Patent Publication Number: US-11047685-B2

Title: Configuration to reduce non-linear motion

Description:
PRIORITY CLAIM 
     Under 35 U.S.C. 120, this application is a Continuation Application and claims priority to U.S. patent application Ser. No. 15/814,373, filed Nov. 15, 2017, entitled, “CONFIGURATION TO REDUCE NON-LINEAR MOTION,” which application is a Continuation Application of U.S. patent application Ser. No. 14/495,786, filed Sep. 24, 2014, entitled, “CONFIGURATION TO REDUCE NON-LINEAR MOTION,” which application claims benefit under 35 USC 119(e) of U.S. Provisional Patent Application No. 61/929,838, filed on Jan. 21, 2014, entitled, “PERFORMANCE IMPROVEMENTS ON 3-AXIS FRAME MICRO GYROSCOPES,” the entireties of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates generally to angular velocity sensors and more particularly relates to angular velocity sensors that include guided mass systems. 
     BACKGROUND 
     Sensing of angular velocity is frequently performed using vibratory rate gyroscopes. Vibratory rate gyroscopes broadly function by driving the sensor into a first motion and measuring a second motion of the sensor that is responsive to both the first motion and the angular velocity to be sensed. 
     Frequently, a mass, usually referred to as a proof mass, within the sensor is driven into oscillation by an actuator. Rotation of the sensor imparts a Coriolis force to the oscillating mass that is proportional to the angular velocity (or rotation rate), and depends on the orientation of the angular velocity vector with respect to the velocity vector of the proof mass. The Coriolis force, the angular velocity vector, and the proof-mass velocity vector are mutually orthogonal. For example, a proof-mass moving in an X-direction within a sensor rotating about a Y-axis experiences a Z directed Coriolis force. Similarly, a proof-mass moving in an X-direction within a sensor rotating about a Z-axis experiences a Y directed Coriolis force. Finally, a proof-mass moving in an X-direction within a sensor rotating about the X-axis experiences no Coriolis force. Coriolis forces imparted to the proof-mass are usually sensed indirectly by measuring motions within the sensor that are responsive to the Coriolis forces. 
     Conventional gyroscopes that sense angular velocity about an in-plane axis (i.e. X-axis or Y-axis) can be driven out-of-plane, and the Coriolis response is sensed in-plane or vice versa. Out-of-plane drive tends to be less efficient than in-plane drive, requires additional fabrication steps, and is limited by nonlinearities. For example, driving the proof-mass out-of-plane might require a large vertical gap or a cavity underneath the proof-mass to provide sufficient room for the proof-mass to oscillate. Forming a cavity under the proof-mass requires additional fabrication steps and increases cost. Typically electrostatic actuators of the parallel-plate type are used to drive the proof-mass out-of-plane. The actuators are formed between the proof-mass and the substrate. The electrostatic force depends on the gap between the proof-mass and the substrate. Because the proof-mass oscillates out-of-plane, the electrostatic force is nonlinear which tends to limit the device performance Additionally, the electrostatic force is reduced because of the requirement to have large vertical gaps or a cavity under the proof-mass. Achieving large amplitude oscillation requires large force and that might require high-voltage actuation. Adding high-voltage actuation increases the fabrication cost and complexity of the integrated circuits. 
     Furthermore a conventional multi-axis gyroscope might use multiple structures that oscillate at independent frequencies to sense angular rates. Each structure requires a separate drive circuit to oscillate the respective proof-masses. Having more than one drive circuit increases cost and power consumption. 
     Accordingly, what is desired is to provide a system and method that overcomes the above issues. The present invention addresses such a need. 
     SUMMARY 
     Embodiments for modifying a spring mass configuration are disclosed that minimize the effects of unwanted nonlinear motion on a Micro-Electro-Mechanical Systems (MEMS) sensor. The modifications include any or any combination of providing a rigid element between rotating structures of the spring mass configuration, tuning a spring system between the rotating structures and coupling an electrical cancellation system to the rotating structures. In so doing unwanted nonlinear motion such as unwanted 2 harmonic motion is minimized. 
     In an aspect, MEMS sensor is disclosed. The MEMS sensor includes a first and second rotating arm. The first and second rotating arms are coupled to each other and the first and second rotating arms are configured to counter rotate when driven into oscillation. The MEMS sensor also includes at least one travelling system. The at least one travelling system is coupled to the first and second rotating arms. Finally, the MEMS sensor includes at least one actuator for driving the at least one travelling system into oscillation. The at least one travelling system moves in a first direction when driven into oscillation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates four different spring-mass configurations  10 ,  11 ,  12  and  13 , respectively. 
         FIGS. 2A and 2B  illustrate an embodiment of a single axis gyroscope comprising a guided mass system. 
         FIG. 3  illustrates an embodiment of a single axis gyroscope comprising a guided mass system in accordance with the present invention. 
         FIG. 4  shows a modification of a guided mass system to eliminate the 2nd harmonic component of the drive motion. 
         FIG. 5  illustrates another embodiment of a single axis gyroscope comprising a balanced guided mass system in accordance with an embodiment of the present invention. 
         FIGS. 6 a  and 6 b    illustrates an embodiment of a tri-axis gyroscope comprising a multiple guided mass system in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention relates generally to angular velocity sensors and more particularly relates to angular velocity sensors that include guided mass systems. The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. Various modifications to the preferred embodiments and the generic principles and features described herein will be readily apparent to those skilled in the art. Thus, the present invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features described herein. 
     Micro-Electro-Mechanical Systems (MEMS) refers to a class of devices fabricated using semiconductor-like processes and exhibiting mechanical characteristics such as the ability to move or deform. MEMS often, but not always, interact with electrical signals. A MEMS device may refer to a semiconductor device implemented as a Microelectromechanical system. A MEMS device includes mechanical elements and optionally includes electronics for sensing. MEMS devices include but are not limited to gyroscopes, accelerometers, magnetometers, and pressure sensors. 
       FIG. 1  illustrates four different spring-mass configurations  10 ,  11 ,  12  and  13 , that could be utilized in a MEMS sensor, respectively. A first spring-mass configuration  10  includes a spring-mass system  10 A. The spring mass system  10 A includes a lever arm  20 A, a proof mass  30 A, a linear spring  40 A, and a hinge  50 A attached to a stable point  60 A. The proof mass,  30 A, in the spring mass system  10 A has three degrees of freedom. The proof mass  30 A can rotate by an angle θ about an axis passing from the center of the hinge  50 A and normal to a first plane in this embodiment, the XY plane, and it can translate in X and Y direction as it rotates in the X-Y plane. Although it is not shown in  FIG. 1  in detail, hinge  50 A has a finite translational compliance, and linear spring  40 A has a finite rotational compliance. If it is assumed that the length of the spring  40 A is negligible and the length of the lever arm  20 A is L. The X direction motion of the mass  30 A is given by the equation:
 
