WO1999022203A1

WO1999022203A1 - Multi-axis gyroscope

Info

Publication number: WO1999022203A1
Application number: PCT/GB1998/003215
Authority: WO
Inventors: James Stonehouse Burdess; John Neville Fawcett; Alun James Harris
Original assignee: Btg International Limited
Priority date: 1997-10-29
Filing date: 1998-10-28
Publication date: 1999-05-06
Also published as: TW366414B; GB9722865D0

Abstract

The present invention provides a solid-state gyroscope (10) having a primary axis (OZ) and means for detecting cos(n±1)υ or sin(n±1)υ modes of vibration, thereby to facilitate detection of rotation about one or more axis, neither of which is the primary axis (OZ).

Description

MULTI-AXIS GYROSCOPE

The present invention relates to a gyroscopic device or rate sensor and relates particularly, but not exclusively, to such a device suitable for detection of rotation about one, two or three axes.

GB-B-2154739 discloses a compact rate-sensor which uses a cylinder or disc of piezoelectric material to detect motion about the axis of the cylinder. A circularly-symmetrical electrode array deposited on the surface of the cylinder is used to excite and sense vibrations of the piezo-electric material when modified by any movement of the device about the axis of the cylinder. In more detail, this device provides eight electrodes deposited in a regular pattern around the circumference of the piezo-electric cylinder as shown in Figure A of the prior art portion of the attached drawings. Driving electrodes 5-8 are used to excite the cylinder into radial vibration (commonly known as the primary mode) in which the amplitude varies around the circumference and sensing electrodes 7-6 detect the phase and amplitude of the oscillation. Since the cylinder material is piezo-electric, the applied field excites the cylinder into a mode of oscillation in which its shape, when viewed in plan, changes repeatedly between a first flexural vibration and a second flexural vibration similar in shape at right angles to the first flexural vibration. In the absence of any rotational movement about the axis of the cylinder, electrodes 9-12 experience no movement and, therefore, provide no voltage output to a means for determining angular rotation. However, if the cylinder is rotated about said axis with an angular velocity, inertia forces are generated which produce a displacement which is phase displaced to the initial oscillation pattern and, hence, electrodes 9-12 are no longer coincident with the oscillation nodes and provide a voltage output which is proportional to the rate of change and thus can be used to measure the angular velocity.

Whilst the above device provides a very accurate method of determining rotation about the axis of the cylinder, it is unable to detect rotation about other axes and, hence, one must employ three such devices to provide a full three axis gyroscope. In order to appreciate fully the following features of the present invention, we would first draw the reader's attention to Figures B and C of the prior art portion of the drawings in which is shown a circularly-symmetric shell structure with the axis of rotational symmetry aligned with the axis OZ. The vibration of the structure can be described by the displacement, u=(u_x,u_y,u_z), of a typical Point, along the orthogonal directions Pxyz of which Px and Py are normal and tangential to the shell surface at P. For this structure it is known that the modes of vibration describing this displacement occur in degenerate pairs, with each pair possessing common natural frequency ω_n and a spacial circumferential distribution given by U_cn=(U_x cos nθ, U_y sin nθ, U_z cos n θ) and U, .= (U_x sin nθ, - U_ycos nθ, U_zsin nθ) respectively, where n is called the mode number. If the shape of the shell is of no particular form, i.e. has not been designed for matched frequencies, the natural frequencies con will be discreet for different mode numbers n. Figures D & E shows the displacement U_xcos (nθ) for the cases n = 2 and n = 3. However, for particular shapes, i.e. those specifically designed for the purpose, these natural frequencies are not discreet and the natural frequencies con and ωm, corresponding to the mode numbers n and m, can have coincident values, i.e. con = ωm = ωnm. When the shape of the shell structure is designed to produce this coincidence, the shell has four degenerate modes of vibration.

As already mentioned, if one of the modes of vibration, say the displacement given by U_CI1 is maintained in self oscillation at a set amplitude (primary motion of the gyroscope), it is known that a rate of turn Ω_z applied about axis OZ will create Coriolis inertia forces that will excite, in a resonant way the mode given by U_sn. The measurements of this motion

(secondary motion) or the actuation needed to null it will provide a measure of Ωz. For the case n = 2 this principle has been well applied in the prior art known and made of record. However, what has not been appreciated is that rates of turn applied about axis OX and OY

(Ω_x and Ω ) will produce Coriolis forces arising from the primary motion U_cn that will excite modes of vibration with mode numbers (n-1) and (n+1) hereinafter referred to as mode number m (Fig. E). Thus, if the degeneracy between the mode numbers (n,m) is made to correspond to either of the cases (n, n+1) or (n, n-1) then the rates of turn about OX and OY can be measured by recording the resonant responses (or the action required to null) of either modal pair (U_c „_+ι, U_{s n+1}) or (U_c „.,, U_s, ,_,). For a practical device it is preferable to choose n=2 and m=3 as these modes of vibration are dynamically balanced and transmit no resultant force or moment to mechanical ground. In such a case the performance of the gyro would not, at least to a first order, be sensitive to any variation in the ground connection.

