masses 2a, 2b, 2c, 2d, ^^^^ ^^^^ is the pulsation corresponding, in the case of perfect cubic symmetry, to the plane pattern, ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^ , t is the time, ^^^^ ^^^^ is the amplitude of the vibration initially positioned along the x axis, and ^^^^ ^^^^is the amplitude of the vibration initially positioned along the y axis. In the case of the three-dimensional pattern, the vibrations of the positions of each of the masses 2a, 2b, 2c, 2d, can therefore be described, up to a permutation of masses, by the following relations, describing the vibrations of the four masses 2a, 2b, 2c, 2d along isotropic directions in three dimensions: where ^^^^ ^^^^ , …, ^^^^ ^^^^ are the coordinates of the masses 2a, 2b, 2c, 2d, ^^^^ ^^^^ is the pulsation corresponding, in the case of perfect cubic symmetry, to the three-dimensional pattern, ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^ , t is the time, ^^^^ ^^^^ is the amplitude of the vibration initially positioned along the x axis, ^^^^ ^^^^ is the amplitude of the vibration initially positioned along the y axis, and ^^^^ ^^^^is the amplitude of the vibration initially positioned along the z axis. Remarkably, all these movements can be described using the matrix ^^^^^^^^ ^^^^ ^^^^, a pulsation ^^^^ and by a linear combination of the following initial elementary vibrations, corresponding to ^^^^ = ^^^^ = ^^^^ = 0: where ^^^ x ^ a , ^^^^ xb , ^^^ x ^ c , ^^^^ xd are the initial vibrations of the positions of masses a, b, c and d along the x axis and are affected by the coefficient ^^^^ ^^^^ , where ^^^ y ^ a , ^^^^ yb , ^^^ y ^ c , ^^^^ yd are the initial vibrations of the positions of masses a, b, c and d along the y axis and are affected by the coefficient ^^^^ ^^^^ , And where ^^^ z ^ a , ^^^^ zb , ^^^ z ^ c , ^^^^ zdare the initial vibrations of the positions of masses a, b, c and d along the z axis and are affected by the coefficient ^^^^ ^^^^ . The pulse ^^^^ corresponding to the type of pattern considered: − for a linear pattern, ^^^^ = ^^^^ ^^^^ , − for a plane pattern, ^^^^ = ^^^^ ^^^^ , − for a three-dimensional pattern, ^^^^ = ^^^^ ^^^^ The three initial elementary vibration patterns retain the global center of gravity. Indeed, they group together, at the initial instant, for each of the quaternary symmetry axes X, Y, Z, two pairs of masses 2a, 2b, 2c, 2 having opposite vibrations. The following property is then observed: + ^^^^ ^^^^ = − ^^^^ ^^^^ = + ^^^^ ^^^^ = − ^^^^ ^^^^ = ^^^^ ^^^^ cos ^^^^ ^^^^ (Eq.8A)+^^^^ ^^^^ = − ^^^^ ^^^^ = − ^^^^ ^^^^ = + ^^^^ ^^^^ = ^^^^ ^^^^ cos ^^^^ ^^^^ (Eq.8B)+ ^^^^ ^^^^ = + ^^^^ ^^^^ = − ^^^^ ^^^^ = − ^^^^ ^^^^ = ^^^^ ^^^^ cos ^^^^ ^^^^ (Eq.8C)where ^^^^^^^^ , …, ^^^^ ^^^^ are the coordinates of the masses 2a, 2b, 2c, 2d, and ^^^^ ^^^^ , ^^^^ ^^^^ and ^^^^ ^^^^ are the amplitudes corresponding to each of the initial elementary vibrations. The initial vibrations are distributed in all directions under the effect of rotations. However, each of the vibration patterns retains the distribution properties on the different masses 2a, 2b, 2c, 2d corresponding to equations Eq.8A, Eq.8B and Eq.8C, thus making it possible to distinguish the initial vibrations. The measurement of the distribution ( ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ ) of these initial vibrations can then be carried out from the vibration present on each of the masses 2a, 2b, 2c, 2d and corresponding to each of the patterns according to the following equation:

[0002] (Eq.9) where ^^^^ ^^^^ ^^^^is the consequence, under the effect of rotation, on an axis 'i' of the vibration initially present, for ^^^^ = ^^^^ = ^^^^ = 0, on an axis 'j', In the case of perfect cubic symmetry and zero damping, the parameters respect the following theoretical properties: � ^^^^ ^^^^ ^^^^ 2 + ^^^^ ^^^^ ^^^^ 2 + ^^^^ ^^^^ ^^^^ 2 = ^^^^ ^^^^ and it is then possible to choose arbitrarily: - for a linear vibration pattern: ^^^^ ^^^^ = 1 and ^^^^ ^^^^ = ^^^^ ^^^^ = 0 - for a plane vibration pattern: ^^^^ ^^^^ = ^^^^ ^^^^ = 1 and ^^^^ ^^^^ = 0 - for a three-dimensional vibration pattern: ^^^^ ^^^^ = ^^^^ ^^^^ = ^^^^ ^^^^= 1 Figure 13 schematically illustrates a rotation measuring device 16 comprising a resonator 1 as described previously, associated with a vibration regulation module 17, and with a rotation calculation module 18. The regulation module 17 makes it possible to generate and maintain the vibrations of the resonator 1. In an embodiment not illustrated, it remains possible for the regulation module 17 to be integrated into the resonator 1, in other words for the resonator 1 to be provided with a vibration regulation module 17. The regulation module 17 comprises a measurement module 17a, a calculation module 17b and a control module 17c. More specifically, the measurement module 17a makes it possible to calculate data representative of vibration amplitude and phases ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^from the deformation measurements of the resonator 1 provided by measuring means 19. The calculation module 17b uses the data from the measuring module 17a to determine forces to be applied to the masses 2a, 2b, 2c and 2d along the quaternary symmetry axes X, Y and Z, ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^, in order to obtain instructions for amplitudes, phases and relative orientations of the vibration patterns of the resonator 1. According to an alternative embodiment, the calculation module 17b can also use the data from the measurement module 17a to determine forces necessary for the orientation of the vibration patterns relative to the quaternary symmetry axes X, Y, Z. The control module 17c controls the application means 20 as a function of the amplitudes, phases and orientations of forces from the calculation module 17b. The rotation calculation module 18 is configured to calculate a rotation R carried out by the rotation measuring device 16 from data representative of amplitude and phases of vibrations from the measurement module 17a. In practice, cubic symmetry is never perfect ( ^^^^ ^^^^ ≠ ^^^^ ^^^^ ≠ ^^^^ ^^^^) and the vibration damping is never zero. Thus, in order to compensate for these imperfections, the calculation module 17b calculates the necessary forces ( ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ ) to the maintenance of the properties of the vibration, from the measurement of the distributions ( ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ ) of the initial vibration patterns ( ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^) on the three axes of quaternary symmetry X, Y and Z. This thus makes it possible to maintain the relative phase between the distribution of the patterns on the three axes of quaternary symmetry X, Y and Z. The distributions of the patterns on the axes of quaternary symmetry X, Y and Z are respectively ^^^^ ^^^^ ^^^^ + ^^^^ ^^^^ ^^^^ + It is therefore a question of ensuring that the following conditions are respected: This also allows the amplitude of each of the vibration patterns to be maintained by respecting the following conditions: - for a linear vibration pattern, � ^^^^ ^^^^ ^^^^ 2 + ^^^^ ^^^^ ^^^^ 2 + ^^^^ ^^^^ ^^^^ 2 = 1 ; - for a plane vibration pattern, - for a three-dimensional vibration pattern, � ^^^^ ^^^^ ^^^^ 2 + ^^^^ ^^^^ ^^^^ 2 + ^^^^ ^^^^ ^^^^ 2 = 1 ; This also allows the relative geometric orientation of each of the vibration patterns to be maintained by imposing the following conditions: - for a plane vibration pattern, - for a three-dimensional vibration pattern, Alternatively, this also allows maintaining the geometric orientation of each of the vibration patterns relative to the quaternary symmetry axes X, Y and Z, by controlling forces compensating the Coriolis forces, represented by the second term of equation Eq.1: From the forces to be applied to each of the masses 2a, 2b, 2c, 2d, the control module 17c calculates the inter-mass forces, namely two inter-mass forces for each of the six pairs of masses 2a, 2b, 2c, 2d. For example, it may be chosen to direct the inter-mass forces along the normal to the second bisector planes of the ternary symmetry axes 5 of the masses 2a, 2b, 2c, 2d, from six forces ( ^^^^1 ^^^^ ^^^^ … ^^^^1 ^^^^ ^^^^), one per pair of masses. For example, it can be chosen to direct the inter-mass forces according to the normal to the first bisector planes of the ternary symmetry axes 5 of the masses, from six forces ( ^^^^2 ^^^^ ^^^^ … ^^^^2 ^^^^ ^^^^ ), one per pair of masses. In this case, the relationships between the forces applied to the masses 2a, 2b, 2c, 2d and the inter-mass forces can be gathered according to the following matrix equation: (Eq.10) It should be noted that the last three rows of the matrix Eq.10 are necessary to guarantee the pseudo-inversion of the latter. They are therefore arbitrary. In the example of equation Eq.10, they are chosen so as to distribute the forces to be applied on the different application means 20. Furthermore, it is possible to delete up to three other rows without impacting the pseudo-inversion of the matrix. This makes it possible to compare the forces applied by each pair of masses and to correct their relative differences by observing the differences appearing during cyclic deletions of rows. The control module 17c calculates the inter-mass forces to be applied on each of the masses 2a, 2b, 2c, 2d by conventional methods for solving linear systems such as, for example, the following classical pseudo-inverse of least squares: It is also possible to apply forces directly ( ^^^ ^ ^ ^^^ ^^^^, ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^ , ^^^ ^ ^ ^^^ ^^^^) on the masses in the case where there are means of applying forces relative to the case. We will now describe how to measure the displacements of the masses 2a, 2b, 2c, 2d. For example, the measuring means 19 can use the measurements of relative