Abstract:
A microfabricated vibratory rate gyroscope to measure rotation includes two proof-masses mounted in a suspension system anchored to a substrate. The suspension has two principal modes of compliance, one of which is driven into oscillation. The driven oscillation combined with rotation of the substrate about an axis perpendicular to the substrate results in Coriolis acceleration along the other mode of compliance, the sense-mode. The sense-mode is designed to respond to Coriolis accelerationwhile suppressing the response to translational acceleration. This is accomplished using one or more rigid levers connecting the two proof-masses. The lever allows the proof-masses to move in opposite directions in response to Coriolis acceleration. The invention includes a means for canceling errors, termed quadrature error, due to imperfections in implementation of the sensor. Quadrature-error cancellation utilizes electrostatic forces to cancel out undesired sense-axis motion in phase with drive-mode position.

Description:
PRIOR APPLICATION DATA 
     This application claims the benefit of U.S. Provisional Application No. 60/088,681 filed Jun. 9, 1998, and No. 60/091,346 filed Jul. 1, 1998. 
    
    
     IDENTIFICATION OF GOVERNMENT INTEREST 
     This invention was made with Government support under NAS5-97227 awarded by the National Aeronautics and Space Administration (NASA). The Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     This invention relates generally to gyroscopes and more particularly, to vibratory rate gyroscopes utilizing two proof-masses to measure rotation rate. 
     BACKGROUND OF THE INVENTION 
     Rate gyroscopes are sensors that measure rotation rate. Rate gyroscopes have uses in many commercial and military applications including, but not limited to, inertial navigation, vehicular skid control, and platform stabilization. 
     A vibratory rate gyroscope is a sensor that responds to a rotation rate by generating and measuring Coriolis acceleration. Coriolis acceleration is generated by any object (such as a proof-mass) that has some velocity relative to a rotating reference frame. In vibratory rate gyroscopes, one or more proof-masses are suspended from flexures and made to oscillate thus providing a velocity necessary to generate Coriolis acceleration. Measurement of the resulting Coriolis acceleration can then yield an estimate of the rotation rate of the sensor. 
     An idealized version of such a sensor is shown in FIG.  1 . In this figure a three-dimensional, mutually orthogonal coordinate system is shown for reference. The axes are arbitrarily labeled “X”, “Y” and “Z”, to enable description of background material as well as the invention. The axis of oscillation, which is largely coincident with the X-axis, is often referred to as the drive-mode. Coriolis acceleration is generated perpendicular to the drive-mode along the sense-mode, which lies largely along the Y-axis. The Coriolis acceleration generated by the system shown in FIG. 1 is given by: 
     
       
           a   Coriolis =2Ω z   D   x ω x  cos(ω x   t )  Equation 1 
       
     
     where a Coriolis  is the Coriolis acceleration generated along the sense-mode, Ω z  is the rotation rate to be measured about the Z-axis, and ω x  and D x  are the frequency and magnitude of drive-mode oscillation respectively. The Coriolis acceleration causes an oscillatory displacement of the sensor along the sense-mode with magnitude proportional to the generated Coriolis acceleration. Ideally, the drive-mode is coincident with the forcing means used to sustain oscillation (located along the X-axis or drive-axis), and the sense-mode is coincident with the sensing means used to detect displacements due to Coriolis acceleration (located along the Y-axis or sense-axis). The design and fabrication of the proof-mass and the suspension will dictate the actual orientation of the drive- and sense-modes with respect to the driving and sensing axes, however. An important fact to note is that the Coriolis acceleration signal along the sense-axis is in phase with velocity of the drive-mode, which is 90 degrees out-of-phase with proof-mass displacement along the drive-mode. While the Coriolis acceleration is 90 degrees out-of-phase with the proof-mass displacement along the drive-mode, displacements along the sense-mode due to Coriolis acceleration may have a different phase relationship to the proof-mass displacement along the drive-mode depending on several factors including: the relative values of drive-mode oscillation frequency to sense-mode resonant frequency, and the quality factor of the sense-mode. 
