Patent Publication Number: US-8991250-B2

Title: Tuning fork gyroscope time domain inertial sensor

Description:
FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT 
     This invention is assigned to the United States Government and is available for licensing for commercial purposes. Licensing and technical inquiries may be directed to the Office of Research and Technical Applications, Space and Naval Warfare Systems Center, Pacific, Code 7274, San Diego, Calif., 92152; voice (619) 553-572; ssc_pac_t2@navy.mil. Reference Navy Case Number 101330. 
    
    
     BACKGROUND OF THE INVENTION 
     The invention disclosed herein relates to the field of gyroscopic inertial sensing. Highly stable and accurate micro-electrical-mechanical system (MEMS) gyroscopes are needed for navigational inertial sensing. Larger gyroscopes can meet the accuracy requirements needed for inertial navigation, but are expensive and require more space than a MEMS gyroscope. Current MEMS gyroscopes are subject to electronic and mechanical noise, non-linearity, and drift in mechanical parameters which cause error to their measurements. Conventional MEMS tuning fork gyroscopes use capacitance to measure the offset caused by the Coriolis force. A need exists for a more accurate and more stable tuning fork gyroscope. 
     SUMMARY 
     Disclosed herein is an inertial-sensing-capable tuning fork gyroscope comprising a frame, a tuning fork, and at least two digital position triggers. The tuning fork comprises a base and first and second prongs. The base has proximal and distal ends. The proximal end is coupled to the frame and the distal end is coupled to the first and second prongs. The first and second prongs are driven by first and second drivers respectively to oscillate with respect to the frame in a first direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other. The digital position triggers are operatively coupled to the frame and to the tuning fork. Each position trigger is configured to experience at least two trigger events during each oscillation of the tuning fork in a second direction. The second direction is orthogonal to the first direction. 
     The tuning fork gyroscope disclosed herein may be used for inertial sensing according to the method. The first step provides for driving first and second prongs of the tuning fork gyroscope to oscillate with respect to a frame of the tuning fork gyroscope in a first direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other. The second step provides for monitoring closed and open states of two pairs of second-direction-stacked electron-tunneling-tip switches, wherein the second direction is orthogonal to the first direction, and wherein each pair of switches is operatively coupled to the frame and the tuning fork such that each pair of switches passes through at least two closed states during each oscillation of the tuning fork in the second direction. The third step provides for measuring the time interval between closed states of each switch pair to characterize the offset of the tuning fork in the second direction. The fourth step provides for determining the Coriolis forces acting on the tuning fork gyroscope by calculating the offset of the tuning fork in the second direction. 
     An alternative embodiment of the tuning fork gyroscope comprises a frame, a tuning fork, first and second drivers, and first and second pairs of electron-tunneling tip switches. The tuning fork comprises a base and first and second prongs, wherein a proximal end of the base is coupled to the frame and wherein proximal ends of the first and second prongs are coupled to a distal end of the base. The first driver is operatively coupled to the first prong such that the first driver is configured to drive the first prong to oscillate with respect to the frame in a first direction at the first prong&#39;s resonant frequency. The second driver is operatively coupled to the second prong such that the second driver is configured to drive the second prong to oscillate with respect to the frame in the first direction at the second prong&#39;s resonant frequency and 180° out of phase with the first prong. The first pair of electron-tunneling tip switches is operatively coupled to the frame and a first location on the tuning fork such that the first pair of switches is configured to switch from an open state to a closed state at least twice during a complete oscillation of the tuning fork with respect to the frame in the second direction. The second pair of electron-tunneling tip switches is operatively coupled to the frame and to a second location on the tuning fork such that the second pair of switches is configured to switch from an open state to a closed state at least twice during a complete oscillation of the tuning fork with respect to the frame in the second direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Throughout the several views, like elements are referenced using like references. The elements in the figures are not drawn to scale and some dimensions are exaggerated for clarity. 
         FIG. 1  is a top view illustration of an embodiment of a tuning fork gyroscope. 
         FIGS. 2A-2B  represent a perspective view of an example MEMS embodiment of a tuning fork gyroscope. 