Excitation and measurement of vibrational modes of the gyroscope can be achieved in a variety of ways including capacitive, electromagnetic, piezo-electric and piezo-resistive principles. The axi-symmetric form described above by way of example is not a condition which governs the operating principles of the multi-axis gyroscope.

It is an object of the present invention to provide the gyroscope of the vibrating shell type which exploits the above discussed observation and is capable of detecting rotation about one, two or three axes in a single device.

Accordingly the present invention provides a gyroscope comprising; a shell structure having a first axis of symmetry, a primary mode of vibration (U_{c n}) and a primary mode number (n); driving means, for driving the whole structure to vibrate in its primary mode; and detecting means, for detecting Coriolis force induced modes of vibration thereby to detect rotation about an axis, characterised in that said detecting means includes means for detecting a mode of vibration with a mode number of (n-1) or (n+1) thereby to detect rotation about axes other than said first axis.

Preferably, the driving means includes means for driving said shell structure as a cosine function of θ. In a specific arrangement, rotation about a second axis is detected by detecting the existence of a vibration having a sine function of θ.

Conveniently, rotation about the third axis is detected by detection of cosine function of θ.

Alternatively, the driving means includes means for driving the shell structure as a cosine function of θ Advantageously, the detecting means comprises a plurality of movement sensors circumferentially spaced around the shell, said detecting means producing, upon detection of motion of said shell, an output signal proportional to a rate of turn about an associated axis.

In a specific arrangement, the detecting means comprises eight sensors arranged in four pairs, each pair being positioned between the driving means. In a specific arrangement, the sensors of each pair are equi-spaced from each other and adjacent to the driving means.

In a one embodiment of the present invention, the shell structure comprises a cup shaped structure of circular symmetry about said first axis and having a side wall and a base, said driving means acting on the side wall to drive the structure into its primary mode of resonance.

In one arrangement of the above device the detection means comprises detectors positioned for detecting movement of the side walls.

In an alternative arrangement of the above device, the detection means comprises detectors positioned for detecting movement of the base of said shell structure.

In an alternative form of present invention, the shell structure comprises a ring supported on a substrate by means of a plurality of flexible beams.

In the ring arrangement of the present invention the detection means comprises a plurality of detectors positioned for detecting movement of said ring.

In a specific arrangement of the present invention the detecting means comprises twelve detectors equi-spaced around the circumference of the shell structure.

Conveniently, both the second and third axes are perpendicular to each other and each is perpendicular to the first axis. In a particularly advantageous arrangement of the present invention, the detection means further includes means for detecting rotation of said shell about the first axes.

The present invention will now be more particularly described by way of example only with reference to the accompanying drawings in which:

Figures A to E illustrate the arrangement of the prior art and the basic principles behind the present invention;

Figures la and lb are cross sectional and plan views respectively of a first embodiment of the present invention;

Figure 2a is a cross sectional view of a further embodiment of the present invention;

Figure 2b is a view in the direction of arrows AA of Figure 2a;

Figures 3 and 4 illustrate the primary drive vibration pattern and that associated with rotation about axis Z; Figure 5 is a simplified view taken in the direction of arrows V and W in Figures

1 a and 2a and has the sin 3θ and cos 3Θ modes of vibration associated with rotation about axes OX and OY superimposed thereon;

Figures 6 and 7 illustrate in more detail the cos 3Θ mode;

Figures 8 and 9 illustrate in more detail the sin 3Θ mode; Figures 10 and 11 are schematic representations of the detection circuits associated with the Figures la and 2a embodiments;

Figures 12 and 13 illustrate an alternative form of the present invention in which a ring rather than a cup shaped member is employed as the vibrating structure;

Figures 14 and 15 illustrate the vibration pattern created as a result of the Figure 12 and 13 embodiment rotating about axes OX and OY respectively; and

Figure 16 is a plan view of a further embodiment of the present invention.