     To accurately measure rotation rate, the Coriolis acceleration must be easily distinguished from other sources of acceleration. Coriolis acceleration is unique for three reasons: 1) it occurs along the sense-mode which lies largely along the Y-axis, 2) it occurs at the driven-mode oscillation frequency, ω x , and 3) it is in phase with the velocity of the drive-mode oscillation. Further discrimination of Coriolis acceleration can be achieved using dual-mass gyroscopes that generate a differential Coriolis acceleration in response to a rate input. Note that Coriolis acceleration can be difficult to measure in the presence of quadrature error. Quadrature error results in an oscillatory acceleration having three properties (two of which are shared with Coriolis acceleration): 1) it occurs along the Y-axis, 2) it occurs at the driven-mode oscillation frequency, ω x , and 3) it is either in phase or 180-degrees out of phase with the position (not velocity) of the drive-mode oscillation, depending on the sign of the error. For a comprehensive discussion of quadrature error, please see Clark, W. A.,  Micromachined Vibratory Rate Gyroscopes,  Doctoral Dissertation, University of California, 1997. Thus, Coriolis acceleration and quadrature error are distinguished only by their phase relative to the driven-mode oscillation. 
     Forces may be applied to the gyroscope using variable air-gap capacitors formed between one or more plates (or conductive nodes) attached to the proof-mass and one or more plates (or conductive nodes) attached to the substrate. Note that electrostatic forces result between charged capacitor plates. The magnitude and direction of the force is given by the gradient of the potential energy function for the capacitor as shown below.                F   ⇀     =       -     ∇   U       =     -     ∇                [       Q   2       2        C        (     x   ,   y   ,   z     )           ]                   Equation                 2                                
     As an example, an appropriate oscillation in the gyroscope may be generated using a force along a single axis (e.g. the X-axis). Equation 2 implies that any capacitor that varies with displacement along the X-axis will generate an appropriate force. An implementation of a pair of such capacitors is shown in FIG.  2 . This capacitor configuration has a number of advantages including ample room for large displacements along the X-axis without collisions between comb fingers. By applying differential voltages with a common mode bias V DC  across electrically conductive comb fingers  72 ,  73   a  and 72, 73 b  a force that is independent of X-axis displacement and linear with control voltage, v x  is created:                  V   1     =       V   DC     -     v   x                           V   2     =       V   DC     +     v   x                           F   x     =           1   2            ∂   C       ∂   x            V   2   2       -       1   2            ∂   C       ∂   x            V   1   2         =     2                     C   0       X   0            V   DC          v   x                   Equation                 3                                
     where C 0  and X 0  are the capacitance and X-axis air-gap at zero displacement respectively. An equivalent method of applying forces chooses V 1 , V 2  such that: 
     
       
           V   1   =V   DC   −v   x   V   2   =−V   DC   −v   x   Equation 4 
       
     
     Note that in both of these cases the magnitude of the force is proportional to the control voltage, v x , and the DC bias voltage, V DC . This permits the magnitude and direction of the force to be directly controlled by varying either v x  or V DC  while maintaining the other voltage constant. 
     Many methods are known that sense motion or displacement using air-gap capacitors. Details of capacitive measurement techniques are well known by those skilled in the art. These methods may be used for detection of displacement due to Coriolis acceleration, measuring quadrature error, or as part of an oscillation-sustaining loop. Often a changing voltage is applied to two nominally equal-sized capacitors, formed by a plurality of conductive fingers, with values that change in opposite directions in response to a displacement. One method applies voltages to these sensing capacitors in a manner that generates a charge that is measured by a sense interface. (See for example: Boser, B. E., Owe, R. T., “Surface Micromachined Accelerometers,” IEEE Journal of Solid-State Circuits, vol.31, pp. 366-75, March 1996., or Lemkin, M., Boser B. E., “A Micromachined Fully Differential Lateral Accelerometer,” CICC Dig. Tech. Papers, May 1996, pp. 315-318.) Another method uses a constant DC bias voltage applied across two sensing capacitors. Any change in the capacitance values results in current flow that is detected by a sense interface. (See for example Nguyen, C. T.-C., Howe, R. T., “An Integrated CMOS Micromechanical Resonator High-Q Oscillator,” IEEE JSSC, pp. 440-455, April 1999.) Furthermore, some methods of capacitive detection use time-multiplexing (see for example: M. Lemkin, B. E. Boser, “A Three-axis Micromachined Accelerometer With a CMOS Position-Sense Interface and Digital Offset-trim Electronics,” IEEE Journal of Solid-State Circuits, pp. 456-68, April 1999) or frequency multiplexing (see for example Sherman, S. J, et. al., “A Low Cost Monolithic Accelerometer; Product/technology Update,” International Electron Devices Meeting, San Francisco, Calif., December 1992, pp. 501-4) to enable electrostatic forces to be applied to a microstructure and displacement or motion of the microstructure to be sensed using a single set of capacitors. An example of an application in which time- or frequency-multiplexing of capacitor function in such a manner may prove useful includes a force-feedback loop. 