 X   d   =L  sin(θ)≈ Lθ   (Eq-1)
 
where X d  is the x-direction translation motion of the proof mass  30 A. Since the motion of the proof mass  30 A is rotational, there is also Y direction component of the motion of the proof mass  30 A which can be represented as in the equation given below:
 
                     Y   d     =       L   ⁡     (     1   -     cos   ⁡     (   θ   )         )       ≈     L   ⁢       θ   2     2                 (     Eq   ⁢     -     ⁢   2     )               
where Y d  is the Y-direction translation motion of the proof-mass.
 
     If the mass  30 A is driven at a frequency cod which is named as drive frequency, where the drive frequency can be the natural frequency of the spring mass system  10 A, the governing equation for the rotational drive motion of the mass  30 A can be given as:
 
θ=|θ|sin(ω d   t )  (Eq-3)
 
Then X-direction motion of the proof mass  30 A at the drive frequency can be given as:
 
 X   d   ≈L |θ|sin(ω d   t )  (Eq-4)
 
Y direction motion of the proof mass  30 A can be represented by the following equation:
 
     
       
         
           
             
               
                 
                   
                     
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                             ( 
                             
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     As it can be seen in the equations 4 and 5, the Y direction motion of the mass  30 A is at two times the drive frequency. This behavior is due to the nonlinearity of the rotational movement of the proof mass  30 A. If the mass is driven in the X direction with the use of a lever arm  20 A at the drive frequency, there is always a Y direction vibration which is at two times the drive frequency, which is referred to as 2 nd  Harmonic vibration. 
     The 2 nd  Harmonic vibration can be non-ideal for MEMS sensors that are driven in one direction and the sensing motion is in-plane and orthogonal to the drive direction. As an example, if the X direction is the drive direction and the sensing direction is the Y direction, an erroneous signal in Y direction with a frequency that is two times the drive frequency is generated by the nonlinear motion of the lever arms. So, for those cases, it is needed to eliminate the Y direction component of the nonlinear motion by the use of specific structures and elements which may be added to the spring-mass system  10 A. To describe the issues with a guided mass configuration  10 , refer now to the following discussion in conjunction with the accompanying figures. 
       FIG. 2A  illustrates an embodiment of a single axis gyroscope comprising a guided mass system  500 . The guided mass system  500  is disposed in an X-Y plane parallel to a substrate  101  and comprises a guided mass system  100  coupled to a yaw proof mass  518   a . The guided mass system  100  includes guiding arms  104   a  and  104   b  that are flexibly coupled via springs  108   a  and  108   b  to the substrate  101  via at least one anchoring point  106   a . The two guiding arms  104   a  and  104   b  are flexibly coupled to one proof-mass  102   a  via springs  103   a  and  103   b . The yaw proof mass  518   a  is flexibly connected to the proof mass  102   a  via yaw-springs  520   a - 520   d.    
     The proof mass  102   a  and yaw proof mass  518   a , guiding arms  104   a  and  104   b , anchoring point  106   a , and springs  103   a ,  103   b ,  108   a , and  108   b  form a planar four-bar linkage. The springs  103   a ,  103   b ,  108   a , and  108   b  are compliant in-plane about an axis in the Z-direction so that each guiding arm  104   a  and  104   b  can rotate in-plane while the proof-mass  102   a  translates in an X-direction, as shown in  FIG. 2B . Yaw-springs  520   a - 520   d  are stiff in the X-direction such that when the guided mass system  100  translates in the X-direction, the yaw proof-mass  518   a  also translates with the proof mass  102   a.    
     Electrostatic actuators, such as comb drives  109   a  and  109   b , are connected to the proof mass  102   a  to drive the guided mass system  100 . In this embodiment, two electrostatic actuators are utilized. 
     However, one of ordinary skill in the art readily recognizes that one electrostatic actuator can be provided and the use of one electrostatic actuator would be within the spirit and scope of the present invention. In addition, although electrostatic actuators will be described throughout this specification as the actuators being used to drive the guided mass systems, one of ordinary skill in the art recognizes that a variety of actuators could be utilized for this function and that use would be within the spirit and scope of the present invention. For example, the actuators could be piezoelectric, thermal or electromagnetic or the like. 
     The guided mass system  500  can be driven at a drive frequency by a single drive circuit coupled to the actuators  109   a  and  109   b . The drive frequency can be a resonant frequency of the guided mass system  500 . When the guided mass system  500  is driven, the guiding arms  104   a  and  104   b  rotate in-plane and the proof-mass  102   a  and yaw proof mass  518   a  translate in-plane in the X-direction. 