displacements between two masses according to the normal to the second bisector plane of their axes of ternary symmetry 5, from six measurements ( ^^^^ ^^^^ ^^^^1 ^^^^ ^^^^ … ^^^^ ^^^^ ^^^^1 ^^^^ ^^^^) one per pair of masses. For example, the measuring means 19 can use the measurements of relative displacements between two masses according to the normal to the first bisector plane of the axes of ternary symmetry 5 of the masses, from six measurements ( ^^^^ ^^^^ ^^^^2 ^^^^ ^^^^ … ^^^^ ^^^^ ^^^^2 ^^^^ ^^^^), one per pair of masses. The relative displacement measurements indicated above can be gathered according to the following matrix equation: (Eq.11) It should be noted that the last three rows of matrix Eq.11 are necessary to ensure the pseudo-inversion of the latter and correspond to the hypothesis that the motions are globally zero-mean. This is the case when inter-mass forces having a globally zero sum are applied, as described above. Furthermore, it is possible to delete up to three other rows without affecting the pseudo-inversion of the matrix. This allows to correct the differences between the different measurement channels by observing the differences appearing during cyclic deletions of rows. According to the notation used, ^^^^ ^^^^ , …, ^^^^ ^^^^are the coordinates of the masses 2a, 2b, 2c, 2d. The measurement module 17a calculates from the equation Eq.11 the motion of each mass 2a, 2b, 2c, 2d. For the calculation of the motions of the masses 2a, 2b, 2c, 2d, the measurement module 17a uses classical methods for solving linear systems such as, for example, the following classical pseudo-inverse of least squares: It is also possible to measure directly ( ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ) in the case where there are means of measuring displacements relative to the housing. In this case, the measurements will be corrected for the overall movement of the four masses. The measurement module 17a then distributes the calculated movements ( ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ , ) as a function of the initial elementary vibration patterns using equation Eq.9 recalled below: In the case of using a three-dimensional pattern, the distributions ( ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ , ^^^^ ^^^^ ^^^^ ) of the initial vibration patterns ( ^^^^ ^^^^ , ^^^^ ^^^^ , ^^^^ ^^^^ ) allow to reconstruct a rotation matrix ^^^^ ^^^^ accounting for the transformation of the initial vibration, during rotations, according to equation Eq.1. In the case of no defect, this matrix represents the rotation of resonator 1 since the initial instant: ^^^^ ^^^^ ^^^^ ^^^^ ^^^^^^^^^ ^^^^ =� ^^^^ ^^^^ ^^^^ ^^^^ ^^^^^ ^^^^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ In the case of a plane pattern, only the first two columns are measurable, so the third column is completed by the vector product of the first two columns: We then obtain a rotation matrix ^^^^ ^^^^ representing the rotation of resonator 1 since the initial instant: In the case of a linear pattern, only the first column is measured. This vector is representative of the rotation of the vibration initially positioned along the X axis of quaternary symmetry of the resonator. We then obtain a rotation matrix ^^^^ ^^^^ representing the component, perpendicular to the X axis, of the rotation of resonator 1 since the initial instant: ^^^^ ^^^^ Such a resonator 1 is therefore a gyroscope, because it allows the rotation it undergoes to be measured (only two components of the rotation in the case of a linear vibration pattern). The calculation module 18 constructs a rotation matrix R ( ^^^^ ^^^^ , ^^^^ ^^^^ or ^^^^ ^^^^ ), according to the above relations, from a decomposition obtained by the measurement module 17a and, preferably, taking into account the defects of the resonator 1 by corrective terms. First of all, because of the measurement noises and the partial achievement of the objectives of the calculation module 17b, the matrices ^^^^ ^^^^ , ^^^^ ^^^^ or ^^^^ ^^^^ can be ortho-normalized in order to calculate the matrices ^^^^ ∗ , ^^^^ ∗ or ^^^ ∗ ^ ^^^ ^^^^ ^ ^^^^. Otherwise, at any time, a measurement noise, an angular bias and a drift appear. The bias and the drift are dependent on these matrices which are representative of the state of the vibration distribution within the resonator 1. The faults are taken into account, for example, by a calibration carried out periodically in the laboratory allowing to obtain an additional rotation matrix, ^^^^^^^^ ^^^^ ^^^^ ^^^^, corrective and representative of the angular bias and the integral of the drift since the initial time. We then obtain the matrix R, constituting the corrected measurement of the rotation of the resonator 1, by the following calculation: - for a three-dimensional vibration pattern: - ^^^^ = ^^^^ ^^ . ^^^ ∗ ^^^^ ^^^^ ^^^^ ^^^ ^^^^ , (Eq.12.A) - for a plane vibration pattern: - ^^^^ = ^^^^^^^ ^^^^ ^^^^ ^^^^. ^^^^ ^^^^ ∗ , (Eq.12.B) - for a linear vibration pattern: - ^^^^ = ^^^^^^^ ^^^^ ^^^^ ^^^^. ^^^^ ^^^^∗, (Eq.12.C) Figure 14 is a sectional view along the plane perpendicular to the ternary axis of symmetry of the rods 7 of a first mass chosen from the four masses 2a, 2b, 2c and 2d. The arrangement of the rods of the other masses is obtained by rotating the rods 7 through 90°, 180° and 270° about one of the axes X, Y or Z. In the example illustrated in Figure 14, there is no clearance provided between the rods 7 relative to the rods of the other masses. Alternatively, it is possible to provide half-clearances 21 between the rods of the four masses to allow the rods to vibrate (Figure 15). In other words, a movement space is provided between the adjacent rods of the different masses so that the rods can vibrate freely. The minimum movement space of each rod thus corresponds to half-play 21. Figure 16 illustrates an alternative orientation of the mass compared to the orientation of the mass in Figures 14 and 15.In Figures 14 to 16, the rods of the mass have the shape of an equilateral triangle according to a cross-section oriented along a plane perpendicular to the axis of ternary symmetry of the mass. Figure 17 illustrates an exemplary embodiment where the rods have the shape of an equilateral triangle of reduced dimension. Alternatively, it is possible to provide rods with other shapes, for example diamonds or hexagons, as seen in Figures 18 and 19, respectively.