     Provided with a controllable force applied to a structure and a measure of the structure&#39;s deflection, the structure may be driven into oscillation using feedback. The desired oscillation is achieved by measuring the structure&#39;s displacement or velocity then determining the magnitude, and/or phase of the force or forces to apply to the structure. The measurement of the structure&#39;s displacement and the force(s) applied may be electrostatic as described above. In a dual-mass gyroscope the position or velocity detected by the sense interface often reflects relative motion between the two masses, and the forces applied to the two masses may contain a differential force component. Many methods are known to sustain drive-mode oscillation. 
     Because of imperfections introduced in the manufacturing process, the gyroscope driven-mode and sense-axis may not be perfectly orthogonal, thereby causing quadrature error. Imperfections in elements of the suspension are one possible cause of this non-orthogonality. Phase lag in detection circuitry can lead to quadrature error leakage into the sensor output. Results of this leakage may include large sensor output offsets, output-offset drift, and noise. In addition, large quadrature-error signals may cause saturation of sense-mode interfaces. 
     SUMMARY OF THE INVENTION 
     In one aspect, the invention comprises a dual-mass vibratory microstructure, such as a gyroscope, with improved suspension. The microstructure comprises a substrate, two proof-masses, and a suspension system. The suspension connects the two proof-masses to the substrate. In addition, the suspension allows for two modes of compliance: the driven and sensing modes. The suspension may include a plurality of compliant beams and may include at least one rigid beam that serves as a lever connecting the two proof-masses. 
     A further aspect of the invention includes a microstructure and circuitry for canceling errors, termed quadrature error. An example of one source of quadrature error is imperfections in the manufacturing process. Quadrature-error cancellation utilizes electrostatic forces to cancel undesired sense-axis motion either substantially close to in-phase or 180 degrees out-of-phase with drive-mode displacement. A nullifying electrostatic force may be applied in-phase with drive-mode position through a differential bias applied to one or more sets of variable capacitors. Quadrature-error cancellation may be operated open-loop, in which case the differential bias is constant. Alternatively, quadrature-error cancellation may be operated closed-loop, in which case quadrature-error is continuously or periodically measured. The resulting measurement of quadrature error may be used to adjust the differential bias to cancel the error signal. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a better understanding of the nature and objects of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings, in which: 
     FIG. 1 is a conceptual representation of a vibratory rate gyroscope illustrating driven-mode oscillation and sense-mode response. 
     FIG. 2 is a perspective view of a set of interdigitated comb-fingers suitable for sustaining proof-mass oscillation along the drive-mode. 
     FIG. 3 is a conceptual representation of a gyroscopic dual-mass mechanical sense-element that suppresses deflections resulting from translational accelerations along the sense-axis. 
     FIG. 4 is a plan view of a dual-mass gyroscopic mechanical sense-element embodiment that suppresses deflections due to translational accelerations along the sense-axis. 
     FIG. 5 is a plan view of the sense-element in FIG. 4 showing important deflections of the driven-mode. 
     FIG. 6 is a plan view of the sense-element of FIG. 4 showing important sense-mode deflections in response to a Coriolis acceleration. 
     FIG. 7 is a plan view of a second embodiment of the invention that has a modified suspension system and yet has the same major elements. 
     FIG. 8 is a plan view of a third embodiment of the invention that has a modified suspension system and yet has the same major elements. 
     FIG. 9 is a plan view of a fourth embodiment of the invention that has a modified suspension system and yet has the same major elements. 
     FIG. 10 is a plan view of a fifth embodiment of the invention that has a modified suspension system and yet has the same major elements. 
     FIG. 11 is a perspective view of two embodiments of a set of comb-fingers suitable for quadrature-error cancellation. 
     FIG. 12 is a conceptual representation of proof-mass motions due to quadrature error in a gyroscopic dual-mass mechanical sense-element. 
     FIG. 13 is a conceptual representation of proof-mass motions with suppressed quadrature error when quadrature-error cancellation is activated. 
     FIG. 14 is a conceptual representation of proof-mass motions with suppressed quadrature error when balanced quadrature-error cancellation is activated. 
    
    
     Like reference numerals refer to corresponding parts throughout all the views of the drawings. 