Referring now to the drawings in general but particularly to Figures 1 a and 2a, first form of the present invention provides a gyroscope 10 having a generally cup shaped structure 14 of piezo-electric material - e.g. lead zirconate titanate (PZT) which is polarised through the thickness of the shell - supported at axis Z by one end of a stem 18 the other end of which is anchored to a fixed structure shown schematically at 20. The required degeneracy between the n=2 and m=3 modes of vibration is achieved by calculating the appropriate ratio of cylinder length to cylinder radius R in a manner well known to those skilled in the art and therefore also not described herein. Deposited around the circumference of the cup shaped structure are 12 equi-spaced electrodes which may be electro-deposited on the surface in a manner well-known to those skilled in the art and therefore also not described further herein. A further electrode 22 is provided on the inner surface of the structure and, in operation, is held at earth potential by way of terminal T₀. The connection of these electrodes to the actuation/measuring circuit is best described by reference to Figure 10 from which it will be appreciated that the drive electrodes are 1-3, 7-9 and the detection electrodes are 4-6 and 10-12 respectively. In more detail and working from left to right, it will be appreciated that each of electrodes 4-6 and 10-12 are connected to one or more of amplifiers A1-A4 in a manner which facilitates the creation of a voltage at the output side of the amplifiers which is indicative of excitation of one or more of the cos2θ, sin2θ, cos3θ or sin3θ modes of vibration. The magnitude of the voltage being proportional to the rate of turn associated with the mode of vibration. For the purpose of measuring the voltages and hence rates of rotation associated therewith one can employ simple voltmeters VI -V4 connected as sown to lines 50-56 on the output side of amplifiers A1-A4.

When the electrodes of the Figure 1 embodiment are connected as shown in Figure 8, the component voltages at each electrode, its phase and its relationship to the modes of vibration will be as shown in Table 1 below.

Table 1

From this table, it will be appreciated that the cos2θ mode is the primary drive mode and, hence a drive voltage V J is applied to electrodes 1 and 7 whilst this mode can be detected or sensed by measuring the voltages -V_s at electrodes 4 and 10. each of which are fed to amplifier Al . The sin2θ mode is the vibration created as a result of rotation about axis OZ and can be sensed by monitoring the outputs -V_s for sensors 5, 6 and 11, 12 each of which are fed to amplifier A2. The cos3θ mode indicative of rotation about axis OY can be sensed by monitoring electrodes 5 and 11, the output of which is fed to amplifier A3 whilst rotation about axis OX can be sensed by monitoring the sin3θ mode which creates a voltage at electrodes 4, 6, 10 and 12, the outputs of which are fed to amplifier A4.

It will also be appreciated that, as an alternative to the above simple measuring step, one might employ an arrangement in which the drive electrodes are also employed to maintain the primary drive mode (cos2θ) at a set amplitude whilst nulling the secondary modes. This may be done in the manner of the art by applying a nulling voltage to drive electrodes 1-3 and 7-9. If this latter arrangement is employed then the feedback circuit of Figure 10 is operated such that the output of Al is connected to drive electrodes 1 and 7 via amplifiers A5 and A8 so as to maintain the primary mode whilst the output of A2 is connected to electrodes 2,3,8 and 9 via amplifiers A6, A7, A9 and A10 respectively, thereby to null the mode caused by rotation about axis OZ. The output of A3 is directed as a positive and a negative value to A5 and A8 and thence to electrodes 1 and 7 for nulling the cos3θ mode indicative of rotation about axis OY. The output of amplifier A4 is connected as a positive and a negative value to amplifiers A6 and A9 and thence to electrodes 2 and 8 in order to null the sin3θ mode indicative of rotation about axis OX. Figure 1 presents the above date in a tabular form and helps clarify the relationship between the drive and driven electrodes.

The reader's attention is now drawn to Figures 5 to 9 which illustrate the cos3θ and sin3θ modes of vibration. As mentioned earlier, these two modes have the same form but are rotationally displaced relative to each other. Figure 5 illustrates the rotational displacement whilst Figures 6 to 9 illustrate the individual modes in more detail It will be appreciated that the cos3θ mode has tangential radial and axial (OZ) components the latter two of which are shown in figures 6 and 7. This mode is basically three-sided when viewed in the direction of arrow V and the sides oscillate between the two extremes shown in dotted lines. Electrodes 5 and 11 are clearly well placed to detect this mode as they experience maximum deflections and, for reasons which will be explained later herein are well placed relative to the sin 3Θ mode. Referring now to Figures 8 and 9, it will be appreciated that the similar but displaced sin3θ mode produces a vibration pattern having nodes and points of maximum displacement at positions other than those shown in Figures 6 and 7 (cos3θ mode). For example, electrodes 5 and 11 are now at node points and therefore experience no deflection whilst electrodes 6 and 12 are subjected to a maximum deflection and are well placed for detecting the particular mode, particularly as they are at node points for the cos3θ mode. The reader will, therefore, appreciate that whilst a number of other electrodes may be employed to detect each mode, the above arrangement is particularly well suited to the task.

