Configuration to reduce non-linear motion

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 2nd harmonic motion is minimized.

FIELD OF THE INVENTION

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 2ndharmonic 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.

DETAILED DESCRIPTION

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. 1illustrates four different spring-mass configurations10,11,12and13, that could be utilized in a MEMS sensor, respectively. A first spring-mass configuration10includes a spring-mass system10A. The spring mass system10A includes a lever arm20A, a proof mass30A, a linear spring40A, and a hinge50A attached to a stable point60A. The proof mass,30A, in the spring mass system10A has three degrees of freedom. The proof mass30A can rotate by an angle θ about an axis passing from the center of the hinge50A 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 inFIG. 1in detail, hinge50A has a finite translational compliance, and linear spring40A has a finite rotational compliance. If it is assumed that the length of the spring40A is negligible and the length of the lever arm20A is L. The X direction motion of the mass30A is given by the equation:
Xd=Lsin(θ)≈Lθ(Eq-1)
where Xdis the x-direction translation motion of the proof mass30A. Since the motion of the proof mass30A is rotational, there is also Y direction component of the motion of the proof mass30A which can be represented as in the equation given below:

Yd=L⁡(1-cos⁡(θ))≈L⁢θ22(Eq⁢-⁢2)
where Ydis the Y-direction translation motion of the proof-mass.

If the mass30A is driven at a frequency ωdwhich is named as drive frequency, where the drive frequency can be the natural frequency of the spring mass system10A, the governing equation for the rotational drive motion of the mass30A can be given as:
θ=|θ| sin(ωdt)  (Eq-3)
Then X-direction motion of the proof mass30A at the drive frequency can be given as:
Xd≈L|θ| sin(ωdt)  (Eq-4)
Y direction motion of the proof mass30A can be represented by the following equation:

As it can be seen in the equations 4 and 5, the Y direction motion of the mass30A is at two times the drive frequency. This behavior is due to the non-linearity of the rotational movement of the proof mass30A. If the mass is driven in the X direction with the use of a lever arm20A at the drive frequency, there is always a Y direction vibration which is at two times the drive frequency, which is referred to as 2ndHarmonic vibration.

The 2ndHarmonic 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 system10A. To describe the issues with a guided mass configuration10, refer now to the following discussion in conjunction with the accompanying figures.

FIG. 2Aillustrates an embodiment of a single axis gyroscope comprising a guided mass system500. The guided mass system500is disposed in an X-Y plane parallel to a substrate101and comprises a guided mass system100coupled to a yaw proof mass518a. The guided mass system100includes guiding arms104aand104bthat are flexibly coupled via springs108aand108bto the substrate101via at least one anchoring point106a. The two guiding arms104aand104bare flexibly coupled to one proof-mass102avia springs103aand103b. The yaw proof mass518ais flexibly connected to the proof mass102avia yaw-springs520a-520d.

The proof mass102aand yaw proof mass518a, guiding arms104aand104b, anchoring point106a, and springs103a,103b,108a, and108bform a planar four-bar linkage. The springs103a,103b,108a, and108bare compliant in-plane about an axis in the Z-direction so that each guiding arm104aand104bcan rotate in-plane while the proof-mass102atranslates in an X-direction, as shown inFIG. 2B. Yaw-springs520a-520dare stiff in the X-direction such that when the guided mass system100translates in the X-direction, the yaw proof-mass518aalso translates with the proof mass102a.

Electrostatic actuators, such as comb drives109aand109b, are connected to the proof mass102ato drive the guided mass system100. 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 system500can be driven at a drive frequency by a single drive circuit coupled to the actuators109aand109b. The drive frequency can be a resonant frequency of the guided mass system500. When the guided mass system500is driven, the guiding arms104aand104brotate in-plane and the proof-mass102aand yaw proof mass518atranslate 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-mass518ain the Y-direction resulting in motion of the yaw proof-mass518ain the Y-direction. A capacitive electrode522ais used to sense the motion of the yaw proof-mass518ain 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 electrode522a, 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 system500can be simply represented by the spring mass system10A that is shown inFIG. 1. The lever arms104a-104bare similar to the lever arm20A, the springs103a-103b,108a-108band520a-520dof the guided mass system500are compliant in the Y direction. As a result, the spring40A can be a representation of y direction compliance of the springs103a-103b,108a-108band520a-520d. The proof mass102aand the yaw proof-mass518aare attached to the springs103a-103band520a-520d, respectively, as the proof mass30A is attached to the spring40A. Finally, in-plane rotational compliance of the springs108a-108bthat are attached to the anchor106acan be represented by the hinge50A and the stable point60A.

As it is shown inFIG. 2B, the motion of the center of mass of proof mass102ahas a non-linear motion. When the proof mass102aand yaw proof-mass518aare 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 inFIG. 1for the spring-mass configuration10. The motion at two times the drive frequency can also be called the 2ndharmonic motion of the guided mass system500. In the single axis gyroscope shown inFIG. 2A, the 2ndHarmonic motion is sensed by the capacitive electrode522aas an erroneous signal and it may corrupt the readings or saturate the front end electronics.

In certain conditions, guided mass system500can also be used as a dual axis gyroscope. If the springs108aand108bare compliant about a first roll-sense axis in the X-direction then the guiding arms104aand104bcan rotate out-of-plane, whereby out-of-plane rotation of the guiding arms104aand104bcauses the proof mass102aand the yaw proof mass518amove out-of-plane with the guiding arms104aand104b.

While the guided mass system500is 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-mass102aand the yaw proof-mass518ain the Z-direction. The Coriolis force causes the guided mass system500to rotate out-of-plane about the first roll-sense axis. When the guided mass system500rotates out-of-plane, the guiding arms104aand104band the proof mass102aand yaw proof mass518arotate out-of-plane about the first roll-sense axis. The amplitude of the rotation of the guided mass system500is proportional to the angular velocity about the roll-input axis.

A capacitive electrode112aunder the proof mass102ais used to detect the rotation of the guided mass system500about 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 electrode112acould 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 system500ofFIG. 2Acan be modified to eliminate the 2ndharmonic motion by using the methods that are introduced in one or more of the spring mass configurations11,12and13shown inFIG. 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 configuration11is shown inFIG. 1that has components similar to the spring-mass configuration10. Spring mass configuration11includes two spring mass systems11A-11B. Each of the two spring mass systems11A-11B comprise lever arms21A-21B, and a traveling system101A comprising traveling masses31A-31B and connection element21, linear springs41A-41B, hinges51A-51B attached to stable points61A-61B.

The difference between spring-mass configuration11and the spring mass configuration10is connection element21that connects two spring-mass systems11A and11B. In the spring-mass configuration11, while two spring-mass systems11A-11B are operated side by side, they are also connected by the connection element21. Both11A and11B move in the same X direction during the drive operation. But, the Y direction motion of11A and11B are opposing each other. If those two spring-mass systems11A-11B are rigidly connected by the connection element21, then the spring elements41A and41B stretches in opposite directions to accommodate the nonlinear motion due to the rotation of the lever arms21A and21B. As a result of the compensation of the 2ndharmonic motion by the spring elements41A and41B, the net motion on the traveling masses31A and31B in Y direction becomes zero. Consequently, the traveling masses31A and31B can be restricted to move only in the x direction by eliminating the unwanted 2nd harmonic Y direction motion.

Spring mass configuration12includes two spring mass systems12A-12B which comprise lever arms22A-22B, a traveling system101B comprising traveling masses32A-32B and spring element22, linear springs42A-42B, and hinges52A-52B attached to stable points62A-62B. In contrast to spring mass configuration element10, the springs42A and42B have different spring stiffness values. Moreover, an additional component of spring-mass configuration12compared to spring mass configuration10is the spring element22coupled between traveling masses32A and32B. Spring element22is used to eliminate the unwanted 2ndharmonic Y direction motion of the traveling masses32A or32B. Compliance of the spring22can be designed such a way that the 2nd harmonic motion of one of the spring-mass system12B can be used to compensate for the 2ndharmonic motion of the other spring-mass system12A, or vice versa. For example, by ensuring that the spring stiffness the spring42B is equal to the combined stiffness of the spring22and the spring42A, the 2ndharmonic motion of the traveling mass32A can be eliminated due to the balance of the opposing forces as in the spring mass configuration11. In this scenario, traveling mass32B would still have an unwanted 2ndharmonic motion.

A third modification to the spring-mass configuration10is shown as the spring-mass configuration13. Spring mass configuration13includes two spring-mass systems13A-13B which are composed of lever arms23A-23B, and a traveling system1010comprising traveling masses33A-33B, spring element23, transducers73A-73B and74A-74B, linear springs43A-43B, and hinges53A-53B attached to stable points63A-63B.

The additional components of spring-mass configuration13compared to spring mass configuration10are spring element23and transducers73A-73B and74A-74B. By coupling two spring mass systems13A and13B, both of the traveling masses33A and33B can be resonated in the drive direction at a natural drive frequency. Furthermore, by coupling the traveling masses33A and33B using the spring23, the proof masses33A and33B can also resonate in the Y direction at another natural frequency. Transducers73A-73B and74A-74B are used to sense the motion of the traveling masses33A-33B 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 transducers73A-73B and74A-74B can be selected such a way that the 2ndharmonic 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 configuration13, 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 2ndharmonic motion is rejected since the electrodes cancels the opposing (differential) motions in Y direction.

The spring-mass configuration13is given as an example for the electrical cancellation of unwanted 2ndHarmonic 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 configurations11-14described above.

FIG. 3illustrates an embodiment of a single axis gyroscope comprising a guided mass system in accordance with the present invention. The guided mass system600is disposed in an X-Y plane. The guided mass system600includes guiding arms104a,104b,104cand104dthat are flexibly coupled via springs108a,108b,108cand108dto the substrate100via the anchoring points106aand106b. Four guiding arms104a,104b,104cand104dare flexibly coupled to one traveling mass105via springs103a,103b,103cand103d.

Each spring103a-103d,108a-108dis compliant in-plane about an axis in the Z-direction so that each guiding arm104a-104band104c-104dcan rotate anti-phase in the plane while the traveling mass105translates in an X-direction. The yaw proof-masses518aand518bare flexibly connected to the traveling mass105via yaw-springs520a-520dand520e-520h, respectively. The guided mass system600can be driven at a drive frequency by a single drive circuit coupled to the actuators109a-109d. The drive frequency can be a resonant frequency of the guided mass system600. When the guided mass system600is driven, the guiding arms104a-104band104c-104drotate anti-phase in-plane and the traveling-mass105translates in-plane in the X-direction. Yaw-springs520a-520dand520e-520hare stiff in the X-direction such that when the guided mass system is driven, the yaw proof-masses518a-balso translate with the traveling mass105in 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-masses518a-518bin the Y-direction resulting in a common mode motion of the yaw proof-masses518aand518b. The capacitive electrodes522aand522bare used to sense the motion of the yaw proof-masses518aand518bin the Y-direction which provides a measure of the angular velocity about the yaw-input axis.

The configuration shown inFIG. 3can be represented as the spring mass configuration11ofFIG. 1. As in the spring mass configuration11, guided mass system600eliminates the second harmonic motion by combining two guided mass systems by a rigid traveling mass105. Since the motion of the lever arms104a-104band104c-104dare anti-phase with respect to each other, the travelling mass105that is connected to the lever arms104a-104dbalances the opposing 2ndharmonic motion and eliminates the unwanted non-linear component of the drive motion, and the y direction compliance of the spring elements108a-108b,103a-103band108c-108d,103c-103daccommodates the 2ndHarmonic motion by stretching in y direction similar to the spring mass configuration12.

In certain conditions, guided mass system500can also be used as a dual axis gyroscope. If we assume that the springs108a-108band108c-108dare 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 arms104a-104band104c-104dcan rotate anti-phase out-of-plane, whereby out-of-plane rotation of the guiding arms104a-104dcauses the traveling mass105to move out-of-plane with the guiding arms104a-104d.

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 mass105in the Z-direction. The Coriolis force causes the lever arms104a-104band lever arms104c-104drotate anti-phase out-of-plane about the first and second roll-sense axes and the traveling mass105moves in the Z direction. The amplitude of the motion of the roll-travelling mass105is proportional to the angular velocity about the roll-input axis. A capacitive electrode112aunder the traveling mass105is used to detect the motion of the proof-mass. This motion provides a measure of the angular velocity about the roll-input axis.

FIG. 4illustrates a second embodiment of a single axis gyroscope comprising a guided mass system700in accordance with the present invention which minimizes a 2nd Harmonic component of the drive motion.

The guided mass system700comprises two guided mass systems700A and700B, which are same as the guided mass system500. The proof masses102aand102b, consequently two guided mass systems700A and700B, are connected by a coupling spring151. The yaw proof-masses518aand518bare flexibly connected to the proof-masses102aand102b, respectively. The coupling spring151is torsionally compliant about an axis in the X-direction so that the symmetric guided mass systems700A and700B can rotate anti-phase out-of-plane about the first and second roll-sense axes. The coupling spring151is stiff in the Z-direction which prevents the guided mass systems700A and700B from rotating in-phase out-of-plane.

The coupling spring151is stiff in the X-direction such that the proof-mass102aand102bmove together in the X-direction. In this way the two guided mass systems700A and700B are driven together at a drive frequency by a single drive circuit coupled to the actuators109a-109d.

The configuration given inFIG. 4can be represented by the spring mass configuration13given inFIG. 1. As in the spring mass configuration13, two guided mass systems700A and700B are connected by a coupling spring151, so that the proof masses102a-102band518a-518bcan also resonate in the Y direction at a certain natural frequency. Capacitive electrodes522aand522bare used to sense the motion of the proof-masses518aand518bin Y direction, respectively. The sensitive direction of the capacitive electrodes522a-522bcan be selected such a way that the 2ndharmonic motion in the Y direction is rejected but the Coriolis motion in the Y direction is detected.

In the guided mass system700, the proof masses518aand518bmove 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-masses518a-bin the same Y-direction (common mode motion).

Due to the placement of the electrodes522aand522bin the guided mass system700, the capacitance of the electrodes522aand522bchanges in opposite directions while the proof masses518a-518bmove in the same direction.

If the capacitance change on the electrodes is subtracted from each other, the common mode Coriolis response of the proof masses518aand518bis able to be detected.

On the other hand, the 2ndharmonic motions of the proof masses518a-518bin the Y direction are in opposite directions, because the guiding arms104a-104band104c-104dare rotating around opposite directions. Consequently, the 2ndharmonic motion of the proof masses518a-518bwill be cancelled due to the configuration of the electrodes522a-522b.

FIG. 5illustrates another embodiment of a single axis gyroscope comprising a balanced guided mass system1000in accordance with an embodiment of the present invention. The guided mass system1000includes two symmetric guided mass systems900aand900bwhich are connected by a coupling spring302. However, the coupling between the guided mass systems900aand900bdoesn't have to be only a single coupling spring302; the coupling may include various springs and spring-mass systems.

The two symmetric guided mass systems900aand900bare arranged so that the proof-masses102a-102dall move in the X-direction. Hence, the two guided mass systems900aand900bare driven together at a drive frequency by a single drive circuit coupled to the actuators109a-109h.

In the drive motion of the guided mass system1000, the proof-masses102band102cmove together in the same X-direction, since the coupling spring302is stiff in the X-direction. On the other hand, the proof masses102aand102dmove in the opposite X-direction compared to the proof masses102band102c.

Angular velocity about the yaw-input axis will cause Coriolis forces to act on the yaw proof-masses518a-518dresulting in motion of the yaw proof-masses518a-518dalong the Y-direction. The amplitude of the motions of the yaw proof-masses518a-518dis proportional to the angular velocity about the yaw-input axis.

The schematic provided inFIG. 5is a different embodiment of the spring-mass configuration13shown inFIG. 1. The balanced guided mass system1000eliminates the unwanted 2nd harmonic motion of the yaw proof masses518a-518dby electrical cancellation.

Due to the nature of the drive motion explained above, the imparted Coriolis forces on the proof masses518aand518dare in the opposite direction of the imparted Coriolis forces on the proof masses518aand518d. In other words, the Coriolis response motion of the proof masses518band518cvs. the proof masses518aand518dare differential. In order to detect the differential motion effectively within the given electrode placements inFIG. 5, the capacitance change of the electrodes522aand522bdue to the Coriolis motion of the proof masses518a-518bcan be summed up. The capacitance change of the electrodes522cand522dcan also be summed up. Moreover, the detected capacitance change from the electrode pair522c-522dcan be subtracted from the detected capacitance change of the electrode pair522a-522b. As a result of the electrode configuration, the Coriolis motion is detected.

The 2nd harmonic motion direction of the each proof mass518a-518dis illustrated by the arrows541a-541dwhich are shown side by side by the arrows540a-540dthat are showing the Coriolis force direction of the proof masses518a-518d. The given arrow configuration shows that the Coriolis force and the 2nd harmonic motion are in the same direction for the guided mass system900bbut they are in the opposite directions for the guided mass system900a. As a result, the 2nd harmonic motion will be cancelled due to the electrode scheme given above.

The balanced guided mass system1000can also be used as a dual axis gyroscope with a condition where the symmetric guided mass system900ais able to rotate out-of-plane about a first roll-sense axis and the symmetric guided mass system900bis able to rotate out-of-plane about a second roll-sense axis in-plane and parallel to the first roll-sense axis.

The coupling spring302is connected to proof-masses102band102c. The coupling spring302is torsionally compliant about an axis in the X-direction so that the symmetric guided mass systems900aand900bcan rotate anti-phase out-of-plane about the first and second roll-sense axes. The coupling spring302is stiff in the Z-direction which prevents the symmetric guided mass systems900aand900bfrom rotating in-phase out-of-plane.

Angular velocity about the roll-input axis will cause Coriolis forces to act on the proof-masses102a-102din the Z-direction. The Coriolis forces cause the symmetric guided mass systems900aand900bto rotate anti-phase out-of-plane about the first and second roll-sense axes. The amplitudes of the rotations of the symmetric guided mass systems900aand900bare proportional to the angular velocity. Capacitive electrodes112a-112cunder the proof masses102a-102dare used to detect the rotations of the symmetric guided mass systems900aand900b.

FIG. 6aillustrates an embodiment of a tri-axis gyroscope comprising a multiple guided mass system1100in accordance with the present invention. The multiple guided mass system1100includes two guided mass systems500aand500bcoupled to a guided mass system800by coupling springs302aand302b, respectively.

The guided mass systems500a,500band800are arranged so that yaw proof-masses518aand518bcoupled to roll proof masses102a-102dall move anti-phase in the X-direction, the pitch proof-mass650arotates about an axis in the Z-direction. The guided mass system500arotates out-of-plane about a first roll-sense axis. The symmetric guided mass system800rotates out-of-plane about a second roll-sense axis parallel to the first roll-sense axis. The guided mass system500brotates out-of-plane about a third roll-sense axis parallel to the first and second roll-sense axes. The first coupling spring302ais connected to proof-masses102aand102b. The coupling spring302ais stiff in the X-direction such that proof-mass102aand102bmove together in the X-direction. The second coupling spring302bis connected to proof-masses102cand102d. The coupling spring302bis stiff in the X-direction such that proof-mass102cand102dmove together in the X-direction. In this way the guided mass systems500a,500b, and800are driven together at a drive frequency by a single drive circuit coupled to the actuators109a-109h. Moreover, as it can be seen inFIG. 6a, folded flexures are used as coupling springs302a-b.

The coupling spring302ais torsionally compliant about an axis in the X-direction so that the guided mass systems500aand800can rotate out-of-plane about the first and second roll-sense axes anti-phase. The coupling spring302aprevents the symmetric guided mass systems500aand800from rotating out-of-plane in-phase.

The coupling spring302bis also torsionally compliant about an axis in the X-direction so that the guided mass systems500band800can rotate out-of-plane about the second and third roll-sense axes anti-phase. The coupling spring302bprevents the symmetric guided mass systems500band800from rotating out-of-plane in-phase.

Angular velocity about the pitch-input axis will cause Coriolis forces to act on the pitch proof-mass650aresulting in a torque that rotates the pitch proof-mass650aabout the pitch-sense axis. The amplitude of the rotation of the pitch proof-mass650ais proportional to the angular velocity about the pitch-input axis. The capacitive electrodes660aand660bare disposed on opposite sides along the X-direction under the pitch proof-mass650aand 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-masses102aand102bin a Z-direction and on proof-masses102cand102din the opposite Z-direction. The Coriolis forces cause the guided mass systems500a,800, and500bto rotate out-of-plane about the first, second, and third roll-sense axis respectively. The capacitive electrode112bunder the proof masses102aand102band the capacitive electrode112aunder the proof masses102cand102dare used to detect the rotation of the guided mass system1100. 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-masses518aand518bresulting in motion of the yaw proof-masses518aand518banti-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 electrodes522aand522bare used to sense the motion of the respective yaw proof masses518aand518balong the Y-direction.

The multiple guided mass system1100ofFIG. 6acan be represented by the spring mass configuration12shown inFIG. 1. The spring-mass system12A is a representation of one of the guided mass systems500aor500b, and the spring-mass system12B is a representation of the guided mass system800.

The springs103c-103fand108c-108dare compliant in y direction and their compliance can be modeled by an equivalent spring as42B, which is given in spring mass system configuration12inFIG. 1. In the guided mass system500a, the springs108a-108b,103g-103hand520a-520dcan be modeled by the spring42A. The coupling spring302athat connects500aand800can be modeled as spring22. The lever arms104c-104dcan be modeled as the lever arm22B, and the lever arms104a-104bcan be represented as22A.

Y direction spring stiffness of the guided mass system800is much higher than the y direction spring stiffness of the guided mass system500aor500b. The reason is that the springs sets103c-103dand103e-103fhave been equally spread in the guided mass system800, and also the springs652aand652bare very stiff in Y direction.

By using the same 2nd harmonic motion elimination illustrated by spring-mass configuration12ofFIG. 1, the y direction spring stiffness of the springs103c-103f,108c-108d, and652a-652bcan be made equal to the sum of the spring stiffness of the coupling spring302aand the springs108a-108b,103g-103hand520a-520d. As a result, the net nonlinear motion in y direction of the yaw-proof masses518a-518bcan 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 spring302a. The main benefit of using a folded flexure is to increase the y direction translational stiffness of coupling spring302a, while maintaining its out-of plane torsional compliance within the given area. Although, a two-fold folded flexure is used in embodiment1100, folded flexure with many folds can also be used to increase the y direction translational stiffness.

FIG. 6billustrates another embodiment of a tri-axis gyroscope comprising a multiple guided mass system1110in accordance with the present invention. Multiple guided mass system is same as multiple guided mass system1100, except new coupling springs303aand303bare added in between proof masses102a-band102c-drespectively. Main benefit of adding springs303aand303bin multiple guided system1110is to increase the y direction translational stiffness. Moreover, springs303a-bimproves x direction stiffness. As a result, rigidity of multiple guided mass system1110during the drive motion increases and proof masses102a-band102c-dmove 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 2ndharmonic motion is minimized.