Claims

CLAIMS 1. Mechanical resonator (1) comprising: - at least four identical and rigid masses (2a, 2b, 2c, 2d), capable of exhibiting translational vibration modes, - control means (12, 13, 14) comprising o measuring means (19), capable of measuring a relative displacement between each pair of masses in at least two directions, and o application means (20), capable of applying inter-mass forces for each pair of masses in said at least two directions, - a vibration regulation module (17) receiving data from said measuring means (19) and issuing instructions for controlling said application means (20) as a function of said data, and characterized in that the resonator (1) has cubic symmetry, said masses (2a, 2b, 2c, 2d) being nested together and each having an axis of ternary symmetry (5) oriented along a ternary symmetry axis (8) of a cube (9), said masses (2a,2b, 2c, 2d) being connected to each other by first springs (3), and / or being connected to an external support of the resonator (1) by second springs (11).

2. Resonator according to claim 1, wherein the masses (2a, 2b, 2c, 2d) each have a plane of symmetry (4).

3. Resonator according to claim 1 or 2, wherein the masses (2a, 2b, 2c, 2d) each comprise two bases (6) connected by at least three rods (7)., 4. Resonator according to any one of claims 1 to 3, wherein the first springs (3) are positioned perpendicular to each other along the twelve edges (10) of the cube (9).