Referring now to Figure 2, the second arrangement of the present invention employs a plurality of drive and detection electrodes 41-48 around the outer circumference of the structure 14 and a further plurality of detection/drive electrodes 59-70 circumferentially spaced around the base 16. The reader will appreciate that electrodes 41 and 45 are used to drive the primary (cos2θ) mode and this can, if necessary, be sensed by detecting voltages at 43 and 47 in the manner known in the art. If one wishes to detect rotation about axis OZ then sensing is undertaken by measuring the voltages at 44 and 48 and, if desired, electrodes 42 and 46 can be employed to null this mode. Figure 11 illustrates the measurement control circuit employed with this arrangement and from which it will be appreciated that drive electrodes 41 , 42 and 45, 46 and sense electrodes 43,44 and 47, 48 are all connected in a manner well known in the art and therefore not described further herein. Reference to the bottom portion of Figure 11 will, however, highlight that the arrangement and connection of electrodes 59-70 differs significantly from anything known to date. In particular, electrodes 61, 65 and 69 are connected to amplifier A 13, the output of which is used to determine the rate of rotation about axis OY (cos3θ) and which may be fed back to electrodes 59, 63 and 67 to null this mode if desired. The output from electrodes 62, 66 and 70 are fed to amplifier A14 and the output therefrom is used to determine the rate of rotation about axis OX (sin3θ) and which may be fed back to electrodes 60, 64 and 68 if one wishes to null this mode. It should be noted that voltmeters V,-V₄ are not required if one adopts a nulling step and monitors the voltage required to null the mode. In this alternative arrangement, voltmeters V₅-V₈ are employed for measuring the output of amplifiers Al l to A14 and displaying a signal indicative of the measured value/rate of rotation. Tables 2a and 2b tabulate the voltages at each electrode, its phase and its relationship to the modes of vibration for this second embodiment.

Table 2a

Table 2b

The modes of vibration associated with the second embodiment are as shown with reference to the first embodiment. In the embodiments of Figures 12 and 13, the present invention is applied to a planar structure having a chosen or particular depth such as might be created by silicon etching techniques etched from a fine sheet of metal or made using metalelectrochemical deposition techniques. In the embodiment of Figure 12, a ring shown generally at 80 is formed from a twelve sided polygon and each portion thereof is supported from a central structure 82 by means of flexible beams 84. In the alternative arrangement of Figure 13 the sensing element takes the form of a circularly-symmetric ring 80a, which is supported in the same manner as that described with reference to Figure 12, with the support beams 84 possessing the necessary cyclic symmetry to form twelve identical sectors. The modes corresponding to the mode number n=2 are associated with flexure of the polygon in the OXY plane and these have frequencies which only depend on the in-plane dimensions of the structure. Modes corresponding to the mode number m=3 are associated with the flexure of the polygon along OZ and these have natural frequencies which are a function of the thickness of the structure along OZ. This modal degeneracy of the n=2 and m=3 modes can be achieved by an appropriate choice in in plane and out of plane dimensions and the depth of the structure must be determined and set accurately in order to achieve a truly accurate three axis gyro. In the case of a silicon gyroscope, practical control of the depth can be provided employing a BSOI wafer.