         FIG. 3A  is a partial perspective view of the MEMS embodiment of the gyroscope depicted in  FIGS. 2A and 2B . 
         FIG. 3B  is a side view of an embodiment of a digital trigger. 
         FIGS. 4A-4C  illustrate side views of various reference positions of the digital trigger shown in  FIG. 3B . 
         FIG. 5  is a flowchart illustrating one example of how the gyroscope depicted in  FIGS. 2A-3B  may be used for time-domain inertial sensing. 
         FIG. 6  is a plot of the displacement of a tuning fork with respect to a frame. 
         FIG. 7  is a plot of tuning fork displacement against time in the presence of external forcing. 
         FIG. 8A  is a plot of the oscillation amplitude of a tuning fork with respect to a frame. 
         FIG. 8B  is, in part, a pictorial representation of triggering events. 
         FIG. 9  is a top view of an embodiment of a tuning fork gyroscope. 
         FIG. 10  is a side cross-section side view of an embodiment of a tuning fork gyroscope. 
         FIG. 11  is a plot of the displacement of conductive tips over time with respect to a conductive plane. 
         FIG. 12  is a graph showing the displacement of conductive tips. 
         FIG. 13  is another plot of the displacement of conductive tips over time with respect to a conductive plane. 
         FIG. 14  is another graph showing the displacement of conductive tips. 
         FIGS. 15A-15B  are perspective views of an embodiment of a tuning fork gyroscope. 
         FIG. 16  is a perspective view of an embodiment of a tuning fork gyroscope. 
         FIG. 17  is a perspective view of another embodiment of a tuning fork gyroscope. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       FIG. 1  is a top view illustration of a tuning fork gyroscope  10  capable of time-domain inertial sensing. The gyroscope  10  comprises a frame  12 , a tuning fork  14 , first and second drivers  16  and  18  respectively, and at least two digital position triggers  20 . The tuning fork  14  comprises a base  22  and first and second prongs  24  and  26  respectively. The base  22  has a proximal end  28  and a distal end  30 . The base&#39;s proximal end  28  is coupled to the frame  12  and the distal end  30  is coupled to the first and second prongs  24  and  26 . The first and second drivers  16  and  18  are configured to drive the first and second prongs  24  and  26  respectively to oscillate with respect to the frame  12  in a first direction such that the prongs  24  and  26  oscillate at their respective resonant frequencies and 180° out of phase with each other. In  FIG. 1 , the first direction corresponds to the x-direction. However, it is to be understood that the first and second prongs  24  and  26  may be driven to oscillate in any desired direction and the x-direction is only offered as one example. The digital position triggers  20  are operatively coupled to the frame  12  and to the tuning fork  14 . Each position trigger  20  is configured to experience at least two trigger events during each oscillation of the tuning fork  14  in a second direction, which is orthogonal to the first direction. In  FIG. 1 , the second direction corresponds to the z-direction. 
     The gyroscope  10  may be manufactured on any scale. For example, in one embodiment the gyroscope  10  may be monolithically integrated into a micro-electro-mechanical system (MEMS) device. The gyroscope  10  may be used in any orientation. Although the x-y-z coordinate system is depicted in the drawings and referred to herein, it is to be understood that the first, second, and third directions/axes, as used herein, may correspond to any three mutually-orthogonal directions/axes in any three-dimensional coordinate system. 
     The frame  12  may be any size and shape, and be made of any material capable of providing rigid support for the gyroscope  10  such that the frame  12  does not significantly flex and/or deform when exposed to lateral and rotational accelerations of the gyroscope  10 . 
     The first and second drivers  16  and  18  may each be any apparatus capable of causing the first and second prongs  24  and  26  to oscillate at any desired frequency in the x-direction with respect to the frame  12 . Suitable examples of the first and second drivers  16  and  18  include, but are not limited to, variable area actuators, such as electrostatic comb drives (such as are portrayed in  FIG. 2B ), variable gap actuators, such as parallel plate actuators, and other electro-magnetic or piezoelectric mechanisms of actuation. Each of the first and second prongs  24  and  26  may be driven using a continuous oscillating force or by periodic “delta function” forces in phase with the given prong&#39;s harmonic resonance. 
