Vibrator, vibratory gyroscope, and vibration adjusting method

A vibrator of a vibratory gyroscope comprises a main arm having a base part and at least one bending-vibration piece extending from the base part in a direction crossing the longitudinal direction of the base part and a fixing part for fixing one end of the base part, and the base part and the bending-vibration piece are formed so as to extend substantially in a specified plane. Preferably, at the opposite side to one end of the base part, a projection projecting from the bending-vibration piece is provided, or at least a pair of resonant arms resonating with vibration of the base part, said pair of resonant arms projecting from the fixing part are provided. Thanks to this, it has been possible to detect a turning angular rate in a sufficiently high accuracy without providing a projection which has a certain weight and extends from the vibrator toward the axis of turning even in case of arranging the vibrator so that the vibration arm of the vibrator extends perpendicularly to the axis of turning.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a vibrator used for an angular rate sensor 
used for detecting a turning angular rate in a turning system and a 
vibratory gyroscope using the same vibrator, and particularly to a 
vibrator using a piezoelectric member and a vibratory gyroscope using the 
same vibrator. 
2. Description of the Related Art 
Up to now, as an angular rate sensor used for detecting a turning angular 
rate in a turning system, a vibratory gyroscope using a piezoelectric 
member has been used for detecting position of an aircraft, a ship, a 
space satellite, or the like. Recently, it is used in a carnavigation 
system, a movement detecting mechanism of a VTR or a still camera, and the 
like in the field of public livelihood. 
Such a vibratory gyroscope utilizes the phenomenon that when an angular 
speed is applied to a vibrating object, a Coriolis force is generated in 
the direction perpendicular to the vibratory direction. Its mechanism is 
analyzed by using a dynamic model (for example, "Handbook of Elastic Wave 
Device Technologies" (Danseiha-Sosi Gijutsu Handbook) issued by Ohm, Inc., 
pp.491 to 497). Various kinds of piezoelectric vibratory gyroscopes have 
been proposed up to now. For example, a Sperry tuning-fork gyroscope, a 
Watson tuning-fork gyroscope, a regular-triangle prism-shaped tuning-piece 
gyroscope, a cylindrical tuning-piece gyroscope, and the like are known as 
a piezoelectric vibratory gyroscope. 
The inventors are studying various applications of vibratory gyroscopes, 
and have studied using a vibratory gyroscope as a turning rate sensor used 
in a car control method of an automobile body turning rate feedback 
system, for example. Such a system detects the direction of a steering 
wheel itself by a turning angle of the steering wheel. At the same time as 
this, the system detects a the actual turning rate of the car body by 
means of a vibratory gyroscope. The system finds a difference between the 
direction of the steering wheel and the actual body turning rate by 
comparing them with each other, and attains a stable body control by 
compensating a wheel torque and a steering angle on the basis of this 
difference. 
However, any example of the above-mentioned former piezoelectric vibratory 
gyroscopes can detect a turning angular rate only by arranging a vibrator 
in parallel with the axis of turning (what is called a vertical 
arrangement). The turning axis of a turning system to be measured is 
usually perpendicular to the gyroscope mounting part. Accordingly, in 
mounting such a piezoelectric vibratory gyroscope it has been impossible 
to shorten the piezoelectric vibratory gyroscope in height, namely, to 
reduce the piezoelectric vibratory gyroscope in size in the direction of 
the turning axis. 
In recent years, a piezoelectric vibratory gyroscope capable of detecting a 
turning angular rate even when arranging a vibrator perpendicularly to the 
turning axis (what is called a horizontal arrangement) has been proposed 
in a Japanese laid-open publication Tokkaihei No.8-128833. In this 
example, as shown as an example in FIG. 1, a vibrator extends in the 
directions X and Y, namely, extends perpendicularly to the turning axis Z. 
Each of three elastic members 51a, 51b and 51c is provided with a weight 
53 at one end therefor. The elastic members 51a, 51b and 51c are vibrated 
by piezoelectric devices 54 and 55 in the X-Y plane in phase inverse to 
one another. A Coriolis force in the Y direction generated by a turning 
angular rate .omega. around the Z axis is applied to the center of gravity 
of the weight 53. Since the plane of the elastic members 51a, 51b and 51c 
and the center of gravity of the weight 53 are slightly distant in the Z 
direction from each other, the ends of the elastic members 51a, 51b and 
51c are bent reversely to one another in the Z direction by the Coriolis 
forces each of which is applied to the center of gravity of the weight 53. 
A turning angular rate .omega. around the Z axis is obtained by detecting 
this bending vibration by means of piezoelectric devices 56 and 57. 
And up to now, various configurations have been known as a vibratory 
gyroscope using a vibrator which is composed of plural arms and a base 
part joining the plural arms, gives a drive vibration in a specified plane 
to each of the arms, and obtains a turning angular rate on the basis of a 
detection vibration which is perpendicular to this drive vibration and 
corresponds to the applied turning angular rate. For example, a Japanese 
laid-open publication Tokkaihei No. 7-83671 has disclosed a vibratory 
gyroscope using a tuning-fork vibrator made by joining three arms composed 
of a middle drive arm and two detection arms at both sides of the middle 
drive arm in one body at the base part. FIG. 2 shows a configuration 
example of such a former vibratory gyroscope. In the example shown in FIG. 
2, a vibrator 102 forming a vibratory gyroscope is composed of three arms 
which are composed of a middle drive arm 104 and two detection arms 103 
and 105 arranged at both sides of it nearly in parallel with it, and a 
base 106 at which the drive arm 104 and the detection arms 103 and 105 are 
joined in one body with one another. 
In the above-mentioned tuning-fork vibrator 102, the drive arm 104 is 
vibrated in the X-Z plane by an unillustrated driving means provided on 
the drive arm. And the left and right detection arms 103 and 105 are 
resonated in the same X-Z plane. When a turning angular rate .omega. acts 
around the axis Z of symmetry of the tuning-fork vibrator 102, a Coriolis 
force f acts on each of the detection arms 103 and 105. Since the 
detection arms 103 and 105 are vibrating in the X-Z plane, vibration in 
the Y-Z plane is induced in the detection arms 103 and 105. A turning 
angular rate is measured by detecting this vibration by means of an 
unillustrated detecting means provided on each of the detection arms 103 
and 105. 
A piezoelectric vibratory gyroscope disclosed in the above-mentioned 
Japanese laid-open publication Tokkaihei No. 8-128833 can certainly detect 
a turning angular rate using the Coriolis principle even when the vibrator 
is arranged horizontally. However, necessity of providing the weight 53 
makes it insufficient to shorten the gyroscope in height. And when the 
weight 53 is made thin in thickness in order to sufficiently shorten it in 
height, moment by a Coriolis force is made small and a bending vibration 
is made very small, and there is a problem that a measurement sensitivity 
is lowered. 
And in a vibrator of a piezoelectric vibratory gyroscope having the 
above-mentioned configuration, the drive vibration and the detection 
vibration are different in the vibrating direction from each other due to 
the configuration of the vibrator. That is to say, that vibrator needs 
such vibrations in two directions that the elastic members 51a, 51b and 
51c which are vibrating in the X-Y plane need to vibrate also in the Z 
direction. Generally in a piezoelectric vibratory gyroscope, it is 
required to keep always a constant relation between a vibration frequency 
for driving and a vibration frequency for detection in order to keep a 
good measurement sensitivity. Now, considering a single crystal as a 
material for a vibrator, since a single crystal is anisotropic, variation 
in vibration frequency caused by a temperature change varies with the 
direction of vibration. Therefore, attempting to form a vibrator having 
the above-mentioned the configuration out of a single crystal causes a 
problem that even in case of setting a constant relation between a drive 
vibration frequency and a detecting vibration frequency at a certain 
temperature, when the temperature is changed the relation cannot be kept 
and the measurement sensitivity is liable to vary with temperature. 
In a former vibratory gyroscope of the above-mentioned composition shown in 
FIG. 2, in case of forming the vibratory gyroscope by supporting the 
tuning-fork vibrator 102, the vibrator 102 is supported by fixing the 
entire end part 107 of the base part 106 of the tuning-fork vibrator 102 
opposite to the end part at which the drive arm 104 and the detection arms 
103 and 105 exist, or by fixing an unillustrated supporting arm at a 
position of this end part 107 corresponding to the axis Z of symmetry. 
Therefore, it cannot be said that a Coriolis force generated by a turning 
angular rate is efficiently utilized for action of detection vibration in 
the detection arms 103 and 105, and there is a problem that sharpness of 
resonance (Q value) of the detection vibration in the Y-Z plane in the 
detection arms 103 and 105 is low and the measurement sensitivity is low. 
On the other hand, as a turning angular rate detecting method, both of an 
ordinary vibratory gyroscope having a vertically-arranged vibrator and a 
vibratory gyroscope having the above-mentioned horizontally-arranged 
vibrator electrically take in vibration of the vibrator different in mode 
from a drive vibration generated by a Coriolis force as displacement of a 
piezoceramic member, and measures a turning angular rate on the basis of 
the amplitude of the output signal. However, since a vibratory gyroscope 
having a horizontally-arranged vibrator composed of a piezoelectric single 
crystal has a low sensitivity to a turning angular rate due to its 
composition, there is a problem that it deteriorates a detection accuracy 
to measure a turning angular rate on the basis of the amplitude of an 
output signal. 
In order to solve the problem of noises caused by such external factors as 
a voltage fluctuation, a temperature change and the like, a technique 
which pays attention to a fact that a phase difference between the phase 
of a driving signal and the phase of an output signal is changed by a 
Coriolis force in a vertically-arranged tuning-piece vibrator, and 
measures a turning angular rate on the basis of variation of the phase 
difference has been disclosed in Japanese patent publication Tokkohei No. 
4-14734. However, even by applying the above-mentioned detection of a 
turning angular rate on the basis of variation in phase difference to a 
vibratory gyroscope having a horizontally-arranged vibrator composed of a 
piezoelectric single crystal, a satisfactory result cannot be obtained in 
measurement sensitivity and in linearity of a phase difference to a 
turning angular rate. 
A problem the present invention attempts to solve is to make it possible to 
detect a turning angular rate in a sufficiently high accuracy without 
providing a projection having a certain weight from a vibrator toward the 
axis of turning even in case of setting up the vibrator in a direction in 
which a vibrating arm of the vibrator extends perpendicularly to the axis 
of turning. 
Another problem the invention attempts to solve is to provide a vibrator 
which can be simplified in construction, be horizontally arranged in 
mounting, and be reduced in height, a method for adjusting the same 
vibrator, and a vibratory gyroscope using the same vibrator. 
SUMMARY OF THE INVENTION 
An object of the invention is to provide a vibratory gyroscope capable of 
measuring a turning angular rate with high sensitivity by solving the 
above-mentioned problems. 
Another object of the invention is to provide a vibratory gyroscope using a 
horizontally-arranged vibrator composed of a piezoelectric single crystal, 
the vibratory gyroscope being improved in detection accuracy of a turning 
angular rate. 
A vibrator according to a first embodiment of the invention comprises a 
main arm provided with a base part and at least one bending-vibration 
piece extending from the base part in a direction crossing the 
longitudinal direction of the base part, and a fixing part for fixing one 
end of the base part, wherein the base part and the bending-vibration 
piece are formed so that they extend substantially in a specified plane. 
The invention also relates to a vibratory gyroscope for detecting a turning 
angular rate, the vibratory gyroscope including the above discussed 
vibrator, an exciting means for exciting vibration of the vibrator in a 
plane, and a detecting means for detecting a bending vibration of the 
vibrator generated by a Coriolis force to be applied to the vibrator when 
the vibrator turns in the plane and outputting a signal according to the 
detected bending vibration. 
Since according to the invention a drive vibration and a detection 
vibration of a vibrator take place in a specified plane and the invention 
uses a bending vibration as vibration to be detected, the invention can 
detect a turning angular rate with sufficiently high sensitivity without 
providing a projection of a certain weight from the vibrator toward the 
axis of turning, even when setting up the vibrator so that a vibrating arm 
of the vibrator extends perpendicularly to the axis of turning. 
The first preferred embodiment uses a fixing piece which is fixed at both 
ends of it as a fixing part, and a main arm is provided at one side of 
this fixing piece and a resonator piece is provided at the other side of 
the fixing piece. The fixing piece, the main arm and the resonator piece 
are formed so as to extend substantially in a specified plane. That is to 
say, an exciting means and a bending-vibration detecting means can be 
disposed with a fixing piece fixed at both ends between them. Thanks to 
this, since such bad influences as electromechanical coupling and the like 
between the exciting means and the bending-vibration detecting means can 
be prevented, the detection accuracy is improved. 
In the above-mentioned construction, since displacement of the vibrator is 
in a plane, the main arm, the resonator arm, and the fixing piece can be 
made of the same single crystal, for example, a single crystal of quartz, 
LiTaO.sub.3, or LiNbO.sub.3. In this case, the measurement sensitivity can 
be improved. The whole of a vibrator can be made by making a single 
crystal thin plate and processing this single crystal thin plate by means 
of etching or grinding. 
Although the base part and the bending-vibration piece can be made of 
different members from each other, it is particularly preferable that they 
are formed in one body. Although a material for the vibrator is not 
limited in particular, it is preferable to use a single crystal of quartz, 
LiNbO.sub.3, LiTaO.sub.3, a solid solution of lithium niobatelithium 
tantalate (Li(Nb, Ta)O.sub.3, or the like. By using such a single crystal, 
it is possible to improve a detection sensitivity and reduce a detection 
noise. 
And since such a single crystal is particularly insensitive to a 
temperature change, it is suitable for a sensor used in a car where 
thermal stability is necessary. This point is further described. As an 
angular speed sensor using a tuning-fork vibrator, there is, for example, 
a piezoelectric vibratory gyroscope disclosed in the above-mentioned 
Japanese laid-open publication Tokkaihei No. 8-128833. In such a vibrator, 
however, the vibrator vibrates in two directions. That is to say, in FIG. 
1, the vibrator vibrates in the Z direction as well as in the X-Y plane. 
Therefore, particularly in case of forming the vibrator out of such a 
single crystal as described above, it is necessary to match the 
characteristics of the single crystal in the two directions with each 
other. In practice, however, a piezoelectric single crystal is 
anisotropic. 
