Abstract: An angular velocity sensor including a drive extension mode. In one aspect, an angular rate sensor includes a base and at least three masses disposed substantially in a plane parallel to the base, the masses having a center of mass. At least one actuator drives the masses in an extension mode, such that in the extension mode the masses move in the plane simultaneously away or simultaneously towards the center of mass. At least one transducer senses at least one Coriolis force resulting from motion of the masses and angular velocity about at least one input axis of the sensor. Additional embodiments can include a linkage that constrains the masses to move in the extension mode.

Abstract: A micro-electro-mechanical device with a closed feed-back damping loop is provided. Displacement in the mechanical resonator is opposed with a damping force determined by the closed feed-back loop that comprises a filter with a peaked frequency response, and associated phase adjustment. An oscillation-free configuration that allows high signal amplification is achieved.

Abstract: A physical quantity sensor includes a base on which an IC electrically connected to a gyro element is arranged and a wire group arranged on the base. The base includes a first outer edge and a second outer edge that crosses the first outer edge. The wire group includes a CLK wire arranged along the first outer edge and including an internal terminal connected to the IC and an S1 wire arranged along the second outer edge and including an internal terminal connected to the IC. A detection signal of the gyro element is input to the IC via the S1 wire.

Abstract: A functional element includes a driving portion, a first mass portion which is vibrated along the first direction, a first connection portion which is connected to the first mass portion and can perform a first movement in which the first connection portion contracts and extends along the first direction, a second connection portion which is connected to the first connection portion, extends in a second direction intersecting the first direction, and can perform a second movement in which the second connection portion rotates with the second direction as the axis, and a second mass portion which is connected to the second connection portion.

Abstract: A gravity gradiometer having at least three differential accelerometers with a low response to linear accelerations and at least six angular accelerometers that give it the capability of measuring angular rates by integrating the angular accelerations. Both types of accelerometers are based on a compliant mechanism with very low and adjustable stiffness that is achieved by using flexures under compressive load that contribute a negative stiffness to the total elastic response of the mechanism. Both types of accelerometers are operated in a servo-compensation feedback mode so that at no time is the mechanism far from its equilibrium position.

Abstract: An amplifier system has an amplifier for amplifying a plurality of input signals from a plurality of different channels, and a plurality of demodulators each operatively coupled with the amplifier for receiving amplified input signals from the amplifier. Each demodulator is configured to demodulate a single amplified input channel signal from a single channel of the plurality of different channels. The system thus also has a plurality of filters, coupled with each of the demodulators, for mitigating the noise.

Abstract: A precision gyroscope includes a gyroscope, means for receiving an external clock reference, and circuitry coupled to the means for receiving the external clock reference and adapted for stabilizing a temperature and a frequency of the gyroscope.

Abstract: Disclosed herein is an inertial sensor control module. The inertial sensor control module according to a preferred embodiment of the present invention includes: an inertial sensor including a driving mass, a driving unit driving the driving mass of the inertial sensor according to a control signal to the inertial sensor, a control unit connected to the driving unit and generating the control signal to transfer the generated control signal to the driving unit, and a sensing unit connected between the inertial sensor and the control unit and detecting information about whether the driving mass of the inertial sensor is in a stabilized state or information about an inertial force of the inertial sensor to transfer the detected information to the outside or the control unit.

Abstract: An electronic device includes a base body, a functional element that is placed on the base body, and a lid body, formed from silicon, that is placed over the base body so as to cover the functional element. A hole portion and a sealing member that closes the hole portion are disposed in the lid body, in the hole portion, the area of a second opening disposed on a side opposite to a first opening is larger than the area of the first opening disposed on the base body side, and the ratio of the volume of the sealing member to the volume of the hole portion is equal to or higher than 35% and is equal to or lower than 87%.

Abstract: Disclosed herein is an angular velocity sensor including: first and second mass bodies; a first frame provided at an outer side of the first and second mass bodies; a first flexible part connecting the first and second mass bodies to the first frame in a Y axis direction, respectively; a second flexible part connecting the first and second mass bodies to the first frame in an X axis direction, respectively; a second frame provided at an outer side of the first frame; a third flexible part connecting the first and second frames to each other in the X axis direction; and a fourth flexible part connecting the first and second frames to each other in the Y axis direction, wherein the first frame has a thickness in a Z axis direction thinner than that of the second frame.

Abstract: A gyro sensor according to the invention includes a first mass portion including a first detection portion, a second mass portion including a second detection portion, first drive portions vibrating the first mass portion in a direction of a first axis, and a force conversion portion fixed to an anchor portion. The first mass portion and the second mass portion are connected with the force conversion portion. The force conversion portion is displaced with the anchor portion as an axis, and vibrates the second mass portion in a direction of a second axis crossing the first axis in a plane view.

Abstract: A placing member is configured to be supported from an outside by a terminal electrically connected to a terminal electrode, and an X-axis-direction extended portion, a Y-axis-direction extended portion, and a Z-axis-direction extended portion are provided in the terminal. This configuration provides an angular velocity sensor, in which a problem such that Y-axis-direction and Z-axis-direction vibrations applied from the outside cannot be damped is eliminated, and all the vibrations in three axis directions can be damped.

Abstract: A microelectromechanical system (MEMS) resonator, a sensor having the same and a method for manufacturing the MEMS resonator are provided. The MEMS resonator includes a base substrate of the MEMS resonator, the base substrate having a recess portion recessed into one surface thereof, an oscillator mounted at the base substrate and at least partially overlapping the recess portion to be vibrated using an empty space of the recess portion, and a wire connected to the oscillator and the base substrate, respectively, to control a natural frequency of the MEMS resonator by supporting at least part of the oscillator. Accordingly, the natural frequency of the resonator can be easily controlled.

Abstract: Disclosed herein are an apparatus and a method for driving a gyroscope sensor. The apparatus for driving a gyroscope sensor includes: a detection module; a phase conversion module; an inversion module; a switch module selecting and outputting any one of the driving voltage and the inversion voltage for each axis; a driving module supplying driving voltage of a driving axis at the time of the driving and supplying inversion voltage at the time of stopping the driving; and a control unit passing the driving voltage of the driving axis by controlling the switch module according to a switching control signal at the time of the driving and passing the inversion voltage of each axis by controlling the switch module according to the switching control signal at the time of stopping the driving.

Abstract: A method of detecting motion provides a resonator having a mass, moves the mass in a translational mode, and actuates the mass in a given bulk mode. The mass moves in the translational and given bulk modes at substantially the same time and, accordingly, the resonator is configured to detect linear and rotational movement when moving and actuating the mass in the translational and given bulk modes. The method produces one or more movement signals representing the detected linear and rotational movement.

Abstract: An inertial force sensor includes a detecting device which detects an inertial force, the detecting device having a first orthogonal arm and a supporting portion, the first orthogonal arm having a first arm and a second arm fixed in a substantially orthogonal direction, and the supporting portion supporting the first arm. The second arm has a folding portion. In this configuration, there is provided a small inertial force sensor which realizes detection of a plurality of different inertial forces and detection of inertial forces of a plurality of detection axes.

Abstract: An inertia force sensor that shortens a time from power activation until inertia force can be detected includes an oscillator, an oscillation circuit unit, and a detection circuit unit. The oscillation circuit unit functions as a closed loop self oscillation circuit with the oscillator as a resonant element, and includes a CV conversion circuit converting a monitor signal based on electrostatic capacitance according to an oscillating state of oscillator into a monitor signal based on a voltage corresponding to an amount in change of the electrostatic capacitance, and an automatic gain control circuit controlling gain based on the monitor signal converted at the CV conversion circuit to generate a driving signal, and supplying the driving signal to the oscillator. The CV conversion circuit includes an amplifier that amplifies a monitor signal with an amplification factor for a predetermined period after power activation.

Abstract: A microelectromechanical gyroscope, includes: a supporting body; a first movable mass and a second movable mass, which are oscillatable according to a first driving axis and tiltable about respective a first and second sensing axes and are symmetrically arranged with respect to a center of symmetry; first sensing electrodes and a second sensing electrodes associated with the first and second movable masses and arranged on the supporting body symmetrically with respect to the first and second sensing axis, the first and second movable masses being capacitively coupled to the respective first sensing electrode and to the respective second sensing electrode, a bridge element elastically coupled to respective inner ends of the first movable mass and of the second movable mass and coupled to the supporting body so as to be tiltable about an axis transverse to the first driving axis.

Abstract: An angular velocity sensor includes fixing units, a base portion, beam portions that support the base portion with respect to the fixing units, driving vibrating arms connected to the base portion, and detection vibrating arms connected to the base portion. When a width of a detection frequency band is set to f1 [Hz], a resonance frequency in a rotational vibration mode in which the base portion rotates and vibrates around a detection axis with respect to the fixing units in association with the deformation of the beam portions is set to f2 [Hz], and a detuning frequency is set to f3 [Hz], the relation of f1<f2<f3 is satisfied.

Abstract: In an angular velocity sensor, when a width of a detection frequency band is set to f1 [Hz], a resonance frequency in a first rotational vibration mode in which a base portion rotates and vibrates around a detection axis with respect to fixing units in association with the deformation of beam portions is set to f2 [Hz], a detuning frequency is set to f3 [Hz], and a resonance frequency in a second rotational vibration mode, having a phase opposite to that of the first rotational vibration mode, in which the base portion rotates and vibrates around the detection axis with respect to the fixing units in association with the deformation of the beam portions is set to f4, a relation of f1<f2<f3<f4 or a relation of f1<f2<f4<f3 is satisfied.

Abstract: The present disclosure relates to nanoresonator oscillators or NEMS (nanoelectromechanical system) oscillators. A circuit for measuring the oscillation frequency of a resonator is provided, comprising a first phase-locked feedback loop locking the frequency of a controlled oscillator at the resonant frequency of the resonator, this first loop comprising a first phase comparator. Furthermore, a second feedback loop is provided which searches for and stores the loop phase shift introduced by the resonator and its amplification circuit when they are locked at resonance by the first loop. The first and the second loops operate during a calibration phase. A third self-oscillation loop is set up during an operation phase. It directly links the output of the controllable phase shifter to the input of the resonator. The phase shifter receives the phase-shift control stored by the second loop.

Abstract: A MEMS device comprises a proof mass suspended above a substrate, one or more driving combs, and one or more sensing combs. During operation, a DC actuating potential in series with an AC modulation potential is applied to the proof mass, and an AC actuating potential is applied to the one or more driving combs such that the proof mass moves in an oscillatory manner. An inertial sensing system further comprises a sensing element configured to detect a rotation information coupled with an AC signal and an acceleration information coupled with a DC signal.

Abstract: In a high-performance interface circuit for micro-electromechanical (MEMS) inertial sensors, an excitation signal (used to detect capacitance variation) is used to control the value of an actuation signal bit stream to allow the dynamic range of both actuation and detection paths to be maximized and to prevent folding of high frequency components of the actuation bit stream due to mixing with the excitation signal. In another aspect, the effects of coupling between actuation signals and detection signals may be overcome by performing a disable/reset of at least one of and preferably both of the detection circuitry and the MEMS detection electrodes during actuation signal transitions. In a still further aspect, to get a demodulated signal to have a low DC component, fine phase adjustment may be achieved by configuring filters within the sense and drive paths to have slightly different center frequencies and hence slightly different delays.

Abstract: In an angular velocity sensor, an upper electrode of a first piezoelectric element and a lower electrode of a second piezoelectric element are connected to an input terminal of a first Q/V conversion circuit, and a lower electrode of the first piezoelectric element and an upper electrode of the second piezoelectric element are connected to an input terminal of a second Q/V conversion circuit. Thus, vibration noise components of the quantities of charge generated at the first and second piezoelectric elements are cancelled out, and Coriolis components of the quantities of charge generated at the first and second piezoelectric elements are added, whereby only the Coriolis components are extracted.

Abstract: A high-Q, mode-matched, vibratory tuning fork based MEMS device, capable of sensing rotational and translational motion around three axes, and processes of fabrication are disclosed herein. In one embodiment, a MEMS device has first and second proof masses actuated along a first axis, and a third and fourth proof masses actuated along a second orthogonal axis. Each of the proof masses includes an inner mass mechanically coupled to an outer frame. A plurality of electrodes sense rotational or translational motion along the three orthogonal axes.

Abstract: An oscillation type inertia force sensor includes an oscillator, an oscillation circuit unit, and a detection circuit unit. The oscillation circuit unit functions as a self oscillation circuit of a closed loop with the oscillator as a resonant element, and includes an AGC circuit. The AGC circuit includes a VGA circuit, a comparison circuit comparing a predetermined reference voltage with a voltage of the monitor signal to output a control signal based on the compared result, and a pulse width modulation circuit modulating the control signal to a pulse width modulation signal. Based on the pulse width modulation signal, the driving signal is modulated with the output of the VGA circuit switched between an ON state and OFF state to control the degree of the amplification factor of the VGA circuit.

Abstract: A yaw-rate sensor for determining a Coriolis force includes a semiconductor substrate, a mass body mounted so it is movable over the semiconductor substrate, a drive unit for setting the mass body into an oscillating movement, and a detection unit for determining a deflection of the mass body which is caused by the Coriolis force. The detection unit includes a piezoresistive element, whose electrical resistance is a function of the deformation of the piezoresistive element.

Abstract: Disclosed herein is an angular velocity sensor, including: a mass body part; an internal frame supporting the mass body part; a first flexible part each connecting the mass body part to the internal frame; a second flexible part each connecting the mass body part to the internal frame; an external frame supporting the internal frame; a third flexible part connecting the internal frame and the external frame to each other; and a fourth flexible part connecting the internal frame and the external frame to each other, wherein the internal frame, the second flexible part, and the fourth flexible part have an oxide layer formed thereon.

Abstract: Provided is an angular velocity sensor including a plurality of angular velocity detection units each outputting a different detection result, and including a common driving circuit to drive the angular velocity detection units. The angular velocity detection units of the angular velocity sensor of the present invention are configured to have different driving amplitudes when being driven by a driving signal at the same frequency.

Abstract: A micro-mechanical resonator is provided. The micro-mechanical resonator comprises two masses coupled in the direction of a common axis by a spring structure. The spring structure comprises a spring that couples at least a first bar connected to the masses and a second bar extending in the motion axis direction, said spring being arranged to bend in a direction perpendicular to the motion direction of the motion axis. A micro-mechanical resonator matrix, a sensor and a navigation device are also provided.

Abstract: A gyroscope having a vibrating structure, produced by micromachining in a thin planar wafer, the gyroscope including two symmetrical moving assemblies that are coupled by a coupling structure connecting the two assemblies so as to allow mechanical vibration energy to be transferred between them, each moving assembly including a first moving element connected to the coupling structure and able to vibrate with two degrees of freedom in orthogonal directions Ox and Oy of the plane of the wafer, and a second moving element adjacent the first moving element, capable of vibrating only in the Oy direction and connected to the first moving element via linkage element, wherein the linkage element allow the transmission, in phase opposition, to the second moving element of the vibration movement of the first moving element in the Oy direction.

Abstract: Method of angular measurement by means of a sensor comprising an axisymmetric resonator associated with means for setting the resonator into vibration and with means for detecting an orientation of the vibration with respect to a reference frame of the sensor, comprising the steps of applying a precession control so as to slave an orientation of the vibration to an angular setpoint value and of determining an angular measurement on the basis of the precession control. The method comprises a phase of modulating the angular setpoint value in such a way that the said setpoint value uniformly sweeps an angular span of ? radians and that a temporal derivative of the setpoint is deducted from the precession control prior to the determination of the angular measurement.

Abstract: A yaw rate sensor is described which includes a drive device, at least one Coriolis element, and a detection device having at least two detection elements which are coupled to one another with the aid of a coupling device, the drive device being connected to the Coriolis element for driving a vibration of the Coriolis element, and an additional coupling device which is connected to the detection device and to the Coriolis element for coupling a deflection in the plane of vibration of the Coriolis element to the detection device in a direction orthogonal to the vibration.

Abstract: A gyroscope device and method of operation therefor. The gyroscope device can include a power input, a charge pump portion coupled to the power input, a selection mechanism, a switching mechanism, an oscillator driving mechanism coupled to the switching mechanism, and an oscillator coupled to the charge pump portion and to the oscillator driving mechanism. The method of operation can include providing a first or second selection signal from a selection mechanism associated with the outputting of a DC input power or DC output power from a switching mechanism, respectively. These signals, along with an oscillator driving signal from an oscillator driving mechanism, can be used to initiate and maintain oscillation of an oscillator at a steady-state frequency within a predetermined range of frequencies.

Abstract: A digital angular rate sensor system based on frequency modulation (FM) of the rotation rate. The new approach relies on tracking of the resonant frequencies of two high-Q mechanical modes of vibration in a MEMS vibratory gyroscope to produce an inherently digital measurement of the input angular rate. The disclosed system is enabled by a combination of a MEMS vibratory high-Q gyroscope and a new signal processing scheme which takes advantage of a previously ignored gyroscope dynamics effect. The FM nature of the system eliminates noise versus bandwidth and resolution versus dynamic range tradeoffs of conventional vibratory rate gyroscopes. The FM approach allows achieving superior signal-to-noise-ratio through the use of ultra-high Q (1 million) mechanical structure without limiting the measurement bandwidth. Stability of 1e-9 can be achieved in the FM system, providing a 1000 times improvement over the state-of-the-art conventional AM gyroscopes with capacitive pick-off.

Abstract: A vibrating gyroscope has a base and a resonator. The resonator includes a body of generally cylindrical shape terminating in a face. The resonator is capable of vibrating according to a first vibration mode having antinodes distributed on n axes, and a second vibration mode having antinodes distributed on n other axes. The face of the resonator has two piezoelectric assemblies on each axis of the first and of the second vibration modes. Each piezoelectric assembly has at least one piezoelectric element capable of exciting the resonator in vibration and at least one piezoelectric element capable of detecting vibrations of the resonator at the same time.

Abstract: An angular velocity sensor includes a support body, a retaining portion connected to the support body, first to fourth weights, first to fourth arms, a drive unit for driving the first to fourth arms, and a monitor unit for detecting displacements of the first to fourth arms. An X-axis, a Y-axis, and a Z-axis that are perpendicular to each other are defined. The detector unit is symmetrical with respect to both an axis parallel to the X-axis and an axis parallel to the Y-axis. This angular velocity sensor can cancel an undesired signal caused by external disturbances, such as acceleration or impact, thus detecting an angular velocity accurately.

Abstract: An actuator includes a multi-layer part having a multilayered piezoelectric part comprising a plurality of piezoelectric bodies and an electrode part connected to the multilayered piezoelectric part, and a support part displaceably supporting the multi-layer part. The multilayered piezoelectric part is polled in the same direction. One of the piezoelectric bodies expands or contracts in an opposite direction to another piezoelectric body.

Abstract: A microelectromechanical gyroscope structure that comprises a seismic mass, a body element, and a spring structure suspending the seismic mass to the body element. In primary oscillation at least part of the seismic mass oscillates in out-of-plane direction. A first conductor is arranged to move with the seismic mass, and a second conductor is attached to the body element. The conductors include adjacent surfaces that extend in the first direction and the third direction. A voltage element is arranged to create between the first surface and the second surface a potential difference and thereby induce an electrostatic force in the second direction and modulated by the primary oscillation of the seismic mass.

Abstract: A gyro sensor according to the invention includes a driving portion that includes a driving support portion connected to a driving spring portion and a detecting portion that includes a detecting support portion connected to the driving support portion with the detecting spring portion interposed. The driving support portion is configured to vibrate in a first axis (X-axis) direction, and the detecting support portion is configured to be displaced in a second axis (Y-axis) direction orthogonal to the first axis (x-axis). When the resonant frequency of the driving portion is f1, the resonant frequency of the detecting portion is f2, the width of the driving spring portion is w1, and the width of the detecting spring portion is w2, Expression (1) below is satisfied. 0.87(f2/f1)?(w2/w1)?1.13(f2/f1)??(1) (where, w1?w2 and f1?f2).

Abstract: Disclosed herein is an inertial sensor. The inertial sensor includes a sensing unit and a driving-mass-position initialization module. The sensing unit includes a driving mass, a flexible board unit which displaceably supports the driving mass, and a support which supports the flexible board unit to allow the driving mass to move in a suspended state. The flexible board unit has driving electrodes which move the driving mass, and sensing electrodes which sense the movement of the driving mass. The driving-mass-position initialization module includes a position initialization member which reciprocates to initialize the position of the driving mass, and a coil unit which surrounds the position initialization member. An initialization-member-receiving depression is formed in the driving mass. The shape of the initialization-member-receiving depression corresponds to that of the position initialization member.

Abstract: A piezoelectric thin film structure includes a substrate, a silicon oxide film disposed on the substrate, a first aluminum oxide film disposed on the silicon oxide film, a lower electrode layer disposed on the first aluminum oxide film, a piezoelectric film layer disposed on the lower electrode layer, and an upper electrode layer disposed on the piezoelectric film layer.

Abstract: Disclosed herein are an apparatus and a method for driving an inertial sensor. The apparatus for driving an inertial sensor includes a detection unit that detects first acceleration detection voltage and detects angular velocity detection voltage when a wake up signal is input; a wake up signal generation unit that generates the wake up signal when the total of acceleration detection voltage is larger than predetermined voltage; a phase conversion unit that generates driving voltage and inversion driving voltage of the corresponding axis; a driving unit that vibrates the inertial sensor; and a control unit that performs a control to wake up the detection unit, the phase conversion unit, and the driving unit or convert them into a sleep mode according to a control signal, whereby power consumption can be minimized in an apparatus requiring low power like mobile environment.

Abstract: A resonance device includes a base, a mass, a plurality of elastic portions and at least one end surface. The mass has at least one end surface. The elastic portions are connected between the mass and the base, in which the mass is adapted to resonate in a first direction such that the elastic portions are elastically deformed. The block portion is disposed at the base and extends towards the end surface to be aligned to the end surface, in which the gap between the base and the end surface in the first direction is greater than the gap between the block portion and the end surface in the first direction, and the block portion is adapted to block the end surface to limit the moving range of the mass.

Abstract: A microelectromechanical gyroscope that comprises two seismic masses suspended to form a plane of masses. The seismic masses are excited into rotary oscillation about a common primary axis that is in the plane of masses. Detected angular motion causes a rotary oscillation of the first seismic mass about a first detection axis, and of the second seismic mass about a second detection axis. The detection axes are perpendicular to the plane of masses and separated by a non-zero distance.

Abstract: A movable device including a base, a mass, a plurality of elastic portions and at least one block structure is provided. The mass has a plurality of side surfaces. The elastic portions are connected to the side surfaces respectively and connected to the base, where the mass is adapted to move such that the elastic portions are elastically deformed. The block structure is disposed at the base and aligned to at least one of the side surfaces, wherein the block structure is adapted to block the corresponding side surface to limit a moving range of the mass.

Abstract: A sensor is disclosed. The sensor includes a substrate and at least two proof masses. The sensor also includes a flexible coupling between the at least two proof masses and the substrate. The at least two coupling proof masses move in an anti-phase direction normal to a plane of the substrate in response to acceleration.

Abstract: A piezoelectric substrate includes vibrating arms, a base portion to which one end portion of each vibrating arm is connected, spindle portions formed in the other end portion of each vibrating arm, formed to have a large width, and having first groove portions formed therein, and second groove portions that are formed along the resonator center line of each vibrating arm, and flexure-torsional combined resonator is excited. A piezoelectric resonator element has flexural resonator of flexure-torsional combined resonator that is excited as its principal resonator and sets the cutting angle of the piezoelectric substrate, the widths and the depths of the first groove portion and the second groove portion, and the thickness of the vibrating arm such that the frequency-temperature characteristics represent third-order characteristics with respect to the temperature.

Abstract: A gyroscope includes a first drive mass driven in a first drive motion along a first axis, the first drive motion generating a first sense motion of a first sense mass in response to rotation of the gyroscope. The gyroscope further includes a second drive mass driven in a second drive motion along a second axis that is transverse to the first axis. The second drive motion generates a second sense motion of a second sense mass in response to rotation of the gyroscope. A drive spring system interconnects the two drive masses to couple the first and second drive motions so that a single drive mode can be implemented. The sense motion of each sense mass is along a third axis, where the third axis is transverse to the other axes. The sense motion is translational motion such the sense masses remain parallel to the surface of the substrate.

Abstract: A microelectromechanical gyroscope having a microstructure that includes a first mass and a second mass, wherein the first mass is oscillatable according to a first axis and the second mass is constrained to the first mass so as to be drawn along by the first mass according to the first axis and to oscillate according to a second axis, in response to a rotation of the microstructure, a driving device coupled to the microstructure to maintain the first mass in oscillation at the driving frequency, and a reading device that detects displacements of the second mass according to the second axis. The gyroscope is provided with a self-test actuation system coupled to the second mass for applying an electrostatic force at the driving frequency so as to move the second mass according to the second axis.