     The digital trigger  20  may be any apparatus capable of producing digital signals corresponding to various positions of a section of the tuning fork (i.e., the section to which the given digital trigger  20  is attached) with respect to the frame  12 . For example, the digital trigger  20  may be any device capable of experiencing a change in state based on positional changes of the tuning fork  14  relative to the frame  12 . Other examples of the digital trigger  20  include an electron tunneling switch, a capacitive switch, an optical shutter switch, and a magnetic switch. A purpose of the digital trigger  20  is to localize the position of the section to which the given digital trigger  20  is attached and the frame  12  such that an accurate acceleration-independent phase measurement can be performed—thereby increasing stability of a phased-locked loop closure and reducing overall phase noise and jitter of the gyroscope  10 . 
       FIGS. 2A-2B  represent a perspective view of an example MEMS embodiment of the gyroscope  10 . In the embodiment shown, the first and second drivers  16  and  18  are capacitive comb drives, and the digital triggers  20  are stacked pairs of electron tunneling switches (only the top switch is visible in  FIG. 2B ) capable of generating a finite width current pulse which “tunnels from conductive tips  32  on the first and second prongs  24  and  26  to a conductive plane  34  on the frame  12 . 
       FIG. 3A  is a partial perspective view of the MEMS embodiment of the gyroscope  10  depicted in  FIGS. 2A and 2B .  FIG. 3A  shows the orientation of the first prong  24  with respect to the frame  12 . In this embodiment a conductive layer  36  and an optional lower conductive layer  38  are also depicted.  FIG. 3B  is a side view of one embodiment of a digital trigger  20  such as may be used in the example embodiment of the gyroscope  10  depicted in  FIGS. 2A ,  2 B, and  3 A. In this embodiment, the digital trigger  20  comprises a pair of electron tunneling switches  40 . The pair of electron tunneling switches  40  comprises a stacked conductive tips  32 , and stacked conductive planes  34 . The tips  32  and the planes  34  are separated from each other in the y-direction by a gap  42 . The tips  32  and the planes  34  are separated from each other in the z-direction by a dielectric layer  44 . 
       FIGS. 4A-4C  illustrate an embodiment of the digital trigger  20  shown in  FIG. 3B  where the pair of electron tunneling switches is configured to pass through multiple closed states corresponding to multiple reference positions of the first prong  24  with respect to the frame  12  during a single oscillation period. When the first prong  24  is in the first reference position with respect to the frame  12  the tunneling tips  32  are aligned with the conductive planes  34  and the digital trigger  20  is in a closed state such that a current pulse may pass from the tips  32  to the planes  34 , as depicted by the arrows. The electron tunneling tips  32  are aligned with each other in the z-direction and separated from each other in the z-direction by a distance d 1 . The conductive planes  34  are also aligned with each other in the z-direction and separated from each other in the z-direction by the distance d 1 . 
     When the first prong  24  is in the first reference position, or zero force position, such as is depicted in  FIG. 4A , a current pulse passes from the each of the tunneling tips  32  over the gap  42  to a corresponding plane  34 . This embodiment of the digital trigger  20  also comprises second and third reference positions of the first prong  24  with respect to the frame  12 . The first prong  24  is in the second reference position when the first prong  24  is displaced from the first reference position in the z-direction by the distance +d 1 , such as is shown in  FIG. 4B . In the second reference position, the digital trigger  20  is in a closed state such that a current pulse may pass from the lower of the two tips  32  to the upper of the two planes  34 . The first prong  24  is in the third reference position when the first prong  24  is displaced in the z-direction by the distance −d 1 , such as is shown in  FIG. 4C . In the third reference position, the digital trigger  20  is in a closed state such that a current pulse passes from the upper of the two tips  32  to the lower of the two planes  34 . 