     Angular velocity about a yaw-input axis in the Z-direction will cause a Coriolis force to act on the yaw proof-mass  518   a  in the Y-direction resulting in motion of the yaw proof-mass  518   a  in the Y-direction. A capacitive electrode  522   a  is used to sense the motion of the yaw proof-mass  518   a  in the Y-direction which provides a measure of the angular velocity about the yaw-input axis. 
     A variety of types of transducers could be utilized in a system and method in accordance with the present invention. For example, instead of using the capacitive electrode  522   a , one can also use a piezoelectric or optical or the like transducer and its use would be within the spirit and scope of the present invention. 
     The guided mass system  500  can be simply represented by the spring mass system  10 A that is shown in  FIG. 1 . The lever arms  104   a - 104   b  are similar to the lever arm  20 A, the springs  103   a - 103   b ,  108   a - 108   b  and  520   a - 520   d  of the guided mass system  500  are compliant in the Y direction. As a result, the spring  40 A can be a representation of y direction compliance of the springs  103   a - 103   b ,  108   a - 108   b  and  520   a - 520   d . The proof mass  102   a  and the yaw proof-mass  518   a  are attached to the springs  103   a - 103   b  and  520   a - 520   d , respectively, as the proof mass  30 A is attached to the spring  40 A. Finally, in-plane rotational compliance of the springs  108   a - 108   b  that are attached to the anchor  106   a  can be represented by the hinge  50 A and the stable point  60 A. 
     As it is shown in  FIG. 2B , the motion of the center of mass of proof mass  102   a  has a non-linear motion. When the proof mass  102   a  and yaw proof-mass  518   a  are driven in the X direction, there is also a motion in Y direction that is at two times the drive frequency which is due to the nonlinearity of the drive motion as it has been explained in  FIG. 1  for the spring-mass configuration  10 . The motion at two times the drive frequency can also be called the 2 nd  harmonic motion of the guided mass system  500 . In the single axis gyroscope shown in  FIG. 2A , the 2 nd  Harmonic motion is sensed by the capacitive electrode  522   a  as an erroneous signal and it may corrupt the readings or saturate the front end electronics. 
     In certain conditions, guided mass system  500  can also be used as a dual axis gyroscope. If the springs  108   a  and  108   b  are compliant about a first roll-sense axis in the X-direction then the guiding arms  104   a  and  104   b  can rotate out-of-plane, whereby out-of-plane rotation of the guiding arms  104   a  and  104   b  causes the proof mass  102   a  and the yaw proof mass  518   a  move out-of-plane with the guiding arms  104   a  and  104   b.    
     While the guided mass system  500  is driven, an angular velocity about a roll-input axis in the Y-direction that is in the plane of the substrate and orthogonal to the X-direction will cause a Coriolis force to act on the proof-mass  102   a  and the yaw proof-mass  518   a  in the Z-direction. The Coriolis force causes the guided mass system  500  to rotate out-of-plane about the first roll-sense axis. When the guided mass system  500  rotates out-of-plane, the guiding arms  104   a  and  104   b  and the proof mass  102   a  and yaw proof mass  518   a  rotate out-of-plane about the first roll-sense axis. The amplitude of the rotation of the guided mass system  500  is proportional to the angular velocity about the roll-input axis. 
     A capacitive electrode  112   a  under the proof mass  102   a  is used to detect the rotation of the guided mass system  500  about the first roll-sense axis. The rotation provides a measure of the angular velocity about the roll-input axis. A variety of types of transducers could be utilized in the present invention. For example, the capacitive electrode  112   a  could be also piezoelectric or optical or the like and its use would be within the spirit and scope of the present invention. 
     The guided mass system  500  of  FIG. 2A  can be modified to eliminate the 2 nd  harmonic motion by using the methods that are introduced in one or more of the spring mass configurations  11 ,  12  and  13  shown in  FIG. 1 . To describe these configurations and methods in more detail refer now to the following description in conjunction with the accompanying Figures. 
     A second spring-mass configuration  11  is shown in  FIG. 1  that has components similar to the spring-mass configuration  10 . Spring mass configuration  11  includes two spring mass systems  11 A- 11 B. Each of the two spring mass systems  11 A- 11 B comprise lever arms  21 A- 21 B, and a traveling system  101 A comprising traveling masses  31 A- 31 B and connection element  21 , linear springs  41 A- 41 B, hinges  51 A- 51 B attached to stable points  61 A- 61 B. 