In the embodiment of Figures 12 and 13, capacitive actuation and sensing are employed in which the structure is held at earth potential whilst electrodes 1 - 12 are in close proximity to the structure and are electrically isolated from each other and the structure. Electrode pairs (1,7) and (4,10) are employed to drive and sense the primary motion (n=2) of the gyroscope as discussed with reference to Figures 3 and 4. The remaining electrodes are connected in pairs, (2,3), (5,6), (8,9) and (11,12) and are used to sense and actuate(if a feedback loop is employed) the secondary motion caused by a rate of turn about axes OZ. Flexural vibrations along OZ, produced as a result of rotation about axis OX and OY, are detected and actuated by electrode sets 113 - 124 placed directly below or above the structure itself. Each of these electrodes is in line with an associated drive electrode such that they are positioned for detecting the amplitude of motion as illustrated in Figures 14 and 15. Electrode sets (114, 118, 122) and (116, 120, 124) are using to measure and null the secondary motion caused by rotation about axis OX. Correspondingly, the sets (113, 117, 121) and (115, 119, 123) are employed for the detection of rotation about axis OY. Figures 14 and 15 illustrate the modes indicative of rotation about axes OX and OY respectively and from which one will appreciate that these modes have an out of plane component which can be monitored by the sensors associated with this arrangement. These modes have forms, the principal characteristics of which are similar to the sin3θ and cos3θ modes of a perfectly free ring. For the purpose of discussion herein, these two modes will be referred to as the sin3θ and cos3θ modes. In particular, the reader will note the magnitude of the vibration at 114,118 and 122 are maximums for rotation about axis OX (sin3θ) whilst the magnitude of vibration at 113,117 and 121 is zero for this mode. Additionally, the magnitude of vibration at 113,117 and 121 are a maximum when rotation about axis OY is being sensed (cos3θ) and no vibration is experienced at 114 ,119 and 122 during this mode. In view of this vibration pattern, it will be possible to monitor vibrations about each of axes OX and OY independently.

The shape of this latter type of gyroscope would allow the device to be manufactured using conventional machining methods or the chemical etch methods associated with micro- machining technology. Whilst the actual actuation and detection methods associated with these devices are very known in the art and therefore form no specific part of the present invention it is worth appreciating that such devices may employ capacitive actuation as shown in Figures 12 and 13 and piezo-electric methods as shown with reference to Figures 1 and 2 if the structure is manufactured from either PZT, lithium niobate or quartz. Lorentz force actuation used with piezoresistive sensing is also possible.

It is worth noting that the above structure is planar, the Z axis is perpendicular to this plane and the structure is formed from twelve identical sectors. For a general structure formed from p identical sectors, a particular mode has displacements given by u=(u„ ,u_r, υ_p) (i)

In equation (1) U_r is the modal displacement in the r^Ih sector and U,, is the displacement of the first sector; \J_p is .is the displacement of the last sector.

Provided the mode (U, ,U_r, Up) do not satisfy the relationships: U=(U„ ,U„ U,) (2) all displacements are the same in each sector and

U=(U,,-U. ₅ U,,-TJ|), (3) displacements in adjacent sectors are in anti-phase, then the mode described by equation (1) is degenerate and has two identical natural frequencies.

If either of equation (2) or (3) is satisfied the modes are distinct and have unique natural frequencies.

It will be appreciated that if the frequencies of the primary and three secondary modes are distinct (i.e. the modes are untuned) arrangements will still function as a three axis device but with a much reduced sensitivity to applied rate. For maximum sensitivity the modes should be tuned.

In addition to the above, it will be further appreciated that if relationships (2) and (3) are not satisfied the primary and three secondary modes can be tuned. If the n* mode occur in the plane of the structure and the (n±l) mode occurs along the Z direction, then the following modes as shown in table 3 may be used as the primary and secondary (sensing) modes, in which, for example, the primary drive is cos nθ, rotation about the axis OZ is detected by monitoring the secondary sin nθ mode, rotation about axis OY is detected by monitoring the cos (n±l)θ mode and rotation about OX is detected by monitoring the sin (n±l)θ mode

Table 3

For a tuned two axis design one or other of the following may be considered:

(a) Suppose the inplane (n^th) mode does not satisfy (2) and (3) and that the (n±l) mode satisfies one of these relationships. Although the (n±l) modes have distinct natural frequencies one of these frequencies can be tuned to the frequency of the n^, mode. In this case three frequencies are tuned, as shown in table 4 below, and the primary drive could be cos nθ or cos (n±l)θ so long as appropriate changes are made to the monitored modes..

Table 4

(b) For this case the roles of the n^,h and (n±l) modes are interchanged (i.e. the (n±l) modes are degenerate and the n"¹ modes are distinct) and the primary drive modes and suitable detection modes will be as shown in Table 5 below

Table 5

The present invention may also be applied to a single axis gyroscope in which case only two frequencies are tuned and the primary and secondary modes may be as show in Table 6 below. In this particular arrangement one can use, for example, a cosnθ or cos(n±l)θ primary drive mode and select which secondary mode is employed to monitor rotation about the OX, OY or OZ axis Table 6

For the purposes of illustration structures of different values of p have been considered and vibrational modes corresponding to n=2 and (n+l)=3 have been chosen for the primary and secondary modes. Each arrangement will function as a single axis arrangement. Their tuned multi-axis capability has been identified in the following table 7.