Generally in a piezoelectric vibratory gyroscope, in order to keep good 
sensitivity, it is required to keep a constant vibration frequency 
difference between a natural resonance frequency of a drive vibration mode 
and a natural resonance frequency of a detection vibration mode. However, 
a single crystal is anisotropic and a degree of variation in vibration 
frequency caused by a temperature change varies with the crystal face. For 
example, although variation in vibration frequency caused by a temperature 
change is very little when a single crystal is cut along a specific 
crystal face, variation in vibration frequency is very sensitive to a 
temperature change in case of cutting the single crystal along another 
crystal face. 
Thus, when a vibrator vibrates in two directions, at least one of the two 
vibrating faces is a crystal face having a large variation in vibration 
frequency caused by a temperature change. 
On the other hand, as shown in the invention, by making the whole of a 
vibrator vibrate in a specified plane and forming the vibrator out of a 
piezoelectric single crystal it is possible to prevent the vibrator from 
being influenced by anisotropy of a single crystal as described above and 
use only the best crystal face in characteristics of the single crystal in 
the vibrator. 
Concretely, since every vibration of a vibrator takes place in a single 
plane, it is possible to manufacture a vibrator using only a crystal face 
having little variation in vibration frequency caused by a temperature 
change of a single crystal. Therefore, it is possible to provide a 
vibratory gyroscope having a very high thermal stability. 
Among the above-mentioned single crystals, single crystals of LiNbO.sub.3, 
LiTaO.sub.3, and a single crystal of a solid solution of lithium 
niobate-lithium tantalate have particularly large electromechanical 
coupling coefficients. Comparing a single crystal of LiNbo.sub.3 and a 
single crystal of LiTaO.sub.3 with each other, the single crystal of 
LiTaO.sub.3 has a larger electromechanical coupling coefficient and a 
better thermal stability than the single crystal of LiNDbO.sub.3. 
A vibrator according to a second embodiment of the invention is the 
above-mentioned vibrator in which the main arm comprises a pair of 
bending-vibration pieces extending in a direction crossing the 
longitudinal direction of the base part and a tuning-fork vibrator piece 
whose tines extend respectively from the bending-vibration pieces, and the 
base part, the bending-vibration pieces and the tuning-fork vibrator piece 
are formed so as to extend substantially in a specified plane. In the 
above-mentioned construction, since displacement of the vibrator is in a 
plane, the bending vibration piece, the tuning-fork vibrator piece and the 
base part can be made of the same single crystal, for example, a single 
crystal of quartz, LiTaO.sub.3, LiNbO.sub.3, or Li(Nb, Ta)O.sub.3. This 
case is preferable, since the measurement sensitivity can be improved and 
the vibrator can be made of a single crystal thin plate by means of a 
wafer etching process and the like (in case of quartz) or a single crystal 
cutting method of grinding and the like (in case of a single crystal of 
LiTaO.sub.3, LiNbO.sub.3, or the like). 
A vibrator adjusting method of the invention is a method for adjusting a 
vibrator having the above-mentioned construction, the vibrator being 
adjusted to a specified relation between the resonance frequency of 
vibration of said bending vibration piece and tuning-fork vibrator piece 
in said single plane and the resonance frequency of bending vibration of 
said base part in said single plane, by projecting both ends of said 
tuning-fork vibrator piece outwardly from the position of said bending 
vibration piece in said same single plane and reducing the length of at 
least one of the projected parts. 
A vibratory gyroscope of this invention is a vibratory gyroscope for 
detecting a turning angular rate by means of a vibrator of the 
above-mentioned second embodiment, said vibratory gyroscope comprising an 
exciting means, provided in said tuning-fork vibrator piece, for exciting 
vibration of said tuning-fork vibrator piece, and bending vibration piece 
in said single plane; and a bending-vibration detecting means, provided in 
the base part, for detecting a bending vibration taking place in said base 
part in said single plane and outputting a signal according to the 
detected bending vibration. 
And a vibratory gyroscope of this invention is a vibratory gyroscope for 
detecting a turning angular rate by means of a vibrator of the 
above-mentioned second embodiment, said vibratory gyroscope comprising an 
exciting means, provided in said base part, for exciting a bending 
movement of said base part in said single plane; and a bending-vibration 
detecting means, provided in the tuning-fork vibrator piece, for detecting 
vibration taking place in said tuning-fork vibrator piece and bending 
vibration piece in said single plane and outputting a signal according to 
the detected vibration. 
A vibrator according to a third embodiment of the invention is a vibrator 
wherein said vibrator comprises a main arm provided with a pair of said 
bending-vibration pieces extending in a direction crossing the 
longitudinal direction of the base part and a tuning-fork vibrator piece 
whose tines extend respectively from the bending-vibration pieces and 
additionally to this main arm, a fixing piece which is fixed at both ends 
and at which the base part of the main arm is fixed, and a resonator piece 
provided on the fixing piece at a position which is at the opposite side 
to and corresponds to said base part, and wherein said main arm, fixing 
piece, and resonator piece extend in a specified plane. 
It is possible to make a bending movement, having as a fulcrum the fixing 
piece joined with said base part and said resonator piece, take place in 
said base part and said resonator piece. 
A vibrator adjusting method of this invention is a method for adjusting a 
vibrator of the third embodiment, the vibrator being adjusted to a 
specified relation between the resonance frequency of vibration of said 
tuning-fork vibrator piece and bending vibration piece in said single 
plane and the resonance frequency of bending vibration of said base part 
and said resonator piece in said single plane, by reducing length of at 
least one of the projected parts provided at both ends of the bending 
vibration pieces. 
A vibratory gyroscope of this invention is a vibratory gyroscope for 
detecting a turning angular rate by means of a vibrator of the third 
embodiment, said vibratory gyroscope comprising an exciting means, 
provided in said tuning-fork vibrator piece, for exciting vibration of 
said tuning-fork vibrator piece in said single plane; and a 
bending-vibration detecting means, provided in the resonator piece, for 
detecting a bending vibration taking place in said resonator piece in said 
single plane and outputting a signal according to the detected bending 
vibration. 
And a vibratory gyroscope of this invention is a vibratory gyroscope for 
detecting a turning angular rate by means of a vibrator of the third 
embodiment, said vibratory gyroscope comprising an exciting means, 
provided in said resonator piece, for exciting a bending movement of said 
resonator piece in said single plane; and a vibration detecting means, 
provided in the tuning-fork vibrator piece, for detecting vibration taking 
place in said tuning-fork vibrator piece in said single plane and 
outputting a signal according to the detected vibration. 
In any case of the above-mentioned vibratory gyroscopes, it is possible to 
set an exciting means and a bending-vibration detecting means or a 
vibration detecting means at a position more distant from and above a 
vibrator in comparison with a former vibrator having no resonator piece. 
Accordingly, since such bad influences as electro-mechanical coupling and 
the like between the exciting means and the bending-vibration detecting 
means or the vibration detecting means can be prevented, the detection 
accuracy is improved. 
A vibratory gyroscope according to a fourth embodiment of the invention is 
a vibratory gyroscope comprising one of said vibrators, 
a driving means for driving a drive vibration, 
a detecting means for detecting a vibrating state in a vibration mode which 
is caused by the drive vibration generated by the driving means and is 
different from the drive vibration, and 
a phase difference detecting means for detecting a phase difference between 
a reference signal and an output signal, when assuming that an electrical 
signal used for generating a drive vibration is a reference signal and an 
electrical signal taken by the detecting means from a vibration having a 
vibration mode which is caused by the drive vibration and is different 
from the drive vibration; 
said vibratory gyroscope detecting a turning angular rate on the basis of 
variation of the phase difference detected by the phase difference 
detecting means. 
The invention has been developed by finding that in a vibratory gyroscope 
comprising a vibrator composed of a piezoelectric single crystal using 
vibration in a horizontal plane as a drive vibration, it is possible to 
improve detection of a turning angular rate in accuracy by obtaining a 
phase difference between a reference signal based on a drive vibration and 
an output signal based on a detection vibration, and detecting the turning 
angular rate on the basis of the obtained phase difference. That is to 
say, even in such a vibratory gyroscope as a vibratory gyroscope using a 
horizontally-arranged vibrator, said vibratory gyroscope being a little in 
vibration of the vibrator generated by a Coriolis force and low in 
sensitivity, it is possible to improve a gyroscopic signal to be detected 
in the signal-to-noise ratio of a signal to a noise caused by such 
external factors as a voltage fluctuation, a temperature change, and the 
like by using as a material for the vibrator a piezoelectric single 
crystal itself having a high Q value, for example, a single crystal of 
quartz, LiNbO.sub.3, or LiTaO.sub.3. As a result, in a range in which the 
amplitude of a signal called a leakage signal caused by an unnecessary 
vibration due to an insufficient processing accuracy or the like is 7 
times larger than the amplitude of an original gyroscopic signal, it is 
possible to detect a turning angular rate in a range where the detection 
sensitivity is low but linearity of variation in phase difference to a 
turning angular rate is good. Therefore, the detection accuracy can be 
improved. 
A fifth embodiment of the invention is a vibratory gyroscope having said 
vibrator, wherein the vibrator is a plate-shaped vibrator composed of a 
piezoelectric single crystal and layer-shaped parts of plural layers each 
of which is composed of a piezoelectric single crystal are provided 
between one main face and the other main face of the vibrator, and the 
axial directions of polarization of the respective layer-shaped parts are 
different from one another. 
This invention relates to a vibratory gyroscope, wherein said vibrator is 
provided with one electrode provided on one main face and the other 
electrode which is provided on the other main face and is opposite to the 
one electrode. 
This invention relates to a method for making said vibrator vibrate in a 
direction crossing the central face of the vibrator, said method providing 
one electrode on one main face, providing the other electrode opposite to 
the one electrode on the other main face, and applying alternating 
voltages different in polarity from each other, respectively, to the one 
electrode and the other electrode. 
The invention relates to a method for detecting vibration of said vibrator, 
said method providing one electrode on one main face, providing the other 
electrode opposite to the one electrode on the other main face, connecting 
the one electrode and the other electrode with a voltage detecting 
mechanism, and detecting an alternating voltage generated between the one 
electrode and the other electrode by making the vibrator vibrate in a 
direction crossing the one main face and the other main face. 
According to a vibrator and a vibratory gyroscope of the fifth embodiment, 
it is possible to make the vibrator perform a bending vibration in a 
direction crossing, preferably, perpendicular to a main face by forming 
electrodes on a pair of main faces of the vibrator opposite to each other 
and applying an alternating voltage to these electrodes. Furthermore, when 
a bending vibration is excited, an electric field is uniformly applied to 
the inside of the vibrator. Therefore, a locally uniform electric field 
and an internal stress caused by the un-uniform electric field are not 
generated inside the vibrator. 
In a preferred embodiment of the invention, the respective layer-shaped 
parts are composed of plate-shaped members each of which is composed of a 
piezoelectric single crystal and which are different in the direction of 
polarization from one another, and these plate-shaped members are joined 
with one another, respectively, to form the layer-shaped parts. 
And in a particularly preferred embodiment, the axial direction of 
polarization in one layer-shaped part of at least one main face side and 
the axial direction of polarization in the other layer-shaped part of the 
other main face side are reverse to each other. 
Although a piezoelectric single crystal which is a material for the 
vibrator is not limited in particular, it is particularly preferable that 
a single crystal is quartz, lithium niobate, lithium tantalate, a solid 
solution of lithium niobate-lithium tantalate, langasite, or lithium 
tetraborate, and it is more preferable that a single crystal is lithium 
niobate, lithium tantalate, a solid solution of lithium niobate-lithium 
tantalate, or langasite. Among the above-mentioned single crystals, single 
crystals of quartz, LiNbO.sub.3, LiTaO.sub.3, and (Li(Nb, Ta)O.sub.3 have 
particularly large electromechanical coupling coefficients. Comparing a 
single crystal of LiNbO.sub.3 and a single crystal of LiTaO.sub.3 with 
each other, the single crystal of LiTaO.sub.3 has a larger 
electromechanical coupling coefficient and a better thermal stability than 
the single crystal of LiNbO.sub.3. 
And it is possible to exemplify lead zirconate titanate (PZT), relaxer 
compounds (general expression: Pb(A1/3B2/3)O3 where A is Cd, Zn, Mg or the 
like, and B is Nb, Ta, W or the like), a piezoelectric single crystal of a 
mixed crystal system of lead zirconate titanate and a relaxer compound, 
langasite, and lithium tetraborate. 
A vibratory gyroscope of a sixth embodiment of the invention is a vibratory 
gyroscope using a vibrator which is composed of plural arms and a base 
part for joining the plural arms with it, gives a drive vibration in a 
specified plane to the arms, and obtains a turning angular rate from a 
detection vibration corresponding to the applied angular rate of turning, 
said vibratory gyroscope supporting the vibrator at a small domain where 
there is locally a domain having the smallest detection vibration. 
The invention can fix a domain where movement of the vibrator is the 
smallest by supporting the vibrator at a small domain where there is 
locally a domain having the smallest detection vibration in case of 
supporting the vibrator. Accordingly, since it is possible to effectively 
generate a detection vibration by means of a Coriolis force, a Q value of 
the detection vibration becomes high and the sensitivity can be improved. 
Since the detection vibration generated by the Coriolis force is small in 
amplitude, the invention is particularly effective to improve the 
sensitivity. 
And since it increases not only the Q value of detection vibration but also 
the Q value of drive vibration and furthermore can improve also the 
sensitivity to support a vibrator at small domain where there is locally a 
domain having the smallest detection vibration and a small domain where 
there is locally a domain having the smallest drive vibration coincide 
with each other, it is preferable as a preferred embodiment to support the 
vibrator in this way. Furthermore, it is preferable to use as a material 
for a vibrator a piezoelectric material such as piezoceramic or a single 
crystal of quartz, LiTaO.sub.3, LiNbO.sub.3, or the like, and it is more 
preferable in particular to use a single crystal of quartz, LiTaO.sub.3, 
LiNbO.sub.3, or the like. The reason is that a high Q value of a single 
crystal itself can be effectively used. 
In the present invention, a small domain where there is locally a domain 
having the smallest detection vibration or the smallest drive vibration is 
a domain within a range where the amplitude of detection vibration or 
drive vibration is smaller than a thousandth of the maximum amplitude in a 
vibrator. 