     The difference between spring-mass configuration  11  and the spring mass configuration  10  is connection element  21  that connects two spring-mass systems  11 A and  11 B. In the spring-mass configuration  11 , while two spring-mass systems  11 A- 11 B are operated side by side, they are also connected by the connection element  21 . Both  11 A and  11 B move in the same X direction during the drive operation. But, the Y direction motion of  11 A and  11 B are opposing each other. If those two spring-mass systems  11 A- 11 B are rigidly connected by the connection element  21 , then the spring elements  41 A and  41 B stretches in opposite directions to accommodate the nonlinear motion due to the rotation of the lever arms  21 A and  21 B. As a result of the compensation of the 2 nd  harmonic motion by the spring elements  41 A and  41 B, the net motion on the traveling masses  31 A and  31 B in Y direction becomes zero. Consequently, the traveling masses  31 A and  31 B can be restricted to move only in the x direction by eliminating the unwanted 2 nd  harmonic Y direction motion. 
     Spring mass configuration  12  includes two spring mass systems  12 A- 12 B which comprise lever arms  22 A- 22 B, a traveling system  101 B comprising traveling masses  32 A- 32 B and spring element  22 , linear springs  42 A- 42 B, and hinges  52 A- 52 B attached to stable points  62 A- 62 B. In contrast to spring mass configuration element  10 , the springs  42 A and  42 B have different spring stiffness values. Moreover, an additional component of spring-mass configuration  12  compared to spring mass configuration  10  is the spring element  22  coupled between traveling masses  32 A and  32 B. Spring element  22  is used to eliminate the unwanted 2 nd  harmonic Y direction motion of the traveling masses  32 A or  32 B. Compliance of the spring  22  can be designed such a way that the 2nd harmonic motion of one of the spring-mass system  12 B can be used to compensate for the 2 nd  harmonic motion of the other spring-mass system  12 A, or vice versa. For example, by ensuring that the spring stiffness the spring  42 B is equal to the combined stiffness of the spring  22  and the spring  42 A, the 2 nd  harmonic motion of the traveling mass  32 A can be eliminated due to the balance of the opposing forces as in the spring mass configuration  11 . In this scenario, traveling mass  32 B would still have an unwanted 2 nd  harmonic motion. 
     A third modification to the spring-mass configuration  10  is shown as the spring-mass configuration  13 . Spring mass configuration  13  includes two spring-mass systems  13 A- 13 B which are composed of lever arms  23 A- 23 B, and a traveling system  1010  comprising traveling masses  33 A- 33 B, spring element  23 , transducers  73 A- 73 B and  74 A- 74 B, linear springs  43 A- 43 B, and hinges  53 A- 53 B attached to stable points  63 A- 63 B. 
     The additional components of spring-mass configuration  13  compared to spring mass configuration  10  are spring element  23  and transducers  73 A- 73 B and  74 A- 74 B. By coupling two spring mass systems  13 A and  13 B, both of the traveling masses  33 A and  33 B can be resonated in the drive direction at a natural drive frequency. Furthermore, by coupling the traveling masses  33 A and  33 B using the spring  23 , the proof masses  33 A and  33 B can also resonate in the Y direction at another natural frequency. Transducers  73 A- 73 B and  74 A- 74 B are used to sense the motion of the traveling masses  33 A- 33 B in Y direction. Transducers in an embodiment could be capacitive, piezoresistive or the like, although one of ordinary skill in the art readily recognizes that the transducers could a variety of types and that would be within the spirit and scope of the present invention. 
     The sensing direction of the transducers  73 A- 73 B and  74 A- 74 B can be selected such a way that the 2 nd  harmonic component of the drive motion in Y direction can be rejected, but the signals that are useful can be preserved. As an example, in the spring-mass configuration  13 , if it is assumed that the common mode motion in the Y direction is the sensor response, as in the case of a yaw gyroscope undergoing Z-axis rotation, the Y direction 2 nd  harmonic motion is rejected since the electrodes cancels the opposing (differential) motions in Y direction. 
     The spring-mass configuration  13  is given as an example for the electrical cancellation of unwanted 2 nd  Harmonic motion in Y direction; however, there may be different sensing and rejection schemes of transducers, depending on the proof mass and electrode configurations. In other configurations, the common mode motion can be rejected but the differential motion can be detected. 
     The following description will describe different guided mass systems that incorporate on or more of the spring mass configurations  11 - 14  described above. 