       FIG. 5  is a flowchart illustrating one example of how the gyroscope  10  depicted in  FIGS. 2A-3B  may be used for time-domain inertial sensing. The first step  46  provides for driving the first and second prongs  24  and  26  of the tuning fork  14  to oscillate with respect to the frame  14  in the x-direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other. The second step  48  provides for monitoring the closed and open states of the two pairs of electron-tunneling-tip switches  40 . The third step  50  provides for measuring the time interval between closed states of each switch pair  40  to characterize the offset of the tuning fork  14  in the z-direction. The fourth step  52  provides for determining the Coriolis forces acting on the tuning fork gyroscope  10  by calculating the offset of the tuning fork  14  in the z-direction. The oscillation amplitude calculation of a given prong in the z-direction may be based on the time interval between successive closed states of the prong&#39;s switch pair  40 . The Coriolis force acting on a given prong may be expressed as a change in amplitude of the z-direction oscillation of the given prong when both the z-direction resonant frequency and the x-direction resonant frequency of the given prong match. The Coriolis force may be expressed as the z-direction offset of the resonant oscillation of the tuning fork  14  in the z-direction when the resonant frequency of a given prong in the z-direction is much greater than that of the prong&#39;s resonant frequency in the x-direction. 
       FIG. 6  is a plot of the displacement of the tuning fork  14  with respect to the frame  12 . The exemplary time domain-based method represented in  FIG. 5  is in the context of sensing a force, and relies on measuring deflection (also referred to as the bias) of the tuning fork  14 , which may also be characterized as a proof mass/spring-based oscillator that is being driven at a frequency f drv . In one configuration, the oscillations of the oscillator are substantially harmonic. Alternatively, the oscillations may be substantially non-harmonic or (e.g., not perfect sinusoids). 
     As a brief aside, in classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F that is proportional to the displacement x as:
 
 F=−kx.   (Eqn. 1)
 
     If the restoring force is the only force acting on the oscillator system, the system is referred to as a simple harmonic oscillator, and it undergoes simple harmonic motion, characterized by sinusoidal oscillations about the equilibrium point, with constant amplitude and constant frequency f 0  (which does not depend on the amplitude): 
                     f   0     =       1     T   0       =       1     2   ⁢   π       ⁢         k   m       .                 (     Eqn   .           ⁢   2     )               
where:
         k is the spring constant;   m is the oscillator mass   f 0  is the oscillator resonant frequency; and   T 0  is the corresponding period of oscillations.       

     In the plot shown in  FIG. 6  (“harmonic” variant), the driving frequency f drv  is configured to match the natural resonance frequency f 0  of the proof mass/spring-based harmonic oscillator causing a sinusoidal motion of the proof mass, as shown by the trace  54 . A system driven in-resonance typically requires a high-quality factor (Q) oscillating proof-mass system. It will be appreciated, however, that for this embodiment, literally any driving signal that maintains the oscillator in resonance may be used. 
     In another example embodiment (not shown), the proof mass of the oscillator may be driven “off-resonance”, which provides, inter alia, precise control of the oscillation period and, hence, control of sensor accuracy. Off-resonance driven systems typically require a lower Q oscillator. 
     In the absence of any external forcing, the proof mass trajectory is centered at a reference position  56 , as shown in  FIG. 6 . The oscillatory motion of the proof mass is measured using “triggering” events that are generated when the mass passes through trigger points corresponding to predefined physical locations such as the first, second, and third reference positions depicted in  FIGS. 4A-4C . The first reference position corresponds to a neutral (also referred to as a zero-force) point  56 . The second reference position corresponds to a positive trigger point  58 . The third reference position corresponds to a negative trigger point  60 . In the plot of  FIG. 6 , the trigger positions  58  and  60  are configured at the same predetermined distance d 0    62  (also referred to as the trigger gap or trigger spacing) away from the first reference position  56 . As will be appreciated by those skilled in the art, other trigger configurations are compatible with the invention, such as, for example, asymmetric and/or multiple sets of positive and or negative trigger points  58 ,  60 . In one specific variant, a single trigger position (such as the first reference position  56  for example) is utilized. 
