A5-6

PROCEEDINGS OF THE 21ST SENSOR SYMPOSIUM,2004.pp.385〜390

Development of 6-axis Motion Sensors Using Piezoelectric Elements
Kazuhiro Okada, Tetsuya Kakutani, Hiromichi Itano, Yoshiyuki Matsu, Susumu Sugiyama*Wacoh Corporation
4-244-1, sakuragi-cho, ohmiya-ku, Saitama-shi, Saitama 330-0854, Japan*Ritsumeikan University
1-1-1, Noji-higashi, Kusatsu-shi, Shiga 525-8577, Japan

Abstract
In the field of acceleration sensors, 3-axis acceleration sensors that detect acceleration in 3-dimensional space have already beencommercialized, and also in the field of angular velocity sensors, piezoelectric type 2-axis angular velocity sensors have been developed.
By applying such piezoelectric type 2-axis angular velocity sensors, 3-axis angular velocity can be detected with the oscillator’s velocity
components in the directions of two axes, and the detection components of Coriolis force produced by angular velocity in the directionsof two axes. By using this principle, we have succeeded in developing a 3-axis angular velocity sensor (1) that detects 3-axis angularvelocity with one detecting element, which was announced at this symposium last year. By applying the 3-axis angular velocity sensor,acceleration and angular velocity can be discriminated with use of the difference in frequency between the force produced by accelerationand the Coriolis force produced in synchronization with the oscillator’s drive frequency. With this, we have succeeded in developing a6-axis motion sensor that detects 3-axis acceleration and 3-axis angular velocity with one detecting element. This report details theconstruction, detection principle, and detection circuit, as well as the performance, such as sensitivity, cross-axis sensitivity, and linearityof the 6-axis motion sensor using a piezoelectric element, and furthermore the influence of acceleration on angular velocity
characteristics.
Keywords: 6-axis, motion sensor, angular velocity, piezoelectric, Coriolis’ force.
few 2-axis angular velocity sensors have been marketed. The
authors reported on 3-axis angular velocity sensors using
piezoelectric elements at this symposium last year. Recently,
demands for motion sensors that detect acceleration andangular velocity simultaneously have increased in theautomobile market in particular. We have conducted research of6-axis motion sensors (5), (6) to meet such demands. We wish toreport on the 6-axis motion sensor using a piezoelectric element
we have developed recently.

1 Introduction
Operation of objects in 3-dimensional space can beexpressed by parallel motion and rotational motion. Parallel
motion can be expressed by physical quantities, such asdistance, velocity, and acceleration, while rotational motion canbe expressed by the physical quantities of an angle, angularvelocity, and angular acceleration. Thus far, for detection of thesix physical quantities of distance, velocity and acceleration,
which represent parallel motion, and angle, angular velocity
and angular acceleration, which represent rotational motion,
only acceleration sensors and angular velocity sensors havebeen operational in use of micromachining technologies andceramic technologies. As a matter of course, acceleration andangular velocity are important physical quantities in detecting
the motion of objects in 3-dimensional space. In the field ofacceleration sensors, 3-axis acceleration sensors (2)-(4) of thepiezoresistance type, capacitance type, and piezoelectric typehave already been developed, and marketed by many
companies. However, in the field of angular velocity sensors,
1-axis angular velocity sensors are predominant, though only a2 Detection principle of the 6-axis motion sensor
The 6-axis motion sensor detects 3-axis acceleration and3-axis angular velocity with one detecting element. Here, thedetection principles of 3-axis acceleration and 3-axis angularvelocity are explained.
2-1 Detection principle of 3-axis acceleration
The construction of the 6-axis motion sensor is shown in Fig.
1. The piezoelectric element substrate is bonded to the top385

face of the diaphragm made of elinvar, and the oscillator isjoined to the back. The node point of the diaphragm issupported, and fixed to the package. Nine split electrodes areformed on the top face of the piezoelectric ceramic substrate as
shown in Fig. 2. When acceleration acts on the oscillator, force(F=ma) is exerted on the oscillator, and the diaphragm isdeformed. When acceleration in the X-axis direction acts, thediaphragm is deformed as shown in Fig. 3-1, and also when
acceleration in the Z-axis direction acts, it is deformed asshown in Fig. 3-2. With this deformation, charge is producedon the electrodes on the piezoelectric element shown in Fig. 2
as shown in Table 1. By considering the presence or absence
and the sign of this charge, 3-axis acceleration can be detected.

Piezoelectricelement

FxFig. 3-1. Deformation by X-axis direction acts

FzElectrodeFig. 3-2. Deformation by Z-axis direction acts
Table 1. The electric charge produced on the electrodes
ElinvarOscillator

Fig. 1. Cross-section of the 6-axis motion sensor

x1x2

y1y2

X1X2Y1Y2Z

Ax-+00-+000

Ay00-+00-+0

Az+++++++++2-2 Detection principle of 3-axis angular velocity
When an object having a mass moves at a certain velocity,
angular velocity acts on the object with the result that Coriolis
force acts on it. The 3-axis angular velocity sensor also uses theCoriolis force. In the case of 3-axis angular velocity sensors, theobject (oscillator) having a mass is brought into rotationalmotion on the X-Z plane as shown in Fig. 4. In this motion, theoscillator has motion component Vx in the X-axis direction,and has velocity component Vz in the Z-axis direction. As
shown in Fig. 5, when the oscillator moves having velocity
component Vx in the X-axis direction, if angular velocity ωzaround the Z-axis acts, Coriolis force Fy in the Y-axis direction
is produced. Also, when the oscillator moves having velocity
component Vz in the Z-axis direction, if angular velocity ωyaround the Y-axis acts, Coriolis force Fx in the Z-axis direction
is produced. When angular velocity ωx in the X-axis direction
acts, Coriolis force Fy in the Y-axis direction is produced. The
relationship is shown by the following expression (1).

Z
Y1
y1
X1 x1

x2 X2
y2
Y2Fig. 2. Top face of the 6-axis motion sensor

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Fy=2mVz×ωx
Fx=2mVz×ωy
Fy=2mVx×ωzpiezoelectric type 6-axis angular velocity sensor shown in Fig.
1, charge is produced on each electrode as shown in Table 1.
Force in the X-, Y- and Z-axis directions is detected by the four
sector electrodes (x+, x-, y+, y-) placed at the center and thesurrounding ring electrode. Force Fx in the X-axis direction isdetected from the difference in charge produced between thetwo electrodes (x+, x-) placed on the X-axis, and force Fy in theY-axis direction is detected from the difference in charge
produced between the two electrodes (y+, y-) placed on theY-axis, and also force Fz in the Z-axis direction is detected byring electrode Z. Two electrodes (X+, X-) out of the fourelectrodes (X+, X-, Y+, Y-) placed outside the detecting
electrodes, and ring electrode Z placed outermost are used forbringing the oscillator into rotational motion. By applying AC
signals with a phase difference, the oscillator can be brought
into rotational motion on the X-Z plane. The placement of thenine electrodes shown here is determined by FEM analysis.
Especially, the positions of the force detecting electrodes areimportant, which must be placed in the stress concentration
area.

(1)

This expression shows that the angular velocity components(ωx, ωy, ωz) of three axes can be detected by detecting
Coriolis force (Fx, Fy) in the directions of two axes while
giving velocity components (Vx, Vz) in the directions of twoaxes by bringing the oscillator into rotational motion on theX-Z plane. When Coriolis force Fx acts on the oscillator, thediaphragm is deformed as shown in Fig. 3-1 Coriolis force Fxin the X-axis direction is detected as in the case whereacceleration acts in the X-axis direction. Coriolis force Fy in theY-axis direction is also detected in a like manner. The 3-axis
angular velocity sensor we have developed this time uses
piezoelectric ceramic. The piezoelectric effect of thepiezoelectric element is used for both circular motion within theX-Z plane, and detection of Coriolis force in the X-axis
direction and Y-axis direction. Since drive and detection areessential to angular velocity sensors, it can be said that thepiezoelectric element is one of the suitable materials for angularvelocity sensors.

AMP

LPF

X+X-X

Ax

Y+Y-Y

AｙZ+Z-Z

AｚSensorelement

ωxXXZZ

Synchronousdetector

ωyωzReference signal

Drive Circuit
Drive signal

Fig. 4. Rotational motion of the oscillator on the X-Z plane

Oscillator
Phase/Gain controller

Vz

Fig. 6. Circuit block diagram of 6-axis motion sensor
ωz

4 Detection circuit of the 6-axis angular velocity sensor
Vx

ωxFx

ωyFyFyFig. 5. Detection of ωx, ωy and ωz3 Detection of force and driving method of the oscillator
When force in the X, Y and Z-axis directions acts on the387

In this research, the oscillator was brought into rotationalmotion on the X-Z plane in consideration of the detection
sensitivity and noise resistance. The charge produced on thepiezoelectric ceramic by force in the directions of three axes
(Fx, Fy, Fz) is converted to voltage proportional to force (Vx,Vy, Vz). By passing this voltage (Vx, Vy, Vz) through alow-pass filter, 3-axis acceleration components (Ax, Ay, Az)
can be obtained. If force in the X-axis direction and in theY-axis direction (Fx, Fy) is measured the instant when passing
on the X-axis (velocity component Vz), angular velocity ωxand angular velocity ω y are detected. By synchronous
detection of voltage (Vx, Vy) with the drive signal (Dx or Dz),
angular velocity ωx and angular velocity ωy can be detected.
Furthermore, if Coriolis force in the Y-axis direction ismeasured the instant when passing on the Z-axis (velocitycomponent Vx), angular velocity ωz can be detected. By
synchronous detection of voltage (Vy) with the drive signal (Dx,Dz), angular velocity ωz can be detected. The circuit block
diagram of the 6-axis motion sensor is shown in Fig. 6. It canbe seen that 3-axis acceleration can be detected by simply
adding a low-pass filter to the 3-axis angular velocity sensor,
which allows for the configuration of the 6-axis motion sensor.

1Ax
Ay
Az

Output (V)

0.8
0.6
0.4
0.2
0024

68101210121012Acceleration (G)5 Performance of the 6-axis motion sensor(a) Acceleration output of X-axis
The principal axis sensitivity and cross-axis sensitivity of the6-axis motion sensor we have developed this time are shown inFig. 7 and Fig. 8. Performance is shown in Table 2. Linearity
and cross-axis sensitivity of acceleration characteristics areinferior to angular velocity characteristics. This is because there
is a problem with the method of supporting the diaphragm. By
supporting the diaphragm with increased rigidity, theacceleration characteristics are improved. However, the angularvelocity characteristics deteriorate thereby. The acceleration
characteristics and angular velocity characteristics varydepending on the method of supporting the diaphragm, which
are in a trade-off relationship. Next, the angular velocity output
and acceleration characteristics of the time when acceleration±4G acts are shown in Fig. 9. From this figure, it can be seenthat the angular velocity characteristics are not affected byacceleration. Lastly, the angular velocity output andacceleration output of the time when impact acceleration actson the 6-axis motion sensor are shown in Fig. 10. Since theangular velocity output and acceleration output are almost thesame in waveform, it is suggested that signal disturbance of theangular velocity output by impact acceleration can be correctedby the acceleration output. From the above results, we havefound that 3-axis acceleration components (Ax, Ay, Az) and3-axis angular velocity components (ωx, ωy, ωz) can bedetected simultaneously with one detecting element.

1AxAyAz

Output (V)

0.8
0.6
0.4
0.2
002468Acceleration (G)(b) Acceleration output of Y-axis
1Ax
AyAz

Output (V)

0.8
0.6
0.4
0.2
00

Table 2. Performance of 6-axis motion sensor

2468

Acceleration (G)Sensitivity
Cross-axis sensitivity
Non-linearity
Response frequency

Angular velocity
2.5mV/deg/sec
5%3%DC-50Hz

Acceleration
300mV/G
8% (20Hz)5%1-100Hz(c) Acceleration output of Z-axis
Fig. 7. Acceleration characteristics of 6-axis motion sensor

388

600
ωx400

Output (mV)ωy200

ωz0-200-1000100200-200-400-600
Angular velocity (deg/sec)(a) Angular velocity around Z-axis (ωx)(1) Reference of acceleration (2) Acceleration output
600

Fig. 9-1. The acceleration output of the time whenacceleration(±5G) acts

ωx
400

Output (mV)

ωy200

ωz

0-200-100

0100

200-200-400-600
Angular velocity (deg/sec)(b) Angular velocity around Y-axis (ωy)
600
ωx
400

Output (mV)

ωy200

ωz

(1) Reference of acceleration (2) Angular velocity output

0-200-1000100

Fig. 9-2. The angular velocity output of the time whenacceleration(±4G) acts

200-200-400-600
Angular velocity (deg/sec)(c) Angular velocity around Z-axis (ωz)
Fig. 8. Angular velocity characteristics of 6-axis motion sensor

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Acknowledgement
The authors wish to acknowledge Mr. Matsumoto ofToyama Industrial Technology Center for helpful suggestion incarrying out this research and cooperation in making rotarytable measurements and FEM analysis.
References[1] K. Okada et al ”Development of 3-axis Gyro-Sensor Using
Piezoelectric Element” Tech. Dig. ofThe 20th Sensor

Symposium, pp123-126, 2003
[2] K. Okada “Tri-axial piezoresistive accelerometer” Tech. Dig. ofThe 11th Sensor Symposium, pp245-248, 1992
[3] Joost C. Lotters “A Highly Symmetrical Capacitive Traxial(1) Angular velocity output (2) Acceleration output

Accelerometer” ISBN 90-365-0982-3[4] K. Okada et al “Development of Micro-machined Three-axis

Fig. 10. The angular velocity output and acceleration output of
the time when impact acceleration acts

Sensors in Venture Business” Transducer ’01 Munich 1280-1283,
2001[5] N. Taniguchi, H. Itano, K. Okada “The 5-axis Motion Sensor”
Tech. Dig. of The 16th Sensor Symposium, pp41-44, 1998

6 Conclusion[6] Y. Watanabe et al “Five-axis motion sensor with electrostatic

This report has shown that 3-axis angular velocity
components ( ω x, ω y, ω z) and 3-axis acceleration
components (Ax, Ay, Az) can be detected with one detecting
element by bringing the oscillator into rotational motion within
a 2-dimensional plane, and detecting the directions of threeaxes. Also, it has been shown that the angular velocity
characteristics of the 6-axis motion sensor we have developed
this time do not change with acceleration of about ±4G.
Furthermore, with the conventional angular velocity sensors,
their output waveforms would be disturbed by impact
acceleration when it acts, where there would be no means ofcorrection, but with this sensor, we have found the possibility ofcorrecting the angular velocity signal disturbance caused by
impact acceleration because acceleration and angular velocity
are detected simultaneously. In this research, the oscillator wasbrought into rotational motion and Coriolis force was detectedby using the piezoelectric effect of the piezoelectric element,
but the oscillator may be brought into rotational motion by
Coulomb force and Coriolis force being detected bycapacitance. In this case, it is considered that compact andhighly reliable 6-axis motion sensors can be realized with useof micromachining technologies. We think that research in thisfield will advance in synchronicity with market trends in thefuture.

drive and capacitive detection fabricated silicon bulk
micromachining”, Sensors and Actuators A 97-98(2002),
pp109-115

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