       FIG. 3  illustrates an embodiment of a single axis gyroscope comprising a guided mass system in accordance with the present invention. The guided mass system  600  is disposed in an X-Y plane. The guided mass system  600  includes guiding arms  104   a ,  104   b ,  104   c  and  104   d  that are flexibly coupled via springs  108   a ,  108   b ,  108   c  and  108   d  to the substrate  100  via the anchoring points  106   a  and  106   b . Four guiding arms  104   a ,  104   b ,  104   c  and  104   d  are flexibly coupled to one traveling mass  105  via springs  103   a ,  103   b ,  103   c  and  103   d.    
     Each spring  103   a - 103   d ,  108   a - 108   d  is compliant in-plane about an axis in the Z-direction so that each guiding arm  104   a - 104   b  and  104   c - 104   d  can rotate anti-phase in the plane while the traveling mass  105  translates in an X-direction. The yaw proof-masses  518   a  and  518   b  are flexibly connected to the traveling mass  105  via yaw-springs  520   a - 520   d  and  520   e - 520   h , respectively. The guided mass system  600  can be driven at a drive frequency by a single drive circuit coupled to the actuators  109   a - 109   d . The drive frequency can be a resonant frequency of the guided mass system  600 . When the guided mass system  600  is driven, the guiding arms  104   a - 104   b  and  104   c - 104   d  rotate anti-phase in-plane and the traveling-mass  105  translates in-plane in the X-direction. Yaw-springs  520   a - 520   d  and  520   e - 520   h  are stiff in the X-direction such that when the guided mass system is driven, the yaw proof-masses  518   a - b  also translate with the traveling mass  105  in the X-direction. 
     Angular velocity about a yaw-input axis in the Z-direction will cause a Coriolis force to act on the yaw proof-masses  518   a - 518   b  in the Y-direction resulting in a common mode motion of the yaw proof-masses  518   a  and  518   b . The capacitive electrodes  522   a  and  522   b  are used to sense the motion of the yaw proof-masses  518   a  and  518   b  in the Y-direction which provides a measure of the angular velocity about the yaw-input axis. 
     The configuration shown in  FIG. 3  can be represented as the spring mass configuration  11  of  FIG. 1 . As in the spring mass configuration  11 , guided mass system  600  eliminates the second harmonic motion by combining two guided mass systems by a rigid traveling mass  105 . Since the motion of the lever arms  104   a - 104   b  and  104   c - 104   d  are anti-phase with respect to each other, the travelling mass  105  that is connected to the lever arms  104   a - 104   d  balances the opposing 2 nd  harmonic motion and eliminates the unwanted non-linear component of the drive motion, and the y direction compliance of the spring elements  108   a - 108   b ,  103   a - 103   b  and  108   c - 108   d ,  103   c - 103   d  accommodates the 2 nd  Harmonic motion by stretching in y direction similar to the spring mass configuration  12 . 
     In certain conditions, guided mass system  500  can also be used as a dual axis gyroscope. If we assume that the springs  108   a - 108   b  and  108   c - 108   d  are compliant about a first and second roll-sense axis, respectively, where the first and second roll sense axes are parallel to each other and they are in the X-direction, then the guiding arms  104   a - 104   b  and  104   c - 104   d  can rotate anti-phase out-of-plane, whereby out-of-plane rotation of the guiding arms  104   a - 104   d  causes the traveling mass  105  to move out-of-plane with the guiding arms  104   a - 104   d.    
     Angular velocity about a roll-input axis in the Y-direction that is in the plane of the substrate and orthogonal to the X-direction will cause a Coriolis force to act on the traveling mass  105  in the Z-direction. The Coriolis force causes the lever arms  104   a - 104   b  and lever arms  104   c - 104   d  rotate anti-phase out-of-plane about the first and second roll-sense axes and the traveling mass  105  moves in the Z direction. The amplitude of the motion of the roll-travelling mass  105  is proportional to the angular velocity about the roll-input axis. A capacitive electrode  112   a  under the traveling mass  105  is used to detect the motion of the proof-mass. This motion provides a measure of the angular velocity about the roll-input axis. 
       FIG. 4  illustrates a second embodiment of a single axis gyroscope comprising a guided mass system  700  in accordance with the present invention which minimizes a 2nd Harmonic component of the drive motion. 
     The guided mass system  700  comprises two guided mass systems  700 A and  700 B, which are same as the guided mass system  500 . The proof masses  102   a  and  102   b , consequently two guided mass systems  700 A and  700 B, are connected by a coupling spring  151 . The yaw proof-masses  518   a  and  518   b  are flexibly connected to the proof-masses  102   a  and  102   b , respectively. The coupling spring  151  is torsionally compliant about an axis in the X-direction so that the symmetric guided mass systems  700 A and  700 B can rotate anti-phase out-of-plane about the first and second roll-sense axes. The coupling spring  151  is stiff in the Z-direction which prevents the guided mass systems  700 A and  700 B from rotating in-phase out-of-plane. 