     In the plot of  FIG. 6 , the harmonic oscillations of the tuning fork/proof mass (as shown for example by the un-forced trace  54 ) causes each of the triggering points  56 ,  58 , 60  to generate a pair of triggering events marked by the circles  64 , triangles  66 , and squares  68 , respectively, for each full cycle of mass oscillation. 
     Timing of the triggering events  64 ,  66 ,  68  is measured using the same reference clock, and periods between successive crossings of the respective trigger points are computed. That is, the period Tr 1  (denoted by the reference character  70 ) is determined by subtracting the times of the successive trigger events  64  (which correspond to the mass crossing of the reference trigger point  56 ). The period Tr 2  (denoted by the reference character  72 ) is determined by subtracting the times of the successive trigger events  66  (which correspond to the mass crossing of the positive trigger point  58 ). The period Tr 3  (denoted by the reference character  74 ) is determined by subtracting the times of the successive trigger events  68  (which correspond to the mass crossing of the reference point  60 ). 
     When the proof mass is subjected to an external force F ext  of a frequency f ext &lt;f drv , the equilibrium point of the proof mass harmonic oscillations is shifted from the reference zero-force position. That is, a low frequency forces acting on the proof mass results in a low frequency shift (also referred to as the deflection) of the equilibrium point. Because applied inertial forces impact the DC bias of the simple harmonic oscillator, it is by definition immune to other zero-mean frequencies that may be coupled into the harmonic oscillator; that is, any high frequency oscillation centered around mean value (e.g., zero) will average to that mean value. 
       FIG. 7  is a plot of tuning fork displacement against time in the presence of external forcing. As indicated by the trace  76  the oscillations of the proof mass in the presence of external forcing are shifted from the zero-force oscillations trajectory. As a result, the forced oscillation trace  76  is centered around a level (indicated by the line  78 ) that is deflected from the reference point  56 . 
     Similar to the mass motion described with respect to  FIG. 6 , harmonic oscillations of the proof mass in the presence of external forcing (e.g., the trace  76  in  FIG. 7 ) cause each of the triggering points  56 ,  58 , and  60  to generate a pair of triggering events marked by circles  80 , triangles  82 , and squares  84 , respectively, for each full cycle of mass oscillation. The external force acts to create an offset (bias) in the oscillator, which is detected by measuring the time periods between successive triggering points (such as the points  80 ,  82 , and  84  in  FIG. 7 ), as described in detail below. 
     Measured timing of the triggering events  80  is used to compute the period T 1  (denoted by the arrow  86 ), which corresponds to the forced mass crossing of the reference trigger point  56  on the upswing of the mass oscillation. The period T 2  (denoted by the arrow  88 ) is determined by subtracting the times of the successive trigger events  82 , and T 2  corresponds to the mass crossing of the positive trigger point  58 . The period T 3  (denoted by the arrow  90 ) is determined by subtracting the times of the successive trigger events  84 , and it corresponds to the mass crossing of the reference point  60 . The period T 4  (denoted by the arrow  92 ) is determined by subtracting the times of the successive trigger events  80  and corresponds to the forced mass crossing of the reference trigger point  56  on the downswing of the mass oscillation, as illustrated in  FIG. 7 . 
     In one exemplary approach, the measured periods between successive trigger events (i.e., T 1  through T 4 ) are used to obtain an estimate of the proof mass deflection d (denoted by the arrow  94  in  FIG. 7 ) from the reference point. The proof mass deflection d +  around the oscillation maximum (as depicted by the arrow  96  in  FIG. 7 ) is obtained by combining the upswing reference point crossing period T 1  and the positive trigger point  58  crossing period T 2  as follows: 
                       d   +     =       A   +     ⁢   cos   ⁢       π   ⁢           ⁢     T   1       P         ,       A   +     =       d   0         cos   ⁢       π   ⁢           ⁢     T   2       P       -     cos   ⁢       π   ⁢           ⁢     T   1       P             ,           (     Eqn   .           ⁢   3     )               
where: d 0  is the distance between the reference trigger point and the positive trigger point (the trigger gap);
         A +  is the amplitude of the oscillations at the oscillation maxima;   P is the period of oscillations defined as P=T 1 +T 3 ;   d +  is the proof mass deflection estimate around the oscillation maxima;   T 1  is the upswing reference point crossing period; and   T 2  is the positive trigger point crossing period.