Table 7

Figure 16 illustrates a still further embodiment of the present invention in the form of a two axis device 200 formed from four planar sectors 202-208 connected together by a radial and circumferential beam network 210, 212 respectively. The radial beams fix the assembly to mechanical ground at an internal stem 214. Actuators 216, 218 and 220, 222 are provided in the form already discussed earlier herein and act to drive the primary mode of the gyroscope such that sectors 202, 206 rotate in phase with equal amplitude φ and sectors 204, 208 rotate in antiphase to 202, 206 with amplitude - φ . Sensors 224, 226 and 228, 230 detect this motion in a manner already described herein and therefore not repeated now. This primary motion will vary around the circumference of the gyro, as measured by the angle Θ, in a manner which is characterised by the function cos 2 Θ. When a rate of turn is applied about axis OX section 202 is displaced along OZ due to Coriolis inertia forces and sector 206 suffers a similar displacement but in antiphase. This secondary motion is detected by sensors 232, 234 placed above or below sectors 202 and 206. Similar sensors 236, 238 monitor the motion of sectors 204, 208. For a rotation about OX sensors 236, 238 product no output. The motion of the sector assembly along OZ will vary with the circumferential co-ordinate θ in a manner which is represented by cos θ. For a rotation about OY sectors 204 and 208 are displaced in the same manner as described above and sensors 236, 238 are employed to monitor the displacement. Sectors 202 and 206 produce no motion or output. In this case, the nature of the motion of the sector assembly along OZ can be represented by sin θ.

It will be appreciated from the above that other forms of gyroscope may be employed and still adopt a primary motion in the form of the present invention. In this specific example the primary mode is cos 2 θ, i.e. n=2 and the secondary motions are of the form cos θ and sin θ, i.e. m=l.

Claims

1. A gyroscope comprising; a shell structure having a first axis of symmetry, a primary mode of vibration (U_{c n}) and a primary mode number (n); driving means, for driving the whole structure to vibrate in its primary mode; and detecting means, for detecting Coriolis force induced modes of vibration thereby to detect rotation about an axis, characterised in that said detecting means includes means for detecting a mode of vibration with a mode number of (n-1) or (n+1) thereby to detect rotation about axes other than said first axis.

2. A gyroscope as claimed in claim 1 in which the driving means includes means for driving said shell structure as a cosine function of ╬╕.

3. A gyroscope as claimed in claim 2 including means for detecting a vibration having a sine-function of ╬╕, thereby to detect rotation about a second axis.

4. A gyroscope as claimed in claim 2 or claim 3 including means for detecting a vibration having a cosine function of ╬╕, therefore to detect rotation about a third axis.

5. A gyroscope as claimed in claim 1 in which the driving means includes means for driving said shell structure as a sine function of ╬╕.

6. A gyroscope as claimed in anyone of claims 1 to 5 in which a plurality of movement sensors circumferentially spaced around the shell, said detecting means producing, upon detection of motion of said shell, an output signal proportional to a rate of turn about an associated axis.

7. A gyroscope as claimed in any one of the preceding claims in which the detecting means comprises eight sensors arranged in four pairs, each pair being positioned between the driving means.

8. A gyroscope as claimed in claim 7 in which the sensors of each pair are equi-spaced from each other and adjacent to the driving means.

9. A gyroscope as claimed in any one of claims 1 to 8 in which the shell structure comprises a cup shaped structure of circular symmetry about said first axis and having a sidewall and a box, said driving means acting on the side wall to drive the structure into its primary mode of resonance.

10. A gyroscope as claimed in claim 9 in which the detection means comprises detectors positioned for detecting movement of side walls.

11. A gyroscope as claimed in claim 9 in which the detection means comprises detectors positioned for detecting movement of the base of said shell structure.

12. A gyroscope as claimed in any one of claims 1 to 8 in which the shell structure comprises a ring supported on a substrate by means of a plurality of flexible beams.

13 A gyroscope as claimed in claim 12 in which the detection means comprises a plurality of detectors positioned for detecting movement of said ring.

14. A gyroscope as claimed in claim 13 in which the detection means comprises twelve detectors equi-spaced around the circumference of the shell structure.

15. A gyroscope as claimed in any one of the previous claims in which the second and third axes are perpendicular to each other and each is perpendicular to the first axis.

16. A gyroscope as claimed in any one of claims 1 to 15 and in which the detection means further includes means for detecting rotation of said shell about the first axis.