     The coupling spring  151  is stiff in the X-direction such that the proof-mass  102   a  and  102   b  move together in the X-direction. In this way the two guided mass systems  700 A and  700 B are driven together at a drive frequency by a single drive circuit coupled to the actuators  109   a - 109   d.    
     The configuration given in  FIG. 4  can be represented by the spring mass configuration  13  given in  FIG. 1 . As in the spring mass configuration  13 , two guided mass systems  700 A and  700 B are connected by a coupling spring  151 , so that the proof masses  102   a - 102   b  and  518   a - 518   b  can also resonate in the Y direction at a certain natural frequency. Capacitive electrodes  522   a  and  522   b  are used to sense the motion of the proof-masses  518   a  and  518   b  in Y direction, respectively. The sensitive direction of the capacitive electrodes  522   a - 522   b  can be selected such a way that the 2 nd  harmonic motion in the Y direction is rejected but the Coriolis motion in the Y direction is detected. 
     In the guided mass system  700 , the proof masses  518   a  and  518   b  move in the same direction in the drive motion. Hence, an angular velocity about a yaw-input axis in the Z-direction will impart a Coriolis force on the yaw proof-masses  518   a - b  in the same Y-direction (common mode motion). 
     Due to the placement of the electrodes  522   a  and  522   b  in the guided mass system  700 , the capacitance of the electrodes  522   a  and  522   b  changes in opposite directions while the proof masses  518   a - 518   b  move in the same direction. 
     If the capacitance change on the electrodes is subtracted from each other, the common mode Coriolis response of the proof masses  518   a  and  518   b  is able to be detected. 
     On the other hand, the 2 nd  harmonic motions of the proof masses  518   a - 518   b  in the Y direction are in opposite directions, because the guiding arms  104   a - 104   b  and  104   c - 104   d  are rotating around opposite directions. Consequently, the 2 nd  harmonic motion of the proof masses  518   a - 518   b  will be cancelled due to the configuration of the electrodes  522   a - 522   b.    
       FIG. 5  illustrates another embodiment of a single axis gyroscope comprising a balanced guided mass system  1000  in accordance with an embodiment of the present invention. The guided mass system  1000  includes two symmetric guided mass systems  900   a  and  900   b  which are connected by a coupling spring  302 . However, the coupling between the guided mass systems  900   a  and  900   b  doesn&#39;t have to be only a single coupling spring  302 ; the coupling may include various springs and spring-mass systems. 
     The two symmetric guided mass systems  900   a  and  900   b  are arranged so that the proof-masses  102   a - 102   d  all move in the X-direction. Hence, the two guided mass systems  900   a  and  900   b  are driven together at a drive frequency by a single drive circuit coupled to the actuators  109   a - 109   h.    
     In the drive motion of the guided mass system  1000 , the proof-masses  102   b  and  102   c  move together in the same X-direction, since the coupling spring  302  is stiff in the X-direction. On the other hand, the proof masses  102   a  and  102   d  move in the opposite X-direction compared to the proof masses  102   b  and  102   c.    
     Angular velocity about the yaw-input axis will cause Coriolis forces to act on the yaw proof-masses  518   a - 518   d  resulting in motion of the yaw proof-masses  518   a - 518   d  along the Y-direction. The amplitude of the motions of the yaw proof-masses  518   a - 518   d  is proportional to the angular velocity about the yaw-input axis. 
     The schematic provided in  FIG. 5  is a different embodiment of the spring-mass configuration  13  shown in  FIG. 1 . The balanced guided mass system  1000  eliminates the unwanted 2nd harmonic motion of the yaw proof masses  518   a - 518   d  by electrical cancellation. 
     Due to the nature of the drive motion explained above, the imparted Coriolis forces on the proof masses  518   a  and  518   d  are in the opposite direction of the imparted Coriolis forces on the proof masses  518   a  and  518   d . In other words, the Coriolis response motion of the proof masses  518   b  and  518   c  vs. the proof masses  518   a  and  518   d  are differential. In order to detect the differential motion effectively within the given electrode placements in  FIG. 5 , the capacitance change of the electrodes  522   a  and  522   b  due to the Coriolis motion of the proof masses  518   a - 518   b  can be summed up. The capacitance change of the electrodes  522   c  and  522   d  can also be summed up. Moreover, the detected capacitance change from the electrode pair  522   c - 522   d  can be subtracted from the detected capacitance change of the electrode pair  522   a - 522   b . As a result of the electrode configuration, the Coriolis motion is detected. 