 
Similarly, the proof mass deflection d −  around the oscillation minimum is (as depicted by the arrow  98  in  FIG. 7 ) obtained by combining the upswing reference point crossing period T 3  and the negative trigger point crossing period T 4  as follows:
       

                       d   -     =       A     -   0       ⁢   cos   ⁢       π   ⁢           ⁢     T   3       P         ,       A   -     =       d   0         cos   ⁢       π   ⁢           ⁢     T   4       P       -     cos   ⁢       π   ⁢           ⁢     T   3       P             ,           (     Eqn   .           ⁢   4     )               
where: d 0  is the trigger gap;
         A_ is the amplitude of the oscillations at the oscillation minima;   P is the period of oscillations defined as P=T 1 +T 3 ;   d −  is the proof mass deflection estimate around the oscillation minima;   T 3  is the downswing reference point crossing period; and   T 4  is the negative trigger point crossing period.       

     In one variant, two independent estimates, d +  and d − , are used to provide deflection measurements twice in each cycle (which may or may not be every half cycle) of oscillations, hence improving sensor frequency response. In another variant, the independent estimates d + , d −  are combined to produce an averaged deflection d thereby reducing measurement short term error. In yet another variant, an averaging window of variable length is used to further improve measurement precision. 
     In the deflection estimations according to Eqns. 3 and 4, the period of oscillation P is measured every oscillation cycle and the periods T 1  through T 4  are defined in  FIG. 7 . Note that the calculated deflection is independent of the amplitude of oscillation. 
     In one embodiment useful for acceleration force measurements, the accelerations corresponding to the deflection derived from the Eqns. 3 and 4 are obtained as follows: 
     
       
         
           
             
               
                 
                   
                     
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     The derivation of Eqns. 3 and 4 assumes that the external force is constant throughout the measurements of T 1  through T 4 , which places a limit on the highest frequency of the external force that can be accurately resolved using these equations. Therefore, in the case of a continuous driving signal, it is necessary to select a driving frequency f drv  that is higher than the maximum expected forcing frequency: i.e. f ext &lt;f drv . 
     As is seen from Eqns. 3 and 4, the deflection estimates utilize ratios of measured period between reference events T 1  through T 4  and the period of forced oscillations P. Provided that all of these time intervals are obtained using the same reference clock, the final deflection (and, therefore, force) estimate advantageously becomes insensitive to clock systematic errors, such as, for example, drift due to aging, temperature, or other environmental changes. The calculation method of Eqns. 3 and 4 is also insensitive to changes in resonant frequency with temperature or other environmental effects. 
     In another embodiment of the invention, a clock jitter or variation (e.g., on the order of no more than a half clock cycle in one implementation) is purposely introduced into the reference clock such that low frequency inertial forces applied to the sensor can be averaged over time. As is well known, quantization noise or error cannot be averaged; introduction of such jitter advantageously mitigates or eliminates such quantization error, thereby allowing for effective averaging (and hence increasing the accuracy of the device). 
       FIG. 8A  is a plot of the oscillation amplitude of the tuning fork  14  with respect to the frame  12  showing the three triggering points  56 ,  58 , and  60 , described above.  FIG. 8B  is, in part, a pictorial representation of the triggering events  56 ,  58 , and  60 . At trigger event  58  a tunneling discharge pulse  100  tunnels from the tuning fork  14  to the frame  12 . At trigger event  56 , two tunneling discharge pulses  102  and  103  tunnel from the tuning fork  14  to the frame  12 . At trigger event  60 , a tunneling discharge pulse  104  tunnels from the tuning fork  14  to the frame  12 . As the pulses  100 ,  102 ,  103 , and  104  may differ in amplitude due to, for example, variations in applied tunneling voltage (voltage noise) and/or tunneling distance, low noise current amplifiers may be used to amplify the discharge pulses to the rail (that is the maximum current level value of the sensing circuit) so as to produce the amplified pulses  106 ,  108 ,  109 , and  110  respectively, which exhibit substantially rectangular shapes, as shown in  FIG. 8B . Although the amplitude information is lost, the amplified square pulses  106 ,  108 ,  109 , and  110  are advantageously well suited for interfacing with digital circuits. 
     The tuning fork gyroscope  10  provides a compact, mechanically-isolated design to measure the Coriolis force caused by rotation of the gyroscope  10 . Rotation along the length of the first and second prongs  24  and  26  will cause a Coriolis force raising or lowering the prongs out of the original plane (e.g., the x-y plane shown in  FIG. 1 ) 90° out of phase with the prong vibration. If the resonant frequency of a given prong vibrating in and out of the plane is matched to the resonant frequency of the prong vibrating in the plane, then the amplitude of the vertical vibration should be proportional to the total angle rotated. If the two orthogonal vibrations are significantly off resonance from each other, then the vertical offset of the prong will be proportional to the change in rotation times the horizontal prong velocity. 
       FIG. 9  is a top view of an embodiment of the gyroscope  10  wherein the digital position triggers  20  are located on the free ends of the first and second prongs  24  and  26 . In this embodiment, an edge  112  of the conductive plane  34  is curved such that as the prongs oscillate in the x-direction the size of the gap  42  remains substantially the same. 
       FIG. 10  is a side cross-section side view of an embodiment of the gyroscope  10  further comprising a third driver  114  configured to drive the tuning fork  14  to oscillate with respect to the frame  12  in the z-direction. This embodiment of the gyroscope  10  also comprises a capping wafer  116 , an integral frame/base wafer assembly  118 , and a bonding layer  120 . 
       FIG. 11  is a plot of the displacement of the conductive tips  32  in the z-direction over time with respect to the conductive plane  34  of one of the digital triggers  20  depicted in  FIGS. 2A-2B . In  FIG. 11 , the x- and z-direction resonances of the prong to which the digital trigger  20  is coupled are matched. If the z-direction resonant frequency of a given prong matches its x-direction resonant frequency, the Coriolis force due to rotation of the frame  12  about the y-axis will couple into the resonant oscillation and will be expressed as a change in amplitude of the z-direction oscillation of the given prong. The long-dashed line corresponds to pre-existing oscillation of the given prong in the z-direction with respect to the frame  12 . The solid line corresponds to the x-direction displacement of the given prong with respect to the frame  12 . The dotted line represents the total displacement of the given prong in the z-direction with respect to the frame  12 . The dot-dash-dot line corresponds to the displacement of the given prong in the z-direction with respect to the frame  12  attributable to the Coriolis force. 
       FIG. 12  is a plot of the z-direction-displacement of the conductive tips  32  with respect to the conductive plane  34  of one of the digital triggers  20  depicted in  FIGS. 2A-2B  against the x-direction-displacement of the conductive tips  32  with respect to the conductive plane  34 . In  FIG. 12 , the x- and z-direction resonances of the prong, to which the digital trigger  20  is coupled, are matched. The solid line in  FIG. 12  corresponds to the total displacement of the given prong with respect to the frame  12 . The dashed line in  FIG. 12  corresponds to the displacement of the given prong with respect to the frame  12  attributable to the Coriolis force. 
       FIG. 13 , like  FIG. 11 , is a plot of the z-direction-displacement over time of the conductive tips  32  with respect to the conductive plane  34  of one of the digital triggers  20  depicted in  FIGS. 2A-2B . However,  FIG. 13  differs from  FIG. 11  in that in  FIG. 13 , the x- and z-direction resonances of the prong to which the digital trigger  20  is coupled are mis-matched, but instead, the z-direction resonant frequency of the prong is much greater than that of the x-direction resonant frequency. In this scenario, the Coriolis force may be determined by calculating the z-direction offset of a previously initiated resonant z-direction oscillation. The initial vertical and horizontal resonant oscillation of the prong may be induced by using capacitive forcing to an initial vertical and horizontal displacement. Besides capacitive forcing, the initial resonant z-direction oscillation may also be caused by a resonant tone generator, or any other forcing means. By averaging the results from the two prongs (vibrating in the x-direction 180° out of phase) non-rotational acceleration effects can be eliminated from the measurement. The solid line in  FIG. 13  corresponds to pre-existing oscillation of the given prong in the z-direction with respect to the frame  12 . The dash-dot-dash line in  FIG. 13  corresponds to the x-direction displacement of the given prong with respect to the frame  12 . The dotted line in  FIG. 13  represents the total displacement of the given prong in the z-direction with respect to the frame  12 . The dashed line in  FIG. 13  corresponds to the displacement of the given prong in the z-direction with respect to the frame  12  attributable to the Coriolis force. 
       FIG. 14  is a plot of the z-direction-displacement of the conductive tips  32  with respect to the conductive plane  34  of one of the digital triggers  20  depicted in  FIGS. 2A-2B  against the x-direction-displacement of the conductive tips  32  with respect to the conductive plane  34  where the x- and z-direction resonances of the prong, to which the digital trigger  20  is coupled, are mis-matched. The solid line in  FIG. 14  corresponds to the total displacement of the given prong with respect to the frame  12 . The dashed line in  FIG. 14  corresponds to the displacement of the given prong with respect to the frame  12  attributable to the Coriolis force. 
       FIGS. 15A-15B  are perspective views of an embodiment of the gyroscope  10 . In this embodiment, the digital position triggers  20  are located on opposite sides of the distal end  30  of the base  22 . Although four digital triggers  20  are depicted in  FIGS. 15A-15B , it is to be understood that any number of at least two digital switches  20  may be used with the gyroscope  10 , and that the four digital triggers  20  merely represent one example embodiment. In this embodiment, when a torque, due to Coriolis forces  122 , is applied to the tuning fork  14 , the base twists causing relative motion between the distal end  30  of the base  22  and the frame  12  (not shown in  FIGS. 15A-15B ) such that the Coriolis forces acting on both prongs may be combined into one time domain measurement. In this embodiment, half of each digital trigger  20  may be mounted to the distal end  30  of the base  22 , as shown in  FIGS. 15A-15B  while the corresponding half of each digital trigger  20  may be mounted to the frame  12  (not shown). Each half of the digital trigger  20  may comprise a z-direction-stacked set of electron tunneling tips.  FIG. 15B  illustrates how the shape of the base  22  may be altered in order to tune the rotational resonant frequency of the tuning fork  14  to match, or mismatch, the Coriolis force depending on the desired mode of operation. 
       FIG. 16  is a perspective view of an embodiment of the gyroscope  10  wherein the tuning fork  14  further comprises first and second arms  124  and  126  respectively having proximal and distal ends  128  and  130  respectively. The proximal ends  128  of the first and second arms  124  and  126  are coupled to the distal end of the base  30 . The position triggers  20  are located on the distal ends  130  of the first and second arms  124  and  126 . The first and second prongs  24  and  26  are subjected to oscillating driving forces  132  such that the first and second prongs  24  and  26  oscillate at their resonant frequencies 180° out of phase with each other. When the gyroscope  10  is subjected to a rotation about the y-axis, Coriolis forces  122  cause deflection of the first and second prongs, which in turn causes the tuning fork  14  to twist. The twisting of the tuning fork  14  causes displacement of the distal ends  130  of the first and second arms  124  and  126 , which can be measured by the digital triggers  20 . 
       FIG. 17  is a perspective view of an embodiment of the gyroscope  10  wherein the tuning fork  14  further comprises third and fourth arms  134  and  136 .  FIG. 17  also illustrates an alternate orientation of the digital triggers  20 . 
     From the above description of the gyroscope  10 , it is manifest that various techniques may be used for implementing the concepts of gyroscope  10  without departing from its scope. The described embodiments are to be considered in all respects as illustrative and not restrictive. It should also be understood that gyroscope  10  is not limited to the particular embodiments described herein, but is capable of many embodiments without departing from the scope of the claims.