5. Resonator according to any one of claims 1 to 4, wherein the first springs (3) are straight rods stressed axially and / or in bending.

6. Resonator according to any one of claims 1 to 5, wherein the second springs (11) are arranged at each end of the masses (2a, 2b, 2c, 2d), in particular in symmetrical extension of the first springs (3).

7. Resonator according to claim 6, wherein the second springs (11) are straight rods stressed axially and / or in bending.

8. Resonator according to claim 6 or 7, wherein the second springs (11) have an axial stiffness and / or a bending stiffness different from an axial stiffness and / or a bending stiffness of the first springs (3). 9.Resonator according to any one of claims 1 to 8, in which the masses (2a, 2b, 2c, 2d) are each made of at least two assembled parts.

10. Resonator according to any one of claims 1 to 9, in which the control means (12, 13) are transducers, in particular electrostatic or piezoelectric transducers, making it possible to measure deformations and / or to apply forces.

11. Resonator according to claim 10, in which the transducers are arranged parallel to a first and / or a second plane bisecting the ternary axes of symmetry of each pair of two masses (2a, 2b, 2c, 2d) and make it possible to measure a displacement and to apply forces along a. normal respectively to the first and / or second bisector plane of the ternary symmetry axes of each pair of two masses (2a, 2b, 2c, 2d).

12. Resonator according to claim 10 or 11, dependent on claim 3, in which the transducers are in the form of plates and are arranged on the rods (7) of the masses (2a, 2b, 2c, 2d), so that each plate placed on the rod (7) of a mass (2a, 2b, 2c, 2d) corresponds to another associated plate which is parallel to it and arranged nearby on the rod (7) of another mass (2a, 2b, 2c, 2d).

13. Resonator according to any one of claims 1 to 10, in which the control means (14) are transducers of the microelectromechanical system (MEMS) type. 14.Resonator according to claim 13, in which the transducers are glued to the masses (2a, 2b, 2c, 2d) on the six faces of the cube (9) and integrate the first springs (3), the second springs (11) and means of fixing to a housing (15) which envelops them, the transducers being capable of carrying out measurements of relative deformation between two masses (2a, 2b, 2c, 2d) and of applying inter-mass forces. 15.Rotation measuring apparatus (16) provided with a resonator (1) according to any one of the preceding claims, said resonator (1) further comprising a rotation calculation module (18) configured to calculate a rotation (R) of said apparatus from data representative of amplitude and phases of vibrations from said vibration regulation module (17), the vibration regulation module (17) being configured to generate translational vibration modes from three initial elementary vibration patterns, understood as bases for modal decomposition of any vibration, having the property of creating a zero overall vibration at the frequency of the natural modes.

16. Rotation measuring apparatus (16) according to claim 15, wherein the vibration regulation module (17) maintains a relative phase. between a distribution of the patterns on three orthogonal axes, in particular the quaternary symmetry axes (X, Y, Z) of the resonator (1), an amplitude of each of the patterns and a relative orientation of each of the patterns between them.

17. Rotation measuring apparatus (16) according to claim 15 or 16, in which the vibration regulation module (17) positions at predetermined values, according to a time law, amplitudes, phases and orientations of each of said elementary patterns, the time law being capable of exploiting the symmetries of the defects of the resonator (1) in order to average them.

18. Rotation measuring apparatus (16) according to claim 17, in which the defects of the resonator (1) are identified using an angular reference external to the resonator (1), used continuously or punctually. 19.Method for measuring rotation of a rotation measuring device (16) according to any one of claims 15 to 18, characterized in that it comprises at least: − a step of measuring the relative displacements between the masses (2a, 2b, 2c, 2d) for each pair of masses; − a step of calculating the movement of each mass (2a, 2b, 2c, 2d) as a function of the measurements of the relative displacements; − a step of decomposing the calculated movements of each mass (2a, 2b, 2c, 2d) as a function of the initial elementary vibration patterns; and − a step of constructing a rotation matrix (R) from the decomposition obtained, preferably taking into account the defects of the resonator (1) by corrective terms.

20. Rotation measurement method according to claim 19, characterized in that it comprises a step of providing rotation speed information from the forces calculated by the vibration regulation module (17).

21. Rotation measurement method according to claim 20, characterized in that it provides rotation information from the integral, carried out using rotation matrices or quaternions, of the rotation speed information.

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