     DETAILED DESCRIPTION OF THE INVENTION 
     A dual-mass gyroscope with an improved suspension system is conceptually illustrated in FIG.  3 . The suspension system holds the proof-masses and allows for two modes of compliance. One mode of compliance is in the drive mode. This mode of compliance is driven into oscillation thereby supplying the velocity necessary to generate Coriolis acceleration. Note the drive-mode motions of the proof-masses are 180 degrees out of phase with respect to each other, as represented by the arrows in FIG.  3 . Another mode of compliance is the sense-mode, which may be excited by Coriolis acceleration. In a dual-mass gyroscope, the Coriolis acceleration has the same magnitude on each proof-mass, but is applied in opposite directions due to the 180-degree phase shift between the two proof-mass motions in the drive mode. Thus, by driving the two masses differentially, a differential Coriolis acceleration is made available for measurement. 
     One advantage of the suspension system described below is suppression of responses due to translational accelerations applied to the gyroscope. By connecting both proof-masses to at least one stiff, pivoting beam  51 , shown in FIG. 3, the two proof-masses are constrained to move in opposite directions along the sense-axis. This constraint suppresses unwanted responses to translational accelerations applied along the sense-axis but does not affect desired responses to Coriolis accelerations. 
     FIG. 4 illustrates a first embodiment of a mechanical sense-element  100  for a dual-mass vibratory rate gyroscope in accordance with the invention. The sense-element  100  generates Coriolis acceleration through the interaction of the rotation rate to be measured and the vibrating proof-masses  130  and  131 . A suspension system, which includes the set of beams  104  through  127  and lever  128 , attaches the proof-masses  130  and  131  to the substrate  101  at two points  102  and  103  defined as anchors. Typically, most beams in the suspension system are longer than they are wide with aspect ratios exceeding a 10 to 1 length to width ratio. This results in beams that are compliant to bending but relatively stiff to compression and extension. Note that beams may be chosen to have different widths or lengths to obtain the desired bending and axial compliance characteristics described below. In addition, each beam may be formed as a single structure as drawn, or a composite structure made from a combination of substantially parallel beams. When the sense-element is formed in a substantially planar material, such as a silicon wafer or layer of polysilicon on a dielectric or on a silicon wafer, flexure dimensions are defined in the following manner: flexure thickness is defined as the thickness of the substantially planar surface into which the microstructure is formed, flexure width is defined as the smallest characteristic dimension perpendicular to the flexure thickness, and flexure length is defined as a remaining characteristic dimension perpendicular to both the flexure thickness and flexure width. 
     The suspended proof-masses  130  and  131  are made to oscillate in an anti-phase motion, the driven mode, which is illustrated in FIG.  5 . Driven-mode oscillations result in substantial deflections of beams  104  through  111 , while the remaining beams stay largely straight. Since beams  104  through  111  are principally involved in the driven-mode deflections, the compliance of the driven mode is largely determined by these beams. 
     Once the proof-masses  130  and  131  are driven into oscillation, the structure responds to substrate rotation rate by oscillating in an anti-phase motion, the sense-mode, as illustrated in FIG.  6 . The compliance of the deflection shown in FIG. 6 is largely determined by the set of beams  112  through  115  that deflect along the Y-axis. The remaining beams  116  through  119  and  124  through  127  contribute to the compliance of the sense-mode but are typically not dominant contributors. The two proof-masses are forced to move in opposite directions along the Y-axis by the rotating lever  128  and the beams  116  through  127  that connect the lever and the proof-masses. The axial stiffness of beams  116  through  127 , coupled with the rotational compliance of beams  116  through  119 , enable rotation, but not translation, of the lever  128 . Thus, motions of the proof-masses  130  and  131  are constrained to track the ends of the lever  128 . Note that the lever realized by this configuration rejects common-mode displacement, where common-mode displacement is defined as displacement of the lever ends in the same direction. Since the lever  128  effectively constrains common-mode displacement, the effect of translational accelerations on proof-mass displacement along the sense-axis is suppressed. To raise the resonant-frequency of parasitic vibrational modes, additional flexures such as  151   a-d,    152   a-d  may be attached between the outside of the proof-masses  130   b,    131   b  and the substrate  101   c,  anchored by anchors  150   a-c  as illustrated in a second embodiment shown in FIG.  7 . 