     The 2nd harmonic motion direction of the each proof mass  518   a - 518   d  is illustrated by the arrows  541   a - 541   d  which are shown side by side by the arrows  540   a - 540   d  that are showing the Coriolis force direction of the proof masses  518   a - 518   d . The given arrow configuration shows that the Coriolis force and the 2nd harmonic motion are in the same direction for the guided mass system  900   b  but they are in the opposite directions for the guided mass system  900   a . As a result, the 2nd harmonic motion will be cancelled due to the electrode scheme given above. 
     The balanced guided mass system  1000  can also be used as a dual axis gyroscope with a condition where the symmetric guided mass system  900   a  is able to rotate out-of-plane about a first roll-sense axis and the symmetric guided mass system  900   b  is able to rotate out-of-plane about a second roll-sense axis in-plane and parallel to the first roll-sense axis. 
     The coupling spring  302  is connected to proof-masses  102   b  and  102   c . The coupling spring  302  is torsionally compliant about an axis in the X-direction so that the symmetric guided mass systems  900   a  and  900   b  can rotate anti-phase out-of-plane about the first and second roll-sense axes. The coupling spring  302  is stiff in the Z-direction which prevents the symmetric guided mass systems  900   a  and  900   b  from rotating in-phase out-of-plane. 
     Angular velocity about the roll-input axis will cause Coriolis forces to act on the proof-masses  102   a - 102   d  in the Z-direction. The Coriolis forces cause the symmetric guided mass systems  900   a  and  900   b  to rotate anti-phase out-of-plane about the first and second roll-sense axes. The amplitudes of the rotations of the symmetric guided mass systems  900   a  and  900   b  are proportional to the angular velocity. Capacitive electrodes  112   a - 112   c  under the proof masses  102   a - 102   d  are used to detect the rotations of the symmetric guided mass systems  900   a  and  900   b.    
       FIG. 6 a    illustrates an embodiment of a tri-axis gyroscope comprising a multiple guided mass system  1100  in accordance with the present invention. The multiple guided mass system  1100  includes two guided mass systems  500   a  and  500   b  coupled to a guided mass system  800  by coupling springs  302   a  and  302   b , respectively. 
     The guided mass systems  500   a ,  500   b  and  800  are arranged so that yaw proof-masses  518   a  and  518   b  coupled to roll proof masses  102   a - 102   d  all move anti-phase in the X-direction, the pitch proof-mass  650   a  rotates about an axis in the Z-direction. The guided mass system  500   a  rotates out-of-plane about a first roll-sense axis. The symmetric guided mass system  800  rotates out-of-plane about a second roll-sense axis parallel to the first roll-sense axis. The guided mass system  500   b  rotates out-of-plane about a third roll-sense axis parallel to the first and second roll-sense axes. The first coupling spring  302   a  is connected to proof-masses  102   a  and  102   b . The coupling spring  302   a  is stiff in the X-direction such that proof-mass  102   a  and  102   b  move together in the X-direction. The second coupling spring  302   b  is connected to proof-masses  102   c  and  102   d . The coupling spring  302   b  is stiff in the X-direction such that proof-mass  102   c  and  102   d  move together in the X-direction. In this way the guided mass systems  500   a ,  500   b , and  800  are driven together at a drive frequency by a single drive circuit coupled to the actuators  109   a - 109   h . Moreover, as it can be seen in  FIG. 6 a   , folded flexures are used as coupling springs  302   a - b.    
     The coupling spring  302   a  is torsionally compliant about an axis in the X-direction so that the guided mass systems  500   a  and  800  can rotate out-of-plane about the first and second roll-sense axes anti-phase. The coupling spring  302   a  prevents the symmetric guided mass systems  500   a  and  800  from rotating out-of-plane in-phase. 
     The coupling spring  302   b  is also torsionally compliant about an axis in the X-direction so that the guided mass systems  500   b  and  800  can rotate out-of-plane about the second and third roll-sense axes anti-phase. The coupling spring  302   b  prevents the symmetric guided mass systems  500   b  and  800  from rotating out-of-plane in-phase. 
     Angular velocity about the pitch-input axis will cause Coriolis forces to act on the pitch proof-mass  650   a  resulting in a torque that rotates the pitch proof-mass  650   a  about the pitch-sense axis. The amplitude of the rotation of the pitch proof-mass  650   a  is proportional to the angular velocity about the pitch-input axis. The capacitive electrodes  660   a  and  660   b  are disposed on opposite sides along the X-direction under the pitch proof-mass  650   a  and detect the rotation of the pitch proof-mass about the pitch-sense axis. The rotation provides a measure of the angular velocity about the pitch-input axis. 
     Angular velocity about the roll-input axis will cause Coriolis forces to act on the proof-masses  102   a  and  102   b  in a Z-direction and on proof-masses  102   c  and  102   d  in the opposite Z-direction. The Coriolis forces cause the guided mass systems  500   a ,  800 , and  500   b  to rotate out-of-plane about the first, second, and third roll-sense axis respectively. The capacitive electrode  112   b  under the proof masses  102   a  and  102   b  and the capacitive electrode  112   a  under the proof masses  102   c  and  102   d  are used to detect the rotation of the guided mass system  1100 . This rotation provides a measure of the angular velocity about the roll-input axis. 
     Angular velocity about the yaw-input axis will cause Coriolis forces to act on the yaw proof-masses  518   a  and  518   b  resulting in motion of the yaw proof-masses  518   a  and  518   b  anti-phase along the Y-direction. The amplitude of the motion of the yaw proof-masses along the Y-direction is proportional to the angular velocity. The capacitive electrodes  522   a  and  522   b  are used to sense the motion of the respective yaw proof masses  518   a  and  518   b  along the Y-direction. 
     The multiple guided mass system  1100  of  FIG. 6 a    can be represented by the spring mass configuration  12  shown in  FIG. 1 . The spring-mass system  12 A is a representation of one of the guided mass systems  500   a  or  500   b , and the spring-mass system  12 B is a representation of the guided mass system  800 . 
     The springs  103   c - 103   f  and  108   c - 108   d  are compliant in y direction and their compliance can be modeled by an equivalent spring as  42 B, which is given in spring mass system configuration  12  in  FIG. 1 . In the guided mass system  500   a , the springs  108   a - 108   b ,  103   g - 103   h  and  520   a - 520   d  can be modeled by the spring  42 A. The coupling spring  302   a  that connects  500   a  and  800  can be modeled as spring  22 . The lever arms  104   c - 104   d  can be modeled as the lever arm  22 B, and the lever arms  104   a - 104   b  can be represented as  22 A. 
     Y direction spring stiffness of the guided mass system  800  is much higher than the y direction spring stiffness of the guided mass system  500   a  or  500   b . The reason is that the springs sets  103   c - 103   d  and  103   e - 103   f  have been equally spread in the guided mass system  800 , and also the springs  652   a  and  652   b  are very stiff in Y direction. 
     By using the same 2nd harmonic motion elimination illustrated by spring-mass configuration  12  of  FIG. 1 , the y direction spring stiffness of the springs  103   c - 103   f ,  108   c - 108   d , and  652   a - 652   b  can be made equal to the sum of the spring stiffness of the coupling spring  302   a  and the springs  108   a - 108   b ,  103   g - 103   h  and  520   a - 520   d . As a result, the net nonlinear motion in y direction of the yaw-proof masses  518   a - 518   b  can be eliminated by the help of the balance of the opposing forces in y direction. As it was mentioned before a folded flexure is used as coupling spring  302   a . The main benefit of using a folded flexure is to increase the y direction translational stiffness of coupling spring  302   a , while maintaining its out-of plane torsional compliance within the given area. Although, a two-fold folded flexure is used in embodiment  1100 , folded flexure with many folds can also be used to increase the y direction translational stiffness. 
       FIG. 6 b    illustrates another embodiment of a tri-axis gyroscope comprising a multiple guided mass system  1110  in accordance with the present invention. Multiple guided mass system is same as multiple guided mass system  1100 , except new coupling springs  303   a  and  303   b  are added in between proof masses  102   a - b  and  102   c - d  respectively. Main benefit of adding springs  303   a  and  303   b  in multiple guided system  1110  is to increase the y direction translational stiffness. Moreover, springs  303   a - b  improves x direction stiffness. As a result, rigidity of multiple guided mass system  1110  during the drive motion increases and proof masses  102   a - b  and  102   c - d  move together in the x direction. 
     Embodiments for modifying a spring mass configuration are disclosed that minimize the effects of unwanted nonlinear motion on a MEMS sensor. The modifications include any or any combination of providing a rigid element between rotating structures of the spring mass configuration, tuning a spring system between the rotating structures and coupling an electrical cancellation system to the rotating structures. In so doing unwanted nonlinear motion such as unwanted 2 nd  harmonic motion is minimized. 
     Although the present invention has been described in accordance with the embodiments shown, one of ordinary skill in the art will readily recognize that there could be variations to the embodiments and those variations would be within the spirit and scope of the present invention. Accordingly, many modifications may be made by one of ordinary skill in the art without departing from the spirit and scope of the present invention.