A vibratory gyroscope of a seventh embodiment of the invention is a 
vibratory gyroscope having a vibrator composed of an arm of a 
piezoelectric member, wherein said arm has a hollow part and a pair of 
electrodes are provided on each of the parts between which the hollow part 
of the arm is disposed. 
In this invention, to provide a pair of electrodes on each of the parts 
between which the hollow part of the arm is disposed prevents an 
unnecessary displacement from being generated by an electric field flowing 
from one pair of electrodes to the other pair of electrodes, since there 
is no piezoelectric member at that place. Accordingly, since noises can be 
removed, it is possible to make a high-accuracy angular speed detection. 
Although the hollow part is not limited in size in particular, it is 
preferable to form the hollow part equal to or longer than the electrode 
in the longitudinal direction of the electrode, because a leakage electric 
field does not cause an unnecessary displacement of the arm at all since 
there is no piezoelectric member to contribute the displacement. And since 
it is necessary to provide the hollow part correspondingly to the 
electrodes, it is preferable to provide the hollow part at a range of 1/3 
to 2/3 arm length distant from the base of the arm in the arm of this 
invention which is more curved at a position closer to its base and in 
which each of the electrodes needs to be provided at a range of 1/3 to 2/3 
arm length distant from the arm base. Furthermore, it is preferable to use 
a 130-degree Y plate of lithium tantalate (LiTaO.sub.3) as a piezoelectric 
member, since to provide the hollow part of the invention is very 
effective to a large influence of a leakage electric field which this 
invention takes as a problem.

DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION 
A first preferred embodiment of the present invention is described with 
reference to the drawings in the following. FIG. 3 is a front view showing 
a vibrator of an embodiment of the invention, FIG. 4(a) is a front view 
for explaining a direction of vibration of a linear vibrator, FIG. 4(b) is 
a front view for explaining a direction of vibration of the vibrator of 
FIG. 3, and FIGS. 5(a), 5(b) and 5(c) are schematic diagrams for 
explaining vibration directions of the respective parts of the vibrator of 
FIG. 3 and the principle of vibration of it. 
In a main arm 101A of a vibrator 2 of FIG. 3, a base part 3 extends from 
and perpendicularly to a fixing part 1, and one end part 3a of the base 
part 3 is fixed on the fixing part 1. Specified exciting means 5A and 5B 
are provided in the base part 3. Two bending-vibration pieces 4A and 4B 
extending perpendicularly to the base part 3 are provided at the other end 
part 3b of the base part 3. 
A vibration mode of this vibrator 2 is described. As schematically shown in 
FIG. 5(a), the base part 3 is bent in the direction of arrow H around a 
joint 26 of it and the fixing member 1 by applying a drive voltage to the 
exciting means 5A and 5B. With this bending, not only the base part 3 of 
the vibrator 2 but also each point of the bending-vibration pieces 4A and 
4B are moved as shown by arrow I. A velocity vector of this movement is 
assumed as V. 
In this embodiment, the Z axis is the axis of turning, and the vibrator 2 
is turned around the Z axis. For example, when the vibrator 2 is moved in 
the direction of arrow H and the whole vibrator 2 is turned around the Z 
axis as shown by arrow w, a Coriolis force acts as shown by arrow J. As a 
result, as shown in FIG. 5(b), the bending-vibration pieces 4A and 4B are 
bent in the direction of arrow J around a joint 25 of the other end part 
3b of the base part 3 and the bending-vibration pieces. 
On the other hand, as shown in FIG. 5(c), when the base part 3 is driven in 
the direction of arrow K and the whole vibrator 2 is turned around the Z 
axis as shown by arrow .omega., a Coriolis force acts as shown by arrow L. 
As a result, the bending-vibration pieces 4A and 4B are bent in the 
direction of arrow L around the joint 25 of the other end part 3b of the 
base part 3 and the bending-vibration pieces. In this way, the 
bending-vibration pieces 4A and 4B can be vibrated as shown by arrows A 
and B. 
In this way, it is possible to convert a Coriolis force generated in the 
X-Y plane in the bending-vibration pieces 4A and 4B to a bending vibration 
around the joint 25 of the bending-vibration pieces 4A and 4B, and obtain 
a turning angular rate on the basis of the bending vibration. Thanks to 
this, even in case that the vibrator is arranged perpendicularly to the 
axis Z of turning (horizontally arranged), a turning angular rate can be 
detected in high sensitivity. 
The sensitivity of detection by the vibrator 2 shown in FIGS. 3 and 5 is 
furthermore described. As shown in FIG. 4(a), the inventors use a vibrator 
8A and 8B in the shape of a long and narrow stick, set the vibrator 8B in 
the X-Y plane, and extend and contract it. Hereupon, 8A represents a state 
where the vibrator is extended and 8B represents a state where the 
vibrator is contracted. Hereupon, a moment when the vibrator is going to 
extend as shown by arrow E toward the state 8A from the state 8B is 
considered. When the vibrator 8B is turned around the Z axis, a Coriolis 
force acts as shown by arrow F. However, since displacement of such a 
piezoelectric member caused by longitudinal vibration is small and its 
resonance frequency is low, the sensitivity cannot be made high. 
On the other hand, as shown in FIG. 4(b), the invention vibrates the base 
part 3 as shown by arrow G and thus vibrates the bending-vibration pieces 
4A and 4B as shown by arrow D. In this way, it is possible to obtain a 
much larger amplitude, a much larger vibration speed and a greater 
Coriolis force than the case of FIG. 4(a). 
And in case of using the vibrator shown in FIGS. 3 and 5, it is possible to 
excite a bending vibration in the bending-vibration pieces 4A and 4B as 
shown by arrows A and B. When the vibrator 2 turns in the X-Y plane, a 
Coriolis force is applied to each of the bending-vibration pieces and the 
Coriolis forces of the bending-vibration pieces are applied to the base 
part 3. By this, the base part 3 performs a bending vibration around the 
joint 26 as shown by arrow G. It is possible to detect the bending 
vibration of the base part 3 and output a signal according to the detected 
bending vibration. 
In case of forming the vibrator out of a piezoelectric single crystal, 
electrodes are used as exciting means and detecting means 5A, 5B, 6A, 6B, 
6C and 6D. However, the vibrator can be formed out of an elastic material, 
and in this case, piezoelectric members provided with electrodes can be 
used as exciting means and detecting means 5A, 5B, 6A, 6B, 6C and 6D. And 
in case that there is one of the exciting means (or detecting means) 5A 
and 5B, at least one of excitation and detection of vibration can be 
performed. And in case that there is one of the detecting means (or 
exciting means) 6A, 6B, 6C and 6B, at least excitation (or detection) of 
vibration can be performed. 
In embodiments shown in FIGS. 6 to 8, a main arm is provided at one side of 
a fixing piece part both ends of which are fixed, a resonant piece is 
provided at the other side of the fixing piece part, and the fixing piece 
part, the main arm and the resonant piece are formed so as to extend 
substantially in a specified plane. 
In the embodiment of FIG. 6, an exciting means side and a detecting means 
side are separated by a fixing piece part 12. Concretely, both ends of the 
fixing piece part 12 are fixed by fixing members 11. A main arm 101B is 
provided at one side of the fixing piece part 12. The main arm 101B is 
provided with a long and narrow base part 16 and two bending-vibration 
pieces 4A and 4B extending from an end part 16b of the base part 16 in a 
direction perpendicular to the longitudinal direction of the base part 16. 
A resonant piece 32 is provided at the other side of the fixing piece part 
12. The resonant piece 32 is provided with a rectangular supporting part 
13 extending from and perpendicularly to the fixing piece part 12, and 
specified exciting means 5A and 5B are provided in the supporting part 13. 
Two vibration pieces 15A and 15B extending perpendicularly to the 
supporting part 13 are provided at the other end 13b side of the 
supporting part 13. The end part 16a of the base part 16 and the end part 
13a of the supporting part 13 are joined to the fixing piece part 12. In 
this way, both sides of the fixing piece part 12 are nearly line-symmetric 
to each other. 
A vibration mode of this vibrator 10 is described. By applying a driving 
voltage to the exciting means 5a and 5B, the supporting part 13 and the 
pair of vibration pieces 15A and 15B are vibrated around the joint 27 of 
the fixing piece part 12 and the supporting part 13 as shown by arrow M. 
In resonance with this vibration, the base part 16 and the pair of 
vibration pieces 4A and 4B are vibrated around the joint 26 of the fixing 
part 12 and the base part 16 as shown by arrow D. 
When the whole of this vibrator 10 is turned around the axis Z of turning, 
a Coriolis force acts on each of the bending-vibration pieces 4A and 4B as 
described above. As the result, the bending-vibration pieces 4A and 4B are 
vibrated around the joint 25, respectively, as shown by arrows A and B. 
In this way, it is possible to convert a Coriolis force generated in the 
X-Y plane in the bending-vibration pieces 4A and 4B by the bending 
vibration of the resonant piece 32 to a bending vibration around the joint 
25 of the bending-vibration pieces 4A and 4B, and obtain a turning angular 
rate on the basis of this bending vibration. Thanks to this, even in case 
that the vibrator is arranged perpendicularly to the axis Z of turning 
(horizontally arranged), a turning angular rate can be detected in high 
sensitivity. 
In the embodiment of FIG. 6, in the vibrator 10, the resonant piece 32 and 
the main arm 101B are mirror-symmetric in shape to each other in relation 
to the fixing piece part 12, and by this the natural resonance frequencies 
of the respective vibration modes of the resonant piece and the main arm 
are matched with each other. However, it is not necessary that the 
resonant piece 32 and the main arm 101B are line-symmetric in shape to 
each other in relation to the fixing piece part 12. 
In a vibrator 20 of FIG. 7, since a main arm 101B composed of a base part 
16 and a pair of bending-vibration pieces 4A and 4B, and a fixing piece 
part 12 are the same in shape as those shown in FIG. 6, description of 
them is omitted. A long and narrow rectangular resonant piece 21 extends 
from the fixing piece part 12 perpendicularly to it. Exciting means 5A and 
5B are provided near an end part 21a at the fixing piece part 12 side of 
the resonant piece 21. 
By applying a driving voltage to the exciting means 5A and 5B, the resonant 
piece 21 is vibrated around the joint 27 of it and the fixing piece part 
12 as shown by arrow M. In resonance with this vibration, the base part 16 
and the pair of bending-vibration pieces 4A and 4B are vibrated around the 
joint 26 of them and the fixing member 11 as shown by arrow D. 
In this way, the whole vibrator is more simplified in structure in 
comparison with the embodiment of FIG. 6 by forming the resonant piece 21 
into a long and narrow rectangle. So as not to make large a frequency 
difference between the vibration frequency at the exciting side and the 
vibration frequency at the detection side of the fixing piece part 12, it 
is necessary to adjust both sides so that they are nearly equal in moment 
to each other. Comparing the resonant piece 21 of FIG. 7 with the resonant 
piece 32 of FIG. 6 from this viewpoint, in FIG. 7 there are no vibration 
pieces 15A and 15B, and there are no weights for them. Therefore, it is 
necessary that the height of the top end 21b of the resonant piece 
projecting from the fixing piece part 12 is higher than the height of the 
resonant piece 32 projecting from the fixing piece part 12, namely, that 
the resonant piece 21 is heavier in weight than the supporting part 13. 
Accordingly, the resonant piece 21 projecting from the fixing piece part 
12 tends to increase in height. 
In a vibrator 22 of FIG. 8, since a main arm 101B composed of a base part 
16 and a pair of bending-vibration pieces 4A and 4B, and the fixing piece 
part 12 are the same in shape as those shown in FIG. 6, description of 
them is omitted. A resonant piece 31 is provided on the fixing piece part 
12. The resonant piece 31 is provided with a rectangular supporting part 
30 extending from the fixing piece part 12 perpendicularly to it, and the 
supporting part 30 is provided with exciting means 5A and 5B. An ended 
part 23 in the shape of a broad rectangle is formed at the top end side of 
the supporting part 30. 
By applying a driving voltage to the exciting means 5A and 5B, the resonant 
piece 31 is vibrated around the joint 27 of it and the fixing piece part 
12 as shown by arrow M. In resonance with this vibration, the base part 16 
and the pair of bending-vibration pieces 4A and 4B are 55 vibrated around 
the joint 26 of them and the fixing piece part 12 as shown by arrow D. 
In this way, by providing the expanded part 23 in the resonant piece 31, it 
is possible to make lower in height the resonant piece 31 projecting from 
the fixing piece part 12 and furthermore make a vibration frequency of the 
resonant piece 31 closer to a vibration frequency of the base part 16 and 
bending-vibration pieces 4A and 4B side. 
In vibrators of the present invention, the longitudinal direction of a 
bending-vibration piece and the longitudinal direction of a base part do 
not have to be necessarily perpendicular to each other. And a 
bending-vibration piece may be straight or curved in shape. In case that a 
pair of bending-vibration pieces are provided, however, it is preferable 
that both of them have mirror-symmetry to each other in relation to the 
base part. 
In a main arm 101C of a vibrator 40 of FIG. 9, bending-vibration pieces 33A 
and 33B intersect the extending direction of a base part 3 at a specified 
angle .theta.. Although the intersecting angle is not a right angle, the 
intersecting angle is preferably 45.degree. to 135.degree., and it is 
particularly preferably 70.degree. to 100.degree.. Due to this, the 
natural resonance frequencies of vibration modes of vibrations N and P of 
the bending-vibration pieces 33A and 33B vary slightly in comparison with 
the natural resonance frequency of the vibration mode of the 
bending-vibration piece of the vibrator shown in FIG. 3. 
In a main arm 101D of a vibrator 41 of FIG. 10, bending-vibration pieces 
34A and 34B are in the shape of a slightly curved arc. Due to this, the 
natural resonance frequencies of vibration modes of vibrations Q and R of 
the bending-vibration pieces 34A and 34B vary slightly in comparison with 
the vibrator shown in FIG. 9. The shapes as shown in FIGS. 9 and 10 can be 
adopted also in the vibrators shown in FIGS. 6, 7, and 8. 
Generally in a piezoelectric vibratory gyroscope, in order to keep a good 
measurement sensitivity, it is required to keep a constant vibration 
frequency difference between the natural resonance frequency of a drive 
vibration mode and the natural resonance frequency in a detection 
vibration mode. In vibrators of the present invention, when the natural 
resonance frequency of a vibration mode of a base part and the natural 
resonance frequency of a vibration mode of a bending-vibration piece 
become close to each other, the sensitivity becomes good but the response 
speed is deteriorated. When a frequency difference between the natural 
resonance frequency of a vibration mode of a base part and the natural 
resonance frequency of a vibration mode of a bending-vibration piece 
becomes large, the response speed becomes good but the sensitivity is 
deteriorated. 
Due to this, by removing a weight at the top end of the bending-vibration 
piece, it is possible to vary the natural resonance frequency of a 
vibration mode of the bending-vibration piece. And by providing a 
projection projecting from the bending-vibration piece at the opposite 
side to the fixed end part of the base part and removing a weight of this 
projection, it is possible to vary the natural resonance frequency of a 
vibration mode of the base part. 
For example, in a main arm 101E of a vibrator 42 of FIG. 11, a projection 
35 projecting from bending-vibration pieces 4A and 4B is provided at the 
other end part 3b side of the base part 3. And the natural resonance 
frequency of a vibration mode of vibration D of the base part is varied by 
performing a process of removing a weight from a part 37 of the projection 
35. And the natural resonance frequencies of vibration modes of vibrations 
A and B of the bending-vibration pieces 4A and 4B can be varied 
independently of each other by performing a process of removing weights 
from the top ends 36A and 36B of the bending-vibration pieces 4A and 4B. 
This removing process can be performed by a laser irradiation process or a 
machining process. 
Next, an embodiment in which a vibrator of the invention is provided with 
at least a pair of resonant pieces which resonate with vibration of the 
base part and project from the fixing part is described. 
As shown in FIGS. 3 to 11, a vibratory gyroscope utilizing a bending 
vibration of a main arm or a resonant piece can attain such a high 
sensitivity that it cannot be obtained up to now in case of adopting a 
vibrator extending perpendicularly to a turning system. As a result of a 
further study of the inventors, however, it has been found that the 
following problem remains. That is to say, since a main arm composed of a 
bending-vibration piece and a base part is formed so as to project from a 
fixing part, for example, in case of using a bending vibration of the 
bending-vibration piece as a drive vibration and detecting a bending 
vibration around the fixing part of the base part, it has been found that 
the vibration of the base part is apt to damp comparatively soon and there 
is room for improvement in the Q value of the detection vibration. 
As a result of study for solving this problem, the inventors have thought 
of projecting at least one pair of resonant arms together with a base part 
from a fixing part and resonating the resonant arms with vibration of the 
base part. In this case, although it is possible to use vibration of the 
resonant arms and the base part as a drive vibration, it is more 
preferable to use vibration of the resonant arms and the base part as a 
detection vibration. Since since a detection vibration bearing a 
gyroscopic signal is much smaller in amplitude than a drive vibration, a 
greater effect of improvement of the Q value can be obtained. 
FIGS. 12 to 14 show vibratory gyroscopes of such embodiments. 
In a vibrator 44 of a vibratory gyroscope 43 of FIG. 12, a main arm 101F 
projects from a fixing part 1, and a pair of resonant arms 48A and 48B 
project at both sides of the main arm 101F. A base part 3 projects from 
the fixing part 1, bending-vibration pieces 45A and 45B extending 
perpendicularly to the base part 3 are formed at an end part 3b side of 
the base part 3, and weights 47A and 47B are formed at the top ends of the 
bending-vibration pieces 45A and 45B. The bending-vibration pieces 45A and 
45B are provided, respectively, with exciting means (detecting means) 46A, 
46B, 46C and 46D. 
The resonant arms 48A and 48B projecting from the fixing part 1 are 
provided, respectively, with detecting means (exciting means) 49A, 49B, 
49C and 49D, and weights 50A and 50B are formed, respectively, at the top 
ends of the resonant arms. 
A preferable vibration mode in this case is described with reference to 
FIGS. 13(a) to 13(c). As described above, the bending-vibration pieces 45A 
and 45B are excited to bending-vibrate as shown by arrow S in FIG. 13(a). 
A Coriolis force acts as shown by arrow T when the whole vibrator is 
turned as described above. There are plural vibrations excited in the base 
part and a pair of resonant arms by this Coriolis force. 
FIG. 13(b) shows the secondary vibrations. In this case, the base part 3 
and the resonant arms 45A and 45B are bending-vibrated reversely in phase 
to each other, and simultaneously with this, the bending-vibration pieces 
45A and 45B are vibrated so as to deviate from a straight line 58. FIG. 
13(c) shows the primary vibrations. In this case, the base part 3 and the 
resonant arms 45A and 45B also are bending-vibrated reversely in phase to 
each other, and simultaneously with this, the bending-vibration pieces 45A 
and 45B also are vibrated so as to deviate from a straight line 58. The 
vibrations of the bending-vibration pieces 45A and 45B are reverse in 
phase to each other, respectively, in case of the primary vibrations and 
the secondary vibrations. 
Hereupon, although any of the primary vibration and the secondary vibration 
may be used as a detection vibration, it is necessary to select it so that 
a frequency difference between the natural resonance frequency of a drive 
vibration and the natural resonance frequency of a detection vibration can 
be within a certain range. 
In a vibrator 60A of a vibratory gyroscope 59A of FIG. 14, a main arm 101G 
projects from a fixing part 1, a base part 3 projects from the fixing part 
1, and bending-vibration pieces 61A and 61B extending perpendicularly to 
the base part 3 are formed at an end part 3b side of the base part 3. 
Since there are not parts corresponding to the weights 47A and 47B, it is 
necessary to lengthen the bending-vibration pieces accordingly. The 
bending-vibration pieces 61A and 61B are provided, respectively, with 
exciting means (detecting means) 46A, 46B, 46C and 46D. 
A pair of resonant arms 62A and 62B project from the fixing part 1, and a 
resonant arms 62A and 62B are provided, respectively, with detecting means 
(exciting means) 49A, 49B, 49C and 49D. 
In this invention, in case of using resonant arms, it is possible to vary 
the natural resonance frequency of vibration of a so-called spurious mode 
by making different in projection height the resonant arms projecting from 
both positions of the fixing part. This embodiment is described with 
reference to a vibratory gyroscope 59B shown in FIGS. 15 and 16. 
In a vibrator 60B, a main arm 101H projects from a projection la of a 
fixing part 1. That is to say, a base part 3 projects, and 
bending-vibration pieces 61A and 61B extending perpendicularly to the base 
part 3 are formed at an end part 3b side of the base part 3. The 
bending-vibration pieces 61A and 61B are provided, respectively, with 
driving electrodes 46A, 46B, 46C and 46D. And a pair of resonant arms 63A 
and 63B project from the fixing part 1, and the resonant arms 63A and 63B 
are provided, respectively, with detecting electrodes 49A, 49B, 49C and 
49D. 
In a perspective view of FIG. 16, the driving electrodes and the detection 
electrodes are shown in cross-sectional views. 
A cut-off part 74 of dimension a is provided outside each of the resonant 
arms, and by this a projection 1a of a in height is projected from the 
fixing part 1. As a result, it is possible to deviate the natural 
resonance frequency of vibration of a spurious mode from the natural 
resonance frequency of a drive vibration. 
For example, in a vibrator shown in FIG. 15, in case of using a bending 
vibration of the bending-vibration pieces 61A and 61B as a drive 
vibration, and adjusting its natural resonance frequency to 8750 Hz, 
bending vibrations of the resonant arms 63A and 63B reverse in phase to 
each other as shown by arrow U in FIG. 15 are in a spurious mode. Natural 
resonance frequencies of these vibrations are 8700 Hz as shown in FIG. 17, 
in case of a=0 as shown in FIG. 14. As a result, since a frequency 
difference between the natural resonance frequency of the drive vibration 
and the natural resonance frequency of the spurious mode is 50 Hz, a 
signal generated by the vibrations reverse in phase of the resonant arms 
is made much larger than a gyroscopic signal. 
As shown in FIG. 17, however, the natural resonance frequency of a spurious 
mode is greatly varied with the increase of height a. Particularly by 
making the a 1.0 mm or more, it is possible to greatly deviate the natural 
resonance frequency of a spurious mode from the natural resonance 
frequency of a drive vibration. 
In this way, to make different in height the resonant arms projecting from 
both positions of the fixing part is effective to reduce noises caused by 
vibration in a spurious mode, and for the purpose of this, the a is 
particularly preferably 1.0 mm or more. This is preferably 6.0 mm or less. 
In the vibratory gyroscopes of the embodiments described above, in case of 
forming a vibrator out of a piezoelectric single crystal, 
bending-vibration pieces, a base part or resonant arms are 
bending-vibrated by applying a voltage in the direction perpendicular to 
the page face. Such a bending-vibration method for vibrating the arms is 
particularly useful in case of using a single crystal, for example, of 
lithium niobate, lithium tantalate, or a solid solution of lithium 
niobate-lithium tantalate. 
As described above, however, the vibrators of the embodiments of FIGS. 3 to 
16 can be naturally applied also to another piezoelectric single crystal 
such as quartz crystal or the like as adopting the same form of a drive 
vibration and a detection vibration. However, since this case is different 
in direction of an effective piezoelectric axis of the piezoelectric 
single crystal from the case of lithium niobate and the like, it is 
necessary to properly change the driving electrode and the detection 
electrode in shape in order to utilize the effective piezoelectric axis 
for bending vibration. 
FIGS. 18 to 20 all show vibratory gyroscopes of particularly preferred 
embodiments in case that a vibrator is formed by using a piezoelectric 
single crystal having the triad axis of symmetry (a-axis) in a specified 
plane like a quartz crystal and its c-axis is perpendicular to the 
specified plane. 
In such a form, it is preferable to set a voltage applying direction in a 
bending-vibration piece and a signal voltage direction in a resonant arm 
along the a-axis. FIGS. 18 and 19 relate to such embodiments. 
In a vibrator 60C of a vibratory gyroscope 59C of FIG. 18, a main arm 101I 
and a base part 3 project from a fixing part 1, and bending-vibration 
pieces 64A and 64B extending perpendicularly to the base part 3 are formed 
at an end part 3b side of the base part 3. The bending-vibration pieces 
64A and 64B are provided, respectively, with driving electrodes 65A and 
65B. These drive electrodes are shaped as shown in a sectional view taken 
along A-A', and the drive electrode 65A is grounded and the drive 
electrode 65B is connected to an alternating-current power source 68. By 
this, a voltage is applied in the direction of the a-axis in the 
bending-vibration pieces 64A and 64B, and a bending vibration is 
generated. 
The longitudinal directions of a pair of resonant arms 66A and 66B are 
inclined at an angle of 120.degree. to the bending-vibration pieces 64A 
and 64B. The detection electrodes 67A and 67B in the resonant arms 66A and 
66B are the same in shape as the drive electrodes 65A and 65B. As the 
result, a voltage is applied in the direction of the a-axis also in the 
resonant arms 66A and 66B. Therefore, both of a piezoelectric constant 
utilized in a bending-vibration piece and a piezoelectric constant 
utilized in a resonant arm are increased and come to the same degree. 
In a vibrator 60D of a vibratory gyroscope 59D of FIG. 19, a main arm 101J 
and a base part 3 project from a fixing part 1, and bending-vibration 
pieces 70A and 70B extending in the directions inclined at an angle of 
120.degree. to the base part 3 are formed at an end part 3b side of the 
base part 3. Weights 71A and 71B are provided, respectively, at the ends 
of the bending-vibration pieces 70A and 70B. 
The bending-vibration pieces 70A and 70B are provided, respectively, with 
drive electrodes 72A and 72B. These drive electrodes are shaped as shown 
in a sectional view taken along A-A', and the drive electrode 72B is 
grounded and the drive electrode 72A is connected to an 
alternating-current power source 68. By this, a voltage is applied in the 
direction of the a-axis in the bending-vibration pieces 70A and 70B, and a 
bending vibration is generated. 
The longitudinal direction of a pair of resonant arms 75A and 75B is 
inclined at an angle of 120.degree. to the bending-vibration pieces 70A 
and 70B. The shape of the detection electrodes 76A, 76B, 76C and 76D is 
shown in a sectional view taken along B-B', and the detection electrodes 
76D are grounded and a detection signal is taken out from the detection 
electrodes 76C. As the result, a signal voltage is generated in the 
direction of the a-axis also in the resonant arms 75A and 75B. 
As shown in the embodiment of FIG. 20 for example, in case of extending a 
bending-vibration arm and resonant arms in the vertical direction, a 
detection signal can be taken out by inclining the longitudinal directions 
of the bending-vibration arm and the resonant arms at an angle of 
10.degree. to 20.degree., preferably 15.degree. to the a-axis. 
That is to say, in a vibrator 60H of a vibratory gyroscope 59H, a main arm 
101N and a base part 3 project from a fixing part 1, and bending-vibration 
pieces 99A and 99B extending perpendicularly to the base part 3 are formed 
at an end part 3b side of the base part 3, and weights 47A and 47B are 
provided, respectively, at the top ends of the bending-vibration pieces. 
The bending-vibration pieces are provided, respectively, with drive 
electrodes 65A and 65B. And a pair of resonant arms 100A and 100B project 
from the fixing part 1 in parallel with the base part 3, and the resonant 
arms 100A and 100B are provided, respectively, with detection electrodes 
67A and 67B. 
Hereupon, both of a voltage applying direction in the bending-vibration 
pieces and a signal voltage direction in the resonant arms form an angle 
of 15.degree. with the a-axis, and therefore, the same piezoelectric 
constant is utilized in both arms. 
In this invention, each of the bending-vibration pieces or the resonant 
arms can be provided with a through hole extending in its longitudinal 
direction. Thanks to this, the sensor sensitivity can be improved by 
lowering the natural resonance frequency of the bending-vibration pieces 
or the resonant arms and increasing the amplitude of the resonant arms. 
FIGS. 21 and 22 show vibratory gyroscopes of such embodiments of the 
invention. 
In a vibrator 60E of a vibratory gyroscope 59E of FIG. 21, a main arm 101K 
projects from a fixing part 1 and a base part 3 projects from a fixing 
part 1, and bending-vibration pieces 78A and 78B extending perpendicularly 
to the base part 3 are formed at an end part 3b side of the base part 3. 
Weights 47A and 47B are provided, respectively, at the top ends of the 
bending-vibration pieces. Through holes 79A and 79B extending in the 
longitudinal direction of the bending-vibration pieces are formed, 
respectively, in the bending-vibration pieces. And long and narrow drive 
electrodes 80A, 80B, 80C and BOD are provided, respectively, at both sides 
of the through holes of the bending-vibration pieces. 
In this embodiment, a 130.degree. Y plate of lithium tantalate is used and 
the c-axis forms an angle of 50.degree. with the main face of the 
vibrator. The vibrator has the best temperature characteristics at this 
angle. In the bending-vibration pieces, as shown in a sectional view taken 
along A-A', since a voltage applying direction to the drive electrodes 80A 
and 80C, and a voltage applying direction to the drive electrodes 80B and 
80D are reverse to each other, the bending-vibration pieces are bent. 
A pair of resonant arms 81A and 81B project from a fixing part 1 and the 
resonant arms 81A and 81B are provided, respectively, with detection 
electrodes 83A, 83B, 83C and 83D. Through holes 82A and 82B extending in 
the longitudinal direction of the resonant arms are formed, respectively, 
in the resonant arms. And long and narrow detection electrodes 83A, 83B, 
83C and 83D are provided, respectively, at both sides of the through holes 
in the resonant arms. In the resonant arms, as shown in a sectional view 
taken along B-B', a voltage generated in the detection electrodes 83A and 
83C, and a voltage generated in the detection electrodes 83B and 83D are 
reverse to each other. 
In a vibrator 60F of a vibratory gyroscope 59F of FIG. 22, a main arm 101L 
and a base part 3 project from a fixing part 1, and a pair of 
bending-vibration pieces 85A and 85B are formed at an end part 3b side of 
the base part 3, and weights 71A and 71B are provided, respectively, at 
the top ends of the bending-vibration pieces. Each of the 
bending-vibration pieces extends in the direction forming an angle of 
120.degree. to the base part. Through holes 86A and 86B extending in the 
longitudinal direction of the bending-vibration pieces are formed, 
respectively, in the bending-vibration pieces. And drive electrodes 89A 
and 89D are provided on the outside walls of each of the through holes, 
and drive electrodes 89B and 89C are provided on the inside walls of each 
of them. 
In this embodiment, a piezoelectric single crystal plate having the a-axis 
of the triad axis of symmetry in a specified plane like quartz crystal is 
used. In each of the bending-vibration pieces, as shown in a sectional 
view taken along A-A', the drive electrodes 89A and 89D on the outside 
walls are connected to an alternating-current power source 68, and the 
drive electrodes 89B and 89C on the inside walls are grounded. Since a 
combination of the drive electrodes 89A and 89B and a combination of the 
drive electrodes 89C and 89D have voltage applying directions reverse in 
phase to each other, the bending-vibration pieces are bent. 
A pair of resonant arms 87A and 87B project from a projection 1a of a 
fixing part 1 and through holes 88A and 88B extending in the longitudinal 
direction of the resonant arms are formed, respectively, in the resonant 
arms. And as shown in a sectional view taken along B-B', detection 
electrodes 90A and 90D are provided on the outside walls of each of the 
through holes, and detection electrodes 90B and 90C are provided on the 
inside walls of each of them. In the resonant arms, a voltage generated in 
the detection electrodes 90A and 90C, and a voltage generated in the 
detection electrodes 90B and 90D are reverse in phase to each other. 
As shown in this embodiment, a bending-vibration piece or a resonant arm 
can be bent by providing a pair of drive electrodes on the inside and the 
outside wall of each of two sides of a through hole formed in the 
bending-vibration piece or the resonant arm. The detection side also goes 
in the same way. 
In this invention, the above-mentioned main arm and at least a pair of 
resonant arms can be provided at one side of the fixing piece part and a 
resonant piece to resonate with the main arm can be provided at the other 
side of the fixing piece part. In this case, drive electrodes are provided 
on a bending-vibration piece of the resonant piece and detection 
electrodes are provided on the resonant arms. By this, it is possible to 
use a bending vibration of the bending-vibration piece of the resonant 
piece as a drive vibration and use a bending vibration of the resonant arm 
as a detection vibration. Otherwise, drive electrodes are provided on the 
resonant arms and detection electrodes are provided on the 
bending-vibration piece of the resonant piece. By this, it is possible to 
use a bending vibration of the resonant arm as a drive vibration and use a 
bending vibration of the bending-vibration piece of the resonant piece as 
a detection vibration. 
In such a manner, furthermore, a second resonant arm can be provided at the 
other side of the fixing piece part. FIG. 23 is a perspective view roughly 
showing a vibratory gyroscope 59G of this embodiment. 
In this vibrator 60G, a fixing piece part 12 is provided inside a fixing 
member 90. At one side of the fixing piece part 12, a main arm 101L and a 
pair of resonant arms 92A and 92B project from a projection 94A. In the 
main arm 101L, bending-vibration pieces 91A and 91B extending 
perpendicularly to the base part 3 are formed at an end side of the base 
part 3. Drive electrodes 46A, 46B, 46C and 46D are provided on the 
bending-vibration pieces. Weights 93A and 93B are, respectively, provided 
at the top ends of the resonant arms. 
In the bending-vibration pieces 91A and 91B, as shown in a sectional view 
taken along A-A', a voltage applying direction to the drive electrodes 46A 
and 46C side and a voltage applying direction to the driving electrodes 
46B and 46D side are reverse in phase to each other. 
At the other side of the fixing piece part 12, a resonant arm 103 and a 
pair of second resonant arms 97A and 97B project from a projection 94B. In 
the resonant piece 103, bending-vibration pieces 95A and 95B extending 
perpendicularly to a base part 98 are formed at an end side of the base 
part 98. 
Weights 96A and 96B are, respectively, provided at the top ends of the 
resonant arms 97A and 97B. As shown in a sectional view taken along B-B', 
detection electrodes 49A, 49B, 49C and 49D are provided on the resonant 
arms. A signal voltage generated in the detection electrodes 49A and 49C 
side and a signal voltage generated in the detection electrodes 49B and 
49D side are reverse in phase to each other. 
A second embodiment of the invention is described in more detail in the 
following. 
FIG. 24 shows a construction of an example of a vibrator of the invention. 
In the example shown in FIG. 24, a vibrator 108 extends in the X-Y plane 
and is composed of a pair of tuning-fork vibration pieces 109a and 109b, a 
pair of bending-vibration pieces 241a and 241b for joining them in the X-Y 
plane, and a base part 3 for fixing these bending-vibration pieces on an 
external fixing member 1 in the X-Y plane. The one pair of tuning-fork 
vibration pieces 109a and 109b are almost in parallel with each other, and 
are joined with the bending-vibration pieces nearly perpendicularly to 
them. The base part 3 is joined with the nearly middle part 25 between the 
bending-vibration pieces 241a and 241b, and is almost in parallel with the 
tuning-fork vibration pieces 109a and 109b. 
In the vibrator 108 having the above-mentioned construction of the 
invention, when forces F1 and F2 different in direction from each other 
act on both ends of the bending-vibration pieces 241a and 241b of the 
tuning-fork vibrator in parallel with the tuning-fork vibration pieces 
109a and 109b, namely, in the Y direction, a bending motion B having a 
joint 26 where the base part 3 is joined with the fixing part 1 as a 
fulcrum takes place in the X-Y plane in the base part 3. 
Although the tuning-fork vibration pieces, the bending-vibration pieces, 
and the base part which form the vibrator 108 can be formed out of 
separate members, it is preferable to form them in one body from a 
viewpoint of manufacturability and the like in case of forming them out of 
a single crystal in particular. Although a material for them also is not 
limited in particular, it is preferable to use a single crystal of quartz, 
LiNbO.sub.3, LiTaO.sub.3, or Li(Nb, Ta)O3. Using these single crystals 
makes it possible to obtain a good detection sensitivity and reduce 
detection noises. And since they are insensitive to a temperature change, 
they are preferable for a sensor mounted in a car requiring a thermal 
stability. Among the above-mentioned single crystals, since single 
crystals of LiNbO.sub.3 and LiTaO.sub.3 have comparatively large 
electromechanical coupling coefficients, it is preferable to use a single 
crystal of LiNbO.sub.3 or LiTaO.sub.3 rather than a quartz crystal. 
Comparing single crystals of LiNbO.sub.3 and LiTaO.sub.3 with each other, 
a single crystal of LiTaO.sub.3 has a comparatively larger 
electromechanical coupling coefficient than a single crystal of 
LiNbO.sub.3, it is more preferable to use a single crystal of LiTaO.sub.3 
rather than a single crystal of LiNbO.sub.3. 
The vibrator 108 having the above-mentioned construction is used mainly as 
a vibratory gyroscope. A case where a vibrator 1 is used as the first 
invention of a vibratory gyroscope is considered in the following. First, 
the tuning-fork vibration pieces are vibrated exactly reversely in phase 
to each other in the X-Y plane by means of an unillustrated exciting means 
in a turning system having the Z axis as the central axis. When a turning 
angular rate .omega. acts around the Z axis in this state, a Coriolis 
force makes forces F1 and F2 reverse in direction to each other act on the 
tuning-fork vibration pieces along the Y axis. As the result, moments M1 
and K2 having the same direction act on both ends of the bending-vibration 
pieces. These moments M1 and M2 generate a bending vibration B in the X-Y 
plane in the base part 3. A turning angular rate can be measured by 
detecting this bending vibration B as deformation of the base part 3 by 
means of an unillustrated bending-vibration detecting means. 
As described above, since the vibratory gyroscope of this invention 
converts a Coriolis force generated in the same X-Y plane as the 
tuning-fork vibration pieces into a bending vibration of the base part 3 
and obtains a turning angular rate from the bending vibration, it can 
detect a turning angular rate even when the vibrator is arranged 
perpendicularly to the axis of turning (horizontally arranged). 
Accordingly, even in case of mounting the vibratory gyroscope of the 
invention as an angular-speed sensor for the purpose of obtaining a 
turning angular rate of a car body for example, it can be shortened in 
height for the mounting part. 
Although the above-mentioned example vibrates the tuning-fork vibration 
pieces and the bending-vibration pieces in the X-Y plane and obtains a 
turning angular rate from a bending vibration of the base part 3 in this 
state, it is also possible to replace vibration and measurement with each 
other. That is to say, as shown in FIG. 27, in a state of exciting a 
bending vibration B in the fixing part 3 by means of an unillustrated 
exciting means, a Coriolis force generated on the basis of a turning 
angular rate makes forces F1 and F2 having the same direction as each 
other act on the tuning-fork vibration pieces 109a and 109b along the Y 
axis. As the result, moments M1 and M2 having the different directions 
from each other act on both ends of the bending-vibration pieces. In the 
same way, a turning angular rate can be measured by using an unillustrated 
vibration detecting means which detects vibration in the X-Y plane 
generated in the tuning-fork vibrator by these moments M1 and M2 and 
generates a signal according to the detected vibration. This copposition 
is the second invention of a vibratory gyroscope of the invention. 
FIG. 25 shows the construction of another example of a vibrator of the 
invention. In the example shown in FIG. 25, the same symbols are given to 
the same members as the members shown in FIG. 24 and description of them 
is omitted. The examle shown in FIG. 25 is different from the example 
shown in FIG. 24 in that projections 111a and 111b, respectively, 
projecting outer than the tuning-fork vibration pieces 109a and 109b are 
provided at both ends of the bending-vibration pieces 241a and 241b 
forming the tuning-fork vibrator. In the example shown in FIG. 25, 
relation between the resonance frequency of vibration in the X-Y plane of 
the tuning-fork vibrator and the resonance frequency of a bending 
vibration of the base part can be simply adjusted to a specified relation 
by reducing at least one of the projections 111a and 111b in projection 
height. 
Hereupon, when the resonance frequency of the tuning-fork vibrator and the 
resonance frequency of the base part 3 become close to each other, the 
sensitivity becomes good but the response speed is deteriorated, and when 
both of them become distant from each other, the response speed becomes 
good but the sensitivity is deteriorated. Therefore, relation between the 
resonance frequency of vibration in the X-Y plane of the tuning-fork 
vibrator and the resonance frequency of a bending vibration of the base 
part 3 is adjusted to a specified relation in which both of the 
sensitivity and the response speed become good to some degree. 
FIG. 26 shows the construction of a further other example 98 of a vibrator 
of the invention. In the example shown in FIG. 26 also, the same symbols 
are given to the same members as the example shown in FIG. 24 and 
description of them is omitted. The example shown in FIG. 26 is different 
from the example shown in FIG. 24 in that while the tuning-fork vibration 
pieces 109a and 109b project from the bending-vibration pieces in a 
direction opposite to the base part 3 in relation to the bending-vibration 
pieces in the example shown in FIG. 24, the tuning-fork vibration pieces 
109a and 109b project in the same direction as the base part 3 in the 
example shown in FIG. 26. A vibratory gyroscope can be made more compact 
by forming it as shown in FIG. 26. 
The variation examples of a vibrator shown in FIGS. 25 and 26 also are used 
mainly in a vibratory gyroscope in the same way as the vibrator shown in 
FIG. 24, and act also in the same way as the example shown in FIG. 24. At 
that time, as an exciting means, a bending-vibration detecting means, and 
a vibration detecting means which are not illustrated, piezoelectric 
members of piezoceramic or the like can be preferably used in the same way 
as used up to now. And in case of using a vibrator made of a piezoelectric 
single crystal as a vibrator, an exciting means, a bending-vibration 
detecting means and a vibration detecting means can be formed by providing 
electrodes at specified positions. Furthermore, in a vibratory gyroscope 
using a vibrator having the construction shown in FIGS. 24 or 25, since it 
is possible to form an exciting means and a bending-vibration detecting 
means or a vibration detecting means at positions distant from each other 
as well as to shorten the gyroscope in height by horizontally arranging 
it, it is possible to further reduce a bad influence of an 
electromechanical coupling or the like between both of the exciting means 
and the detecting means. 
Moreover, in any example, a vibrator of the invention can excite a drive 
vibration and a detection vibration in the same plane, and can arrange 
both of the vibrations in the same direction. Therefore, even in case of 
forming a vibrator of the invention out of a single crystal of quartz, 
LiNbO.sub.3, LiTaO.sub.3 or the like, if a frequency difference between 
the resonance frequency of a drive vibration and the resonance frequency 
of a detection vibration is adjusted to a certain frequency difference at 
which the detection sensitivity becomes the best, the relation between 
them is kept and is not influenced by anisotropy of the single crystal 
even when temperature varies. Therefore, a good detection sensitivity, a 
small detection noise, and a high thermal stability which are features of 
a single crystal known from the past can be displayed to the maximum. 
A third embodiment of the invention is described in the following. 
In an example shown in FIG. 28, a vibrator is provided with a fixing piece 
part 115 both ends of which are fixed on fixing members 114, and a main 
arm 121 composed of a tuning-fork vibrator 118 formed by joining a pair of 
tuning-fork vibration pieces 119a and 119b with bending-vibration pieces 
241a and 241b in a specified plane and a base part 3 for fixing this 
tuning-fork vibrator on the fixing piece part 115 in a plane. And the 
vibrator is provided with a resonant piece 123 provided on the fixing 
piece part at a position which corresponds to and is opposite to the base 
part 3. In this example, as the resonant piece 123, a resonant piece which 
has the same shape and the same composition as the main arm 121 is 
provided on the fixing piece part at a position line-symmetrical to the 
main arm in relation to the fixing piece part. In this case, a vibration 
frequency of the main arm and the resonance frequency of the resonant 
piece can be made equal to each other. Hereupon, 122 is a joint at the 
resonant piece side, 120a and 120b represent driving electrodes, 117 
represents a detecting electrode, and they are necessary for forming the 
whole vibratory gyroscope out of a single crystal. 
Although the fixing piece part, the main arm, and the resonant piece can be 
formed out of separate members, it is preferable to form them in one body 
from a viewpoint of ease of manufacture or the like in case of forming 
them out of a single crystal in particular. Although a material for them 
is not limited in particular, as described above, it is preferable to use 
a single crystal of quartz, LiNbO.sub.3, LiTaO.sub.3, or Li(Nb, 
Ta)O.sub.3. 
In a vibrator of the invention having the above-mentioned construction, 
when forces F1 and F2 different in direction from each other act on both 
ends of the bending-vibration pieces of the tuning-fork vibrator 118 in 
parallel with the tuning-fork vibration pieces 119a and 119b, namely, in 
the Y direction, a bending vibration B1 having a joint 116 where the base 
part 3 is joined with the fixing piece part 115 as a fulcrum is generated 
in the base part 3 in the X-Y plane. At the same time, a bending vibration 
B2 in the same direction with the joint 116 as a fulcrum is generated by 
this bending vibration B1 of the base part 3. Accordingly, a drive 
vibration of the vibrator is as shown in FIG. 29(a), and a bending 
vibration for detection of the vibrator at this time is as shown in FIG. 
29(b). 
The vibrator having the above-mentioned construction is used mainly as a 
vibratory gyroscope. A case where a vibrator is used as the first 
invention of a vibratory gyroscope is thought with reference to FIG. 28 in 
the following. First, the tuning-fork vibration pieces are vibrated 
completely reverse in phase to each other in the X-Y plane by means of 
drive electrodes 120a and 120b as an exciting means in a turning system 
having the Z axis as the central axis. When a turning angular rate.omega. 
acts around the Z axis in this state, a Coriolis force makes forces F1 and 
F2 along the Y axis in reverse directions to each other act on the 
tuning-fork vibration pieces. As the result, moments M1 and M2 in the same 
direction act on both ends of the bending-vibration pieces of the 
tuning-fork vibrator 118. Thanks to these moments M1 and M2, a bending 
vibration B1 in the X-Y plane is generated in the base part 3 of the main 
arm, and a bending vibration B2 in the X-Y plane is generated also in the 
resonant piece 123. A turning angular rate .omega. can be measured by 
detecting this bending vibration B2 by means of a detecting electrode 117 
as a bending-vibration detecting means provided on the resonant piece. 
As described above, since a vibratory gyroscope of the invention converts a 
Coriolis force generated in the same X-Y plane as the tuning-fork 
vibration pieces into a bending vibration of the base part 3 and the 
resonant piece 123 and obtains a turning angular rate from the bending 
vibration, it can detect a turning angular rate even when the vibrator is 
disposed perpendicularly to the axis of turning (horizontally disposed). 
Accordingly, even in case of mounting the vibratory gyroscope of the 
invention as an angular-speed sensor for the purpose of obtaining a 
turning angular rate of a car body for example, it can be shortened in 
height for the mounting part. And in this examle, since the vibratory 
gyroscope is provided with the main arm and the resonant piece at 
positions symmetrical to each other in relation to the fixing piece part 
115, a driving means provided on the main arm and a detecting means 
provided on the resonant piece can be made distant from each other, and a 
bad influence such as an electro-mechanical coupling or the like can be 
prevented. 
FIGS. 30 to 33 show the construction of other examples of the invention. In 
FIGS. 30 to 33, the same symbols are given to the same members as the 
members shown in FIG. 28 and description of them is omitted. In the 
example shown in FIG. 30, a resonant piece 123 is composed of a 
rectangular resonant piece 124 extending from and perpendicularly to a 
fixing piece part 115. In this case, the vibrator can be simplified in 
construction. In the example shown in FIG. 31, the resonant piece shown in 
FIG. 30 is shortened and an expanded part 126 is provided at the top end 
of a resonant piece 125. Thanks to this, this example can make the 
resonant piece lower in projection height from a fixing piece part and can 
make the vibrator more compact, and moreover can make the resonance 
frequency of the resonant piece closer to a vibration frequency of the 
main arm in comparison with the example shown in FIG. 30. Differently from 
the example shown in FIG. 28, in an example shown in FIG. 32 a pair of 
tuning-fork vibration pieces 119a and 119b is projected in the same 
direction as the base part 3 from the bending-vibration pieces 241a and 
241b. Thanks to this, the gyroscope can be made more compact in comparison 
with the example shown in FIG. 28. 
An example shown in FIG. 33 forms the second invention of a vibratory 
gyroscope of the invention. That is to say, although the vibratory 
gyroscope using the vibrator of the invention shown in FIG. 28 vibrates 
the tuning-fork vibrator 118 in the X-Y plane and obtains a turning 
angular rate from the bending vibration of the resonant piece 9 in that 
state, this example replaces vibration and measurement with each other in 
composition. In the example shown in FIG. 33, in a state where a bending 
vibration B1 is generated in a base part 3 by a drive electrode 250 as an 
exciting means and a bending vibration B2 is generated in a base part 125 
of a resonant piece 123, a Coriolis force generated on the basis of a 
turning angular rate makes forces F1 and F2 along the Y axis in the same 
direction act on the tuning-fork vibration pieces 127a and 127b. As the 
result, moments M1 and M2 in different directions from each other act on 
both ends of the tuning-fork vibrator 128. A turning angular rate can be 
measured by using detecting electrodes 117a and 117b as a vibration 
detecting means for detecting vibration in the X-Y plane generated in the 
tuning-fork vibrator 128 by these moments M1 and M2 and generating a 
signal according to the detected vibration. It is a matter of course that 
a turning angular rate can be also measured by means of only one of the 
detecting electrodes 117a and 117b. In this example, 126 represents a 
joint. 
In variation examples shown in FIGS. 30 to 33, on the assumption that the 
whole of a vibrator is formed out of a single crystal of quartz, 
LiNbO.sub.3 or LiTaO.sub.3, although a driving electrode is provided as an 
exciting means and a detecting electrode is provided as a 
bending-vibration detecting means, in case of forming a vibrator out of 
another material used for a vibratory gyroscope up to now, a piezoelectric 
material of piezoceramic or the like can be preferably used as an exciting 
means, a bending-vibration detecting means and a vibration detecting means 
in the same way as used from the past. 
FIG. 34 shows the construction of a further other example of a vibrator of 
the invention. In the example shown in FIG. 34, the same symbols are given 
to the same members as the members shown in FIG. 28, and description of 
them is omitted. The example shown in FIG. 34 is different from the 
example shown in FIG. 28 in that projections 127a and 127b, respectively, 
extending outer than the tuning-fork vibration pieces 119a and 119b are 
provided at both ends of the bending-vibration pieces 241a and 241b 
forming the tuning-fork vibrator 118. In the example shown in FIG. 34, 
relation between the resonance frequency of vibration in the X-Y plane of 
the tuning-fork vibrator and the resonace frequency of a bending vibration 
of a base part and a resonant piece can be simply adjusted to a specified 
relation by reducing at least one of the projections in projection height. 
Hereupon, when the resonance frequency of the tuning-fork vibrator and the 
resonance frequency of the base part and the resonant piece become close 
to each other, the sensitivity becomes good but the response speed is 
deteriorated, and when both of them become distant from each other, the 
response speed becomes good but the sensitivity is deteriorated. 
Therefore, relation between the resonance frequency of vibration of the 
tuning-fork vibrator and the resonance frequency of a bending vibration of 
the base part and the resonant piece is adjusted to a specified relation 
in which both of the sensitivity and the response speed become good to 
some degree. 
A fourth embodiment of the invention is described in the following. 
FIGS. 35 to 38 illustrate mainly the shapes of vibrators of vibratory 
gyroscopes of the invention. 
FIG. 35 is a perspective view showing a vibrator 98 of this embodiment. 
Since this is almost the same as the vibrator 98 shown in FIG. 26 in this 
specification, description of the duplicated parts is omitted and the 
above-mentioned description is quoted. In FIG. 35, 111a and 111b represent 
projections. 
FIG. 36 is a front view showing another vibrator 101E, and since this is 
almost the same as the vibrator shown in FIG. 11 in this specification, 
description of the duplicated parts is omitted and the above-mentioned 
description is quoted. 
A vibrator as described above can be applied to a vibrator called a 
H-shaped vibrator. For example, a vibrator provided with a fixing piece 
part both ends of which are fixed, a base part provided at one side of the 
fixing piece part, at least one bending-vibration piece extending from the 
base part in a direction crossing the longitudinal direction of the base 
part, and a resonant piece provided at the other side of the fixing piece 
part, wherein the fixing piece part, the base part, the bending-vibration 
piece, and the resonant piece are formed so as to extend substantially in 
a specified plane can be manufactured. 
FIG. 37 is a front view showing a vibrator 10 of this embodiment. Since 
this is almost the same as the vibrator shown in FIG. 6 in this 
specification, description of the duplicated parts is omitted. 
FIG. 38 is a front view showing a three-forked tuning-fork vibrator 131. 
The vibrator 131 is provided with a base part 135 to be fixed on an 
external fixing member and three vibration pieces 132, 133 and 134 of a 
three-forked type projecting from the base part. The vibration pieces 132 
and 134 at both sides comprise main body parts 132a and 134a projecting 
long and slenderly from the base part 135, and weight parts 132b and 134b 
respectively extending from and perpendicularly to the main body parts. 
Detecting electrodes 136 and 137 are formed, respectively, on the 
vibration pieces 132 and 134. A pair of driving electrodes 138A and 138B 
are formed on the middle vibration piece 133. 
In any of the examples shown in FIGS. 35 to 38, since a vibratory gyroscope 
can be formed in a state where a vibrator is horizontally disposed, it is 
possible to shorten the gyroscope in height. And since a specified single 
crystal is used as a vibrator so that the vibrator can be made by means of 
etching, grinding or the like, the vibrator can be simply manufactured and 
the gyroscope can be produced at a low cost. Moreover, as shown in FIG. 
37, in case of providing a vibration piece and a resonant piece on a 
fixing piece part symmetrically to each other in relation to the fixing 
piece part, since a driving means provided on the vibration piece and a 
detecting means provided on the resonant piece can be made distant from 
each other, it is possible to prevent a bad influence caused by an 
electromechanical coupling or the like between both of them. 
A method for detecting a turning angular rate in a vibratory gyroscope 
provided with a horizontal-arrangement vibrator composed of a 
piezoelectric single crystal having the above-mentioned composition is 
described in the following. First, in a method for detecting a turning 
angular rate in a former gyroscope, it is known that a leakage signal due 
to an unnecessary vibration which is generated by an influence of a drive 
signal and is caused by an insufficient machining accuracy or the like is 
contained in an output signal detected by a detecting means. Since when 
this leakage signal is large it is difficult to detect a gyroscopic signal 
caused by a Coriolis force in an output signal, a former method of 
obtaining a turning angular rate from the amplitude of an output signal 
has removed the influence of a leakage signal by means of taking a 
differential output from detecting means provided at two positions. 
Such an influence of a leakage signal becomes hardly a problem in a 
vibratory gyroscope using a vibrator which is a vertical-arrangement 
tuning-piece vibrator as disclosed in the Japanese patent publication 
Tokkohei No. 4-14734 described in the prior art section, furthermore is 
formed out of a constant-elasticity metal, and is high in detection 
sensitivity. Moreover, as disclosed in the Japanese patent publication 
Tokkohei No. 4-14734, in case of detecting a turning angular rate on the 
basis of variation of a phase difference between a drive signal and 
detection signal, since variation of a phase difference is little 
influenced by a leakage signal, the leakage signal becomes hardly a 
problem. 
In case of horizontally disposing a vibrator in the same manner as the 
present invention, since a gyroscopic signal caused by a Coriolis force is 
made small due to its composition and the detection sensitivity is low, it 
is thought in general that the above-mentioned method of detection by a 
phase difference cannot be applied as it is. As the result of studying 
this point in various ways, the inventors have found that a turning 
angular rate can be accurately detected on the basis of a phase difference 
between a reference signal and an output signal even in a range where a 
leakage signal is large and a gyroscopic signal is small, by using a 
piezoelectric single crystal. Additionally, the inventors have found that 
an output signal in a range where a leakage signal is fairly larger and a 
gyroscopic signal is fairly smaller than those in a range which is thought 
to be suitable for measurement in general is better in linearity of a 
phase difference to a turning angular rate and can be measured in higher 
accuracy. 
FIG. 39 is a block diagram showing an example of a phase difference 
detecting means in a vibratory gyroscope of the invention. In FIG. 39, it 
is assumed that an electric signal used for generating a drive vibration 
is a reference signal and an electric signal taken out by a detecting 
means from a vibration which has a vibration mode different from the drive 
vibration and is generated with the drive vibration is an output signal. 
Concretely, in the example shown in FIG. 35, an electric signal supplied to 
an unillustrated driving electrode provided on the tuning-fork vibration 
piece 109a or 109b is a reference signal, and an electric signal detected 
by an unillustrated detecting electrode provided on the base part is an 
output signal. And in the example shown in FIG. 36, an electric signal 
supplied to the exciting means 5A and 5B is a reference signal, and an 
electric signal detected by the detecting means 6A, 6B, 6C and 6D is an 
output signal. Furthermore, in the examle shown in FIG. 37, an electric 
signal supplied to the exciting means 5A and 5B is a reference signal, and 
an electric signal detected by the detecting means 6A, 6B, 6C and 6D is an 
output signal. Still further, in the example shown in FIG. 38, an electric 
signal supplied to the electrodes 136 and 137 is a reference signal, and 
an electric signal detected by the electrodes 138A and 138B is an output 
signal. 
Although in the above-mentioned examples an electric signal used for 
generating a drive vibration is used as a reference signal, an electric 
signal obtained by resonating the drive vibration itself can be used as a 
reference signal. 
In a phase detecting means 139 shown in FIG. 39, an output signal is 
amplified by an alternating-current amplifier 140 and then is supplied to 
a phase different detecting circuit 141. A reference signal is 
preprocessed for waveform-shaping or the like by a reference signal 
preprocessing circuit 142, and then is supplied to a phase different 
detecting circuit 141 in the same way. The phase difference detecting 
circuit 141 detects a phase difference between a preprocessed reference 
signal and an output signal which have been supplied. The detected phase 
difference is supplied to a low-pass filter 143 and a direct-current 
amplifier 144 to be a direct-current signal according to the phase 
difference. A direct-current signal obtained by the above-mentioned phase 
difference detecting means 139 is supplied to a turning angular rate 
detecting circuit 145. The turning angular rate detecting circuit obtains 
a turning angular rate on the basis of a predetermined relation between 
the magnitude of a direct current and a turning angular rate. Since the 
above-mentioned circuit cannot directly obtain a phase difference between 
an output signal and a reference signal as a numerical value, it obtains a 
turning angular rate from the magnitude of a direct-current signal 
according to a phase difference, but it is possible also to directly 
obtain a phase difference as a numerical value and then obtain a turning 
angular rate on the basis of a predetermined relation between a phase 
difference and a turning angular rate. 
Relation between a leakage signal and a gyroscopic signal which form an 
output signal is described in the following. The inventors have obtained a 
phase difference between a reference signal and an output signal and 
examined the relationship between a variation of the obtained phase 
difference and a turning angular rate in a vibratory gyroscope having a 
vibrator which has the construction shown in FIG. 38 and is composed of a 
single crystal of LiTaO.sub.3. The result is shown in FIGS. 40 to 42. FIG. 
40 shows the relation in case that the ratio of a gyroscopic signal to a 
leakage signal is 1:100 at a turning angular rate of 100.degree./second, 
FIG. 41 shows the relation in case that the ratio of a gyroscopic signal 
to a leakage signal is 1:7 at a turning angular rate of 
100.degree./second, and FIG. 42 shows the relation in case that the ratio 
of a gyroscopic signal to a leakage signal is 5:1 at a turning angular 
rate of 100.degree./second. Hereupon, the ratio of the amplitude of a 
signal which is excited by a Coriolis force and is outputted at the time 
of turning at a turning angular rate of 100.degree./second in an output 
signal to the amplitude of a signal which is outputted at the time of 
turning at a turning angular rate of zero in an output signal is referred 
to as the ratio of a gyroscopic signal to a leakage signal at a turning 
angular rate of 100.degree./second. A vector diagram shown in each of the 
figures shows the relationship among an output signal, a gyroscopic signal 
and a leakage signal under each condition in case of taking a phase angle 
in a turning direction with the origin of a vector as the center, and 
taking the magnitude of a signal in a radial direction. And each of the 
figures shows a case where a leakage signal and a reference signal are the 
same in phase, and represents a phase difference between a leakage signal 
and a output signal as a phase difference between a reference signal and 
an output signal. Hereupon, in case that there is a certain phase 
difference between a leakage signal and a reference signal, variation of a 
phase difference is as illustrated. 
From the result shown in FIG. 40, it has been found that in a vibratory 
gyroscope using a horizontal-arrangement vibrator also, in case of using a 
piezoelectric single crystal, it is possible to detect a minute phase 
difference of such a low level as shown in FIG. 40 and obtain a high 
linearity between a phase difference and a turning angular rate in such a 
case. From the result shown in FIG. 41 also, it has been found that it is 
possible to obtain a high linearity although it is not so good as shown in 
FIG. 40. On the other hand, from the result shown in FIG. 42, it has been 
found that the linearity between a phase difference and a turning angular 
rate cannot be kept, the usable range is limited to a turning angular rate 
of .+-.50.degree./second or so, and it is difficult to detect a phase 
difference at a turning angular rate in a range of 70.degree. to 
100.degree./second. The above-mentioned results are collected as relation 
between the linearity of a phase difference to a turning angular rate and 
the ratio of a gyroscopic signal to a leakage signal in FIG. 43. 
Since it is generally thought to need a linearity of .+-.1%, when obtaining 
a range satisfying the above-mentioned conditions from the result shown in 
FIG. 43, it has been found that the above-mentioned relation of linearity 
can be obtained in a range where a leakage signal is so large that the 
ratio of a gyroscopic signal to a leakage signal is 1:7 or more. However, 
too large a leakage signal exceeds the detection limit of a vibrator even 
if it uses a piezoelectric single crystal. Therefore, the upper limit of a 
leakage signal is determined according to the sensitivity of a vibratory 
gyroscope. 
In the present invention, as described above, in a range where the ratio of 
a leakage signal to a gyroscopic signal is larger than a specified ratio 
at a specified turning angular rate, the detection sensitivity is low but 
the linearity of a phase difference to a turning angular rate is good, and 
it is possible to improve the signal-to-noise ratio in relation to noises 
caused by external factors in comparison with the prior art by forming a 
horizontal-arrangement vibrator out of a piezoelectric single crystal good 
in mechanical quality. Since the invention can cope with a large leakage 
signal and does not need a manufacturing apparatus of high machining 
accuracy for manufacturing a vibrator, the invention can greatly reduce 
the manufacturing cost and can dispense with an adjusting process by 
reprocessing performed according to circumstances up to now. And the 
invention dispenses with a circuit and the like for removing a leakage 
signal provided according to circumstances up to now. 
A fifth embodiment of the invention is described in the following. 
The inventors made a vibrator 147 shown in FIG. 44, and performed an 
experiment of detecting a turning angular rate using the vibrator. 
Hereupon, the vibrator is formed out of a piezoelectric single crystal, 
and is provided with a fixing part 2 fixed on an external construction and 
a pair of long and narrow tuning-fork vibration arms 148A and 148B 
projecting from the fixing part 2. A gap 149 is formed between the pair of 
vibration arms. In a coordinate system shown in FIG. 44, main faces 150A 
and 150B of the vibrator are directed to the Y-axis direction, and side 
faces 151A and 151B are directed to the X-axis direction. 
The vibration arms of the vibrator are vibrated in the X direction as shown 
by arrows C and D. When the vibrator is turned around the Z axis as shown 
by .omega. in this state, the vibration arms are respectively vibrated in 
the Y-axis direction as shown by arrows A and B. A turning angular rate is 
computed by detecting this vibration. Theoretically, it is possible to 
first vibrate the vibration arms as shown in arrows A and B, turn the 
vibrator around the Z axis in this state, vibrate the vibration arms as 
shown by arrow C and D, and detect this vibration. 
In such a vibrator 147, the vibration arms 148A and B need to be vibrated 
in the Y-axis direction, or vibrations of the vibration arms in the Y-axis 
direction need to be converted to electric signals. As for such an 
exciting method, a method shown in FIG. 45 is disclosed in "Three-Forked 
Tuning-Fork Resonator Aiming at a Horizontal-Arrangement Vibratory 
Gyroscope Sensor" in pp. 1071 to 1072 of "Japan Society of Acoustics 
Engineers '96 Spring Convention Proceedings II issued in March 1996 by 
Japan Society of Acoustics Engineers". FIG. 45(a) is a plan view of the 
vibration arm 148A or 148B, and FIG. 45(b) is a front view of it. 
Electrodes 152A and 152B are formed, respectively, on the main faces 150A 
and 150B of each vibration arm, and electrodes 153A and 153B are also 
formed, respectively, on the side faces 151A and 151B. The direction of 
polarization of a piezoelectric single crystal forming the vibration arms 
is assumed as a direction shown by arrow E. It is assumed that the 
opposite electrodes 152A and 152B are the same in phase, and the opposite 
electrodes 153A and 153B are the same in phase. At a certain moment the 
opposite electrodes 152A and 152B become negative, and the opposite 
electrodes 153A and 153B become positive. 
At this time, in the upper half part of the vibration arm in FIG. 45(a), an 
electric field is generated slantly upward as shown by arrows F and G. A 
component of this electric field in the Y-axis direction is in the +Y 
direction, which coincides with the direction of polarization E of the 
piezoelectric single crystal. Therefore, the vibration arm is contracted 
as shown by aoK in FIG. 45(b). 
On the other hand, in the lower half part of the vibration arm in FIG. 
45(a), an electric field is generated slantly downward as shown by arrow H 
and I. A component of this electric field in the Y-axis direction is in 
the -Y direction, which is reverse to the direction of polarization E of 
the piezoelectric single crystal. Therefore, the vibration arm is extended 
as shown by arrow J in FIG. 45(b). As the result, the vibration arm is 
bent as shown arrow A(B). 
As a result of a detailed examination of the vibrator performed by the 
inventors, the following problem has been found. That is to say, although 
it is preferable to make larger the magnitude of displacement in a bending 
vibration generated by an applied voltage, it has been found that this has 
a limit. And displacements of bending vibrations in the respective parts 
inside the vibration arm are uniform in magnitude, and internal strain or 
internal stress is generated inside the vibration arm at the time of 
vibration. Due to this, the magnitude of an applied voltage and the 
magnitude of displacement of a bending vibration of the vibration arm do 
not have necessarily a linear relation, and the vibrators have large 
variations in production with regard to the relation between the magnitude 
of an applied voltage and the magnitude of displacement of a bending 
vibration of the vibration arm. 
This is thought to be caused by ununiformity in the internal electric field 
of the vibration arm in FIG. 45(a). For example, an electric field is 
applied as shown in arrow F or H in a domain 154 close to a corner, and in 
these domains, the electrodes 153A and 153B and the electrodes 152A and 
152B are, respectively, close to each other, and so a strong electric 
field is applied to the piezoelectric single crystal at each of these 
domains. On the other hand, an electric field is applied as shown in arrow 
G or I in a domain 155 distant from a corner, and an applied electric 
field is weak in such a domain 155 distant from a corner. In this way, it 
is thought that an electric field greatly varies with the position in the 
piezoelectric single crystal forming a vibrator and this variation appears 
as internal stress and internal strain. 
FIG. 46 is a perspective view showing a vibratory gyroscope of an 
embodiment of the invention, FIG. 47(a) is a plan view of a plane-normal 
vibration arm 158A in FIG. 46, FIG. 47(b) is a front view of the 
plane-normal vibration arm 158A taken in the direction of the X axis, and 
FIG. 48 is a schematic view for explaining operation of a plane-parallel 
vibration 154. 
A vibrator 156 is provided with a fixing part 157 fixed on an external 
fixing member, and a pair of tuning-fork vibration arms 154 and 158A (158B 
or 158C) projecting from the fixing part. The whole vibrator is composed 
of a joined member obtained by joining two plate-shaped members 159A and 
159B to each other. The direction of polarization (shown by arrow 165) of 
the plate-shaped member 159A and the direction of polarization (shown by 
arrow 166) of the plate-shaped member 159B are exactly opposite to each 
other, and are perpendicular to one main face 161A and the other main face 
161B. 
One electrode 163A and the other electrode 163B are respectively formed on 
the main faces of the plane-normal vibration arm 158A. No electrode is 
formed on the respective side faces 162A and 162B of the vibration arm 
158A. And electrodes 155A and 155B are formed on one main face 161A of the 
plane-parallel vibration arm 154, and electrodes 155C and 155D are formed 
on the other main face 161B of it, and no electrode is formed on the 
respective side faces of the vibration arm 154. A gap 160 is provided 
between the vibration arms 154 and 158A. 
In a coordinate system shown in FIG. 46, the main faces of the vibrator are 
directed to the Y-axis direction, and the side faces are directed to the 
X-axis direction. 
The plane-normal vibration arm 158A is vibrated by applying an alternating 
voltage to a pair of electrodes 163A and 163B. In this case, at a certain 
moment one electrode 163A becomes positive and the other electrode 163B 
becomes negative as shown in FIG. 47(a). At this moment a voltage is 
applied from the electrode 163A to the electrode 163B. 
At this time the direction of an electric field and the direction of 
polarization 165 become exactly opposite to each other inside the 
plate-shaped member 159A. As the result, the plate-shaped member 159A is 
expanded as shown by arrow J as shown in FIG. 47(b). On the other hand, 
the direction of an electric field and the direction of polarization 166 
become the same as each other inside the plate-shaped member 159B. As the 
result, the plate-shaped member 159B is contracted as shown by arrow K as 
shown in FIG. 47(b). By this, the whole vibration arm can be 
bending-vibrated as shown by arrow B. At this time the plane-parallel 
vibration arm 154 is resonated as shown by arrow A by setting the 
resonance frequencies of the vibration arms as a specified value. 
When the vibrator is turned around the Z axis as shown by .omega. in this 
state, the vibration arms 154 and 158A are respectively vibrated in the 
X-axis direction as shown by arrows C and D. A turning angular rate is 
computed by detecting a plane-parallel vibration as shown by arrow C by 
means of the plane-parallel vibration arm 154. 
Concretely, as shown in FIG. 48, the electrodes 155A and 155C are connected 
to a voltage detecting apparatus 168, and the electrodes 155B and 155C are 
grounded. When a bending vibration as shown by arrow C is applied to the 
plane-parallel vibration arm 154 in this state, an electric field as shown 
by arrow 167 is excited, and according to this, electromotive forces are 
generated, respectively, between the electrodes 155A and 155B, and between 
the electrodes 155C and 155D. This voltage signal is detected and a 
turning angular rate is detected from this value. 
The plane-normal vibration arm 154 of the vibration can be vibrated in the 
X direction as shown by arrow C. In order to do so, the electrodes 155A 
and 155C are connected to a specified alternating-current power source, 
and an electric field 167 is applied between the electrodes 155A and 155B, 
and between the electrodes 155C and 155D. In this case, in FIG. 48 the 
direction of an electric field and the direction of polarization become 
reverse to each other in domains close to the electrodes 155A and 155C in 
the plane-parallel vibration arm 154, while the direction of an electric 
field and the direction of polarization become nearly equal to each other 
in domains close to the electrodes 155B and 155D. Thanks to this, the 
plane-parallel vibration arm is vibrated as shown by arrow C. On the other 
hand, the plane-normal vibration arm is resonated as shown by arrow D. 
When the vibrator is turned around the Z axis as shown by .omega. in this 
state, the vibration arms 154 and 158A are respectively vibrated in the 
Y-axis direction as shown by arrows A and B. An electromotive force is 
generated between the electrodes 163A and 163B by this vibration of the 
vibration arm 158A. At this time the electrodes 163A and 163B are 
connected to a specified voltage detecting apparatus 168. A turning 
angular rate is computed by measuring this voltage. 
FIGS. 49(a) and 50(a) are, respectively, plan views of vibration arms of 
vibrators of other embodiment of the invention, and FIGS. 49(b) and 50(b) 
are, respectively, front views of the vibration arms of FIGS. 49(a) and 
50(a) taken in the direction of the X axis. The same symbols are given to 
the same components as the components shown in FIGS. 47(a) and 47(b), and 
description of them is omitted. 
In FIGS. 49(a) and 49(b), the vibration arm 158B is composed of a joined 
member obtained by joining a pair of plate-shaped members 169A and 169B to 
each other. The direction of polarization (shown by arrow 180) of the 
plate-shaped member 169A and the direction of polarization (shown by arrow 
181 ) of the plate-shaped member 169B are exactly opposite to each other, 
and are perpendicular to one main face 161A and the other main face 161B. 
An alternating voltage is applied to a pair of electrodes. In this case, at 
a certain moment one electrode 163A becomes negative and the other 
electrode 163B becomes positive as shown in FIG. 49(a). At this moment a 
voltage is applied from the electrode 163B to the electrode 163A. 
At this time the direction of an electric field and the direction of 
polarization become exactly opposite to each other inside the plate-shaped 
member 169A. As the result, the plate-shaped member 169A is expanded as 
shown by arrow J as shown in FIG. 49(b). On the other hand, the direction 
of an electric field and the direction of polarization become equal to 
each other inside the plate-shaped member 169B. As the result, the 
plate-shaped member 169B is contracted as shown by arrow K as shown in 
FIG. 49(b). Thanks to this, the whole vibration arm 158B is 
bending-vibrated as shown by arrows A and B. 
In FIGS. 50(a) and 50(b), the vibration arm 158C is composed of a joined 
member obtained by joining a pair of plate-shaped members 251A and 251B to 
each other. The direction of polarization (shown by arrow 165) of the 
plate-shaped member 251A is perpendicular to the main faces. The direction 
of polarization (shown by arrow 172) of the plate-shaped member 251B is in 
parallel with the main faces. In such a case also, the vibration arm of 
the invention can be moved perpendicularly to the main faces. 
That is to say, an alternating voltage is applied to a pair of electrodes. 
In this case, at a certain moment one electrode 163A becomes positive and 
the other electrode 163B becomes negative as shown in FIG. 50(a). At this 
moment a voltage is applied from the electrode 163A to the electrode 163B. 
At this time the direction of an electric field and the direction of 
polarization become exactly opposite to each other inside the plate-shaped 
member 251A. As the result, the plate-shaped member 251A is expanded as 
shown by arrow J as shown in FIG. 50(b). On the other hand, contraction 
and expansion in such a direction are a little inside the plate-shaped 
member 251B. However, the whole vibration arm 158C is bending-vibrated as 
shown by arrows A and B due to expansion and contraction of the 
plate-shaped member 251A. 
FIGS. 51 to 53 are, respectively, perspective views showing three-forked 
tuning-fork vibrators of vibratory gyroscopes of the invention. In FIGS. 
51 to 53, description of the composition already described in FIG. 47 is 
omitted. 
A vibrator 170 of a vibratory gyroscope shown in FIG. 51 is provided with a 
fixing part 157 fixed on an external fixing member, and three tuning-fork 
vibration arms 171A, 172 and 171B projecting from the fixing part. The 
whole vibrator is composed of a joined member obtained by joining two 
plate-shaped members 159A and 159B to each other. The direction of 
polarization of the plate-shaped member 159A and the direction of 
polarization of the plate-shaped member 159B are exactly opposite to each 
other, and are perpendicular to the main faces 161A and 161B. 
One electrode 163A is formed on one main face 161A of each of the 
plane-normal vibration arms 171A and 171B, and the other electrode 163B is 
formed on the other main face 161B (163B is not illustrated; see FIG. 
47).In the plane-parallel vibration arm 172, the above-mentioned 
electrodes 155A and 155B are formed on one main face, and the opposite 
electrodes 155C and 155D are formed on the other main face (155C and 155D 
are not illustrated; see FIG. 48). 
Gaps 160 are formed, respectively, between the vibration arms 171A and 172 
and between the vibration arms 172 and 171B. In each of coordinate systems 
shown in FIGS. 51 to 53, the main face of the vibrator is directed to the 
Y-axis direction, and the side face is directed to the X-axis direction. 
In FIG. 51, for example, the middle plane-parallel vibration arm 172 is 
excited as shown by arrow Q, and the vibration arms 171A and 171B at both 
sides are resonated, respectively, as shown by arrows P and R. When the 
vibrator 170 is turned around the Z axis as shown by arrow .omega., the 
vibration arms 171A and 171B are vibrated in the Y-axis direction, 
respectively, as shown by arrows S and U. At the same time, the middle 
vibration arm 172 is vibrated in the Y-axis direction as shown by arrow T. 
According to the invention, these vibrations of the vibration arms 171A 
and 171B generate electromotive forces among the electrodes. A turning 
angular rate is detected by measuring this voltage. 
A vibrator 173 shown in FIG. 52 is provided with plane-parallel vibration 
arms 172A and 172B at both sides and a plane-normal vibration arm 171 in 
the middle. The plane-parallel vibration arms at both sides are, 
respectively, driven in the X-axis direction as shown by arrows P and R, 
and the middle plane-normal vibration arm is resonated as shown by arrow 
Q. After this, the operation is the same as the case of FIG. 51. 
And according to the invention, it is possible to drive the middle 
plane-normal vibration arm as shown by arrow T and resonate the 
plane-parallel vibration arms at both sides, respectively, as shown by 
arrows S and U. When the vibrator is turned around the Z axis as shown by 
.omega. in this state, the vibration arms 172A and 172B are vibrated in 
the X-axis direction as shown by arrows P and R. At the same time as this, 
the plane-normal vibration arm 171 is vibrated in the X-axis direction as 
shown by arrow Q. The plane-parallel vibrations of the vibration arms 172A 
and 172B generate electromotive forces between the electrodes 155A and 
155B, and between the electrodes 155C and 155D. A turning angular rate is 
detected by measuring this voltage. 
In a three-forked tuning-fork vibrator 174 of a vibratory gyroscope shown 
in FIG. 53, a plane-parallel vibration arm 172 is provided at one end part 
and a plane-normal vibration arm 171 is provide at the other end part. The 
plane-parallel vibration arm 172 is driven as shown by arrow N, and the 
plane-normal vibration arm 171 is resonated as shown by arrow V. When the 
vibrator 174 is turned around the Z axis as shown by arrow .omega. in this 
state, the vibration arms 172 and 171 are vibrated in the opposite 
directions as shown by arrows W and .OMEGA.. According to the invention, 
an electromotive force is generated between the electrodes by vibration of 
the vibration arm 171. A turning angular rate is detected by measuring 
this voltage. The middle arm 175 is not vibrated. 
And according to the invention, it is possible to drive the plane-normal 
vibration arm 171 as shown by arrow W and resonate the plane-parallel 
vibration arm 172 as shown by arrow .OMEGA.. When the vibrator is turned 
around the Z axis as shown by .omega. in this state, the vibration arms 
171 and 172 are vibrated in the X-axis direction as shown by arrows V and 
N. Hereupon, a turning angular rate is detected by measuring a voltage 
generated by vibration of the plane-parallel vibration arm 172. 
Next, a preferred method for manufacturing a vibrator or a vibration arm of 
the invention is described. In a preferred embodiment of the invention, 
plural plate-shaped members each of which is composed of a piezoelectric 
single crystal are prepared. In this case, the respective plate-shaped 
members are made different from one another in direction of the axis of 
polarization. A base member provided with plural plate-shaped members 
which are different from one another in direction of the axis of 
polarization is manufactured by joining these plate-shaped members with 
one another. Then a vibrator is formed by cutting this base member. 
The plural plate-shaped members can be adhered to one another by adhesives. 
And a laminated member is obtained by laminating the plural plate-shaped 
members and then the laminated member can be internally adhered by a heat 
treatment. It can be thought also to form plural domains which are 
different from one another in direction of the axis of polarization inside 
a single plate-shaped member by heat-treating the single plate-shaped 
member. 
According to the above-mentioned manufacturing method, a vibrator capable 
of performing a bending vibration in directions crossing the main faces of 
the vibrator can be manufactured by forming electrodes on one main face 
and the other main face of the vibrator. That is to say, electrodes for 
making the vibrator perform a bending vibration do not have to be formed 
on the side faces of the vibrator, concretely, on the cut-off faces. 
Accordingly, it is possible to dispense with a process of forming the 
electrodes on the side faces of the vibrator, and thanks to this, the 
manufacturing cost can be remarkably reduced and variations in performance 
generated in production can be also reduced. 
In the above-mentioned manufacturing method, it is particularly preferable 
to form electrodes having a specified plane shape on one main face and the 
other main face of a base member and then form a vibrator by cutting the 
base member. By doing so, electrodes for plural vibrators can be formed by 
one electrode forming process. 
FIGS. 54(a), 54(b) and 54(c) are perspective views showing base members 
185A, 185B and 185C, respectively. The base member 185A is composed of a 
joined member having two plate-shaped members 159A and 159B joined with 
each other. The direction of polarization of the plate-shaped member 159A 
(shown by arrow 165) and the direction of polarization of the plate-shaped 
member 159B (shown by arrow 166) are exactly opposite to each other, and 
are perpendicular to one main face and the other main face. A direction of 
the axis of polarization of the plate-shaped member 159A and a direction 
of the axis of polarization of the plate-shaped member 159B, respectively, 
are directed from the central plane 167 toward the main faces. Vibrators 
as shown in FIGS. 46, 51, 52 and 53 can be manufactured by cutting this 
base member. 
The base member 185B is composed of a joined member having two plate-shaped 
members 169A and 169B joined with each other. A direction of polarization 
of the plate-shaped member 169A (shown by arrow 180) and a direction of 
polarization of the plate-shaped member 169B (shown by arrow 181) are 
exactly opposite to each other, and are perpendicular to one main face and 
the other main face. A direction of the axis of polarization of the 
plate-shaped members are directed from the respective main faces toward 
the central plane. A vibrator as shown in FIG. 49 can be manufactured by 
cutting this base member. 
The base member 185C is composed of a joined member having two plate-shaped 
members 186A and 186B joined with each other. A direction of polarization 
of the plate-shaped member 186A (shown by arrow 182) and a direction of 
polarization of the plate-shaped member 186B (shown by arrow 183) are 
exactly opposite to each other, and are inclined at a specified slant 
angle to one main face and the other main face. 
FIGS. 55 to 57 illustrate a vibrator and a vibratory gyroscope which are 
preferable in case that the axis of polarization of each of the 
plate-shaped members is oriented at a slant angle to the main faces as 
shown in FIG. 54(c). FIG. 55 is a perspective view showing a vibrator 187 
and its electrodes of a vibratory gyroscope of this embodiment, FIG. 56 is 
a plan view showing a plane-normal vibration arm, and FIG. 57 is a plan 
view showing a plane-parallel vibration arm. 
The vibrator 187 shown in FIG. 55 is provided with a fixing part 157 fixed 
on an external fixing member, and three tuning-fork vibration arms 188A, 
189 and 188B. The whole vibrator is composed of a joined member having two 
plate-shaped members 186A and 186B joined with each other. 
One electrode 190A is formed on one main face of each of the plane-normal 
vibration arms 188A and 188B, and the other electrode 190B is formed on 
the other main face. In the plane-parallel vibration arm 189, three 
electrodes 191A, 191B and 191C are formed on one main face, and the 
opposite electrodes 191D, 191E and 191F are formed on the other main face 
at positions, respectively, opposite to the electrodes 191A, 191B and 
191C. Gaps 160 are provided, respectively, between the vibration arms 188A 
and 189, and between the vibration arms 189 and 188B. 
For example, the middle plane-parallel vibration arm is driven as shown by 
arrow Q, and the vibration arms at both sides are resonated as shown by 
arrows P and R. In order to do so, for example, the electrodes 191A, 191C 
and 191E of the plane-parallel vibration arm are grounded, and the 
electrodes 191B, 191D and 191F opposite to them are connected to an 
alternating-current power source 192. In this state, electric fields are 
generated from the electrode 191B toward the electrodes 191A and 191C as 
shown by arrows 198 in one layered part 186A, and electric fields are 
generated from the electrodes 191D and 191F toward the electrode 191E as 
shown by arrows 197 in the other layered part 186B. That is to say, it is 
necessary to make electric fields generated in one layered part and 
electric fields generated in the other layered part reverse in direction 
to each other. 
When the vibrator is turned around the Z axis as shown by .omega. in this 
state, the vibration arms 188A and 188B, respectively, are vibrated in the 
Y-axis direction as shown by arrows S and U. At the same time, the middle 
vibration arm is vibrated in the Y-