     FIG. 8 illustrates a third embodiment  201  of a dual-mass vibratory rate gyroscope of the type shown in FIG.  3 . Although the device in FIG. 8 has a different suspension than the first two embodiments, the behaviors and underlying principles of the three suspensions are similar. In FIG. 8, the two proof-masses  202  and  203  are attached to the substrate  229  by anchors  230  and  231  and the suspension system including: beams  204  through  221 , levers  222  and  223 , and beams  240  and  241 . Beams  204  through  219  deflect along the X-axis and largely determine the driven-mode compliance for the gyroscope. Beams  240  and  241  largely determine the compliance of the sense-mode. Levers  222  and  223  force the two proof-masses  202  and  203  to move in opposite directions along the Y-axis, pivoting about the beams  220  and  221 . Beams  204  through  221  are axially stiff, yet rotationally compliant and thus transmit common-mode Y-axis forces and accelerations between the proof-masses  202  and  203 , through the levers  222  and  223 , to the anchors  230  and  231 . 
     FIG. 9 illustrates a fourth embodiment  100   b  of a dual-mass vibratory rate gyroscope of the type shown in FIG.  3 . Although the embodiment shown in FIG. 9 has a different suspension than the first three embodiments, the behaviors and underlying principles of the four suspensions are similar. Like the first embodiment, a single lever  128   a  is used in conjunction with axially stiff and rotationally compliant beams  116   a  and  117   a  to enable rotation of the lever while suppressing Y-axis translation of the lever ends. The effect of the lever is to constrain the proof-masses  130   a  and  131   a  to move in a differential fashion along the Y-axis. In this embodiment, crab-leg suspensions (formed from beams  112   a,c,d,f  and  104   a,c,d,f ) connect the proof-masses to the substrate. Compliance of the crab-leg suspension beams and compliance of beams  124   a,    125   a,    126   a,    127   a  primarily determine compliance of the sense-mode. Drive-mode compliance is primarily set by the compliance of the crab-leg beams in conjunction with the compliance of beams  124   a,    125   a,    126   a,    127   a.    
     FIG. 10 illustrates a fifth embodiment  201   a  of a dual-mass vibratory rate gyroscope of the type shown in FIG.  3 . Although the embodiment shown in FIG. 10 has a different suspension than the first four embodiments, the behaviors and underlying principles of all five suspensions are similar. Like the third embodiment, two levers  222   a  and  223   a  are used in conjunction with axially stiff and rotationally compliant beams  220   a  and  221   a  to enable rotation of the levers while suppressing Y-axis translation of the lever ends. Optional beam  299  decreases compliance along the drive-axis for in-phase proof-mass motion, attenuating displacements due to X-axis translational accelerations. The effect of the levers is to constrain the proof-masses  202   a  and  203   a  to move in a differential fashion along the Y-axis. In this embodiment, crab-leg suspensions (formed from beams  204   a,c,d,f  and  240   a,c,d,f ) connect the proof-masses to the substrate. Compliance of the crab-leg suspension beams and compliance of beams  208   a,    209   a,    210   a,    211   a  primarily determine compliance of the sense-mode. Drive-mode compliance is primarily set by the compliance of the crab-leg beams in conjunction with the compliance of beams  208   a,    209   a,    210   a,    211   a.    
     In summary, there are several important elements that are common between FIG. 3, FIG. 4, FIG. 7, FIG. 8, FIG. 9, and FIG.  10 . The use of two proof-masses  52  and  53 ,  130  and  131  or  202  and  203 . These proof-masses are mounted in a suspension that has two principal compliant modes. The drive-mode is such that the two proof-masses oscillate differentially (in an anti-phase manner), largely parallel to the drive-or X-axis. The sense-mode is such that the two proof-masses are constrained to move in opposite directions largely parallel to the Y-axis. The sense-mode is constrained with a lever mechanism  51 ,  128 , or  222  and  223  that is attached to the substrate  101  or  229  via anchors  102  and  103  or  230  and  231  using axially stiff yet rotationally compliant beams. Thus the suspension allows the two proof-masses to be driven to oscillate differentially and respond differentially to Coriolis acceleration, while other mechanical responses in the sense-axis are suppressed. 
     In a further aspect of the invention, a differential quadrature-nulling structure may be included with the first through fifth embodiments of the invention. FIG. 11 shows a schematic diagram of two different differential comb-finger structures suitable for reducing quadrature error arising from drive-mode motion coupling into the sense-axis. Comb finger  500  ( 550   a,b ) is attached to a proof-mass, while stationary comb-fingers  501  ( 551 ) and  502  ( 552 ) are attached to the substrate. Two voltages with respect to the proof-mass are applied to the stationary comb fingers. The voltages may be resolved into common-mode and differential voltage components V and ΔV respectively. As comb-finger  500  moves along the negative X-axis, the overlap area of the capacitive plates increases. The change in the overlap area (a linear function of X-axis position) causes a corresponding change in the magnitude of the total force along the Y-axis proportional to X-axis position. This force is represented by the term on the right of the following equation:                        F   Y          (   x   )       =                    2                   ɛ   0            Z   0          (       X   0     -   x     )           Y   0   2          V                 Δ                 V                 =                    (         2                   ɛ   0          Z   0          X   0         Y   0   2          V                 Δ                 V     )       Static                 Force       -         (         2                   ɛ   0          Z   0         Y   0   2          V                 Δ                 V     )        x         Force                 Dependent                 on                                X   -     axis                 Displacement                           Equation                 5                                
     In Equation 5, X 0  and Z 0  are the nominal overlap of the quadrature-nulling structure, Y 0  is the nominal separation distance between the movable comb-finger  500  and the stationary comb-fingers, ε 0  is the permittivity of free space, and x is the displacement of the end of comb-finger  500  from the nominal position. 
     FIG. 12 is a simplified schematic of a two-mass gyroscope with a differential quadrature-error cancellation structure comprised of comb-fingers  500   ab,    501   ab,  and  502   ab.  Comb-finger structures  500   a  and  500   b  are attached to each proof-mass  52   a  and  53   a  to enable cancellation of differential quadrature error. Nominal motion of the proof-masses with quadrature-error, with quadrature-error cancellation disabled (all bias voltages set to zero), and with zero rate input is shown in FIG.  12 . When active, quadrature-error cancellation, shown in FIG. 13, applies voltages that result in cancellation of the undesired differential motion. The displacement-dependent forces generated by these bias voltages rotate the drive-mode such that it becomes perpendicular to the sense-axis. A by product of the quadrature-error cancellation structure shown in FIG.  12  and FIG. 13 is the introduction of a static differential displacement in the sense-mode. This static displacement is of little consequence, however, since Coriolis acceleration occurs as sense mode motion near the drive-mode frequency. In FIG. 13, voltages V 1  and V 2  may have different values or voltages ΔV 1  and ΔV 2  may have different values. Alternatively, voltages V 1  and V 2  may have the same value or voltages ΔV 1  and ΔV 2  may have the same value. All voltages may be either positive or negative depending on the sign of the quadrature-error. The common-mode voltages V 1  and V 2  are given with respect to the potential of the comb-fingers  500   a  and  500   b  respectively. 
     By adjusting common-mode or differential bias voltages, the magnitude and sign of the quadrature-nulling force may be varied. Since quadrature-error is in-phase or 180 degrees out-of-phase with drive-mode displacement, voltages may be chosen to generate forces to null the quadrature error. Bias voltages may be generated open loop. Alternatively, these voltages may be adjusted using feedback of measured quadrature error to drive quadrature-error towards zero. 
     In yet another aspect of the invention, a balanced quadrature-nulling structure comprised of comb fingers  500   cdef,    501   cdef,  and  502   cdef  may be included with the first through fifth embodiments of the invention as schematically shown in FIG.  14 . The static displacement shown in FIG. 13 is greatly attenuated through the use of balanced bias forces on each proof-mass. 
     Primary mechanical-design factors affecting the noise floor of a vibratory rate gyroscope include the size of the sensor, the driven- and sense-mode resonant frequencies of the structure, and the damping of the resonant modes. In order to minimize noise, it is desirable to make the mechanical sense-element as large as possible limited by the fabrication technology and undesirable vibration modes that can occur with large structures. In addition, operation of the device in a vacuum reduces the air damping of the structure, which also reduces noise. The substantially planar nature of the sense-element lends itself well to single-crystal silicon technologies. In these technologies, the structures are typically 10 μm to 500 μm thick and occupy an area from 1 mm 2  to 100 mm 2 . For improved performance, the sensors may operate in a partial vacuum on the order of 100 mTorr. 
     The invention has been described as being advantageous because it may exploit the benefits of single crystal-silicon fabrication technology. However, the embodiments described here may also be fabricated using other technologies and materials including, but not limited to: surface-micromachining, epi-polysilicon, bulk micromachining, plated metal, and quartz. 
     The foregoing description, for the purposes of explanation, used specific nomenclature to provide a thorough understanding of the invention. However, it will be apparent to one skilled in the art that the specific details are not required in order to practice the invention. Thus, the foregoing descriptions of specific embodiments of the invention are presented for the purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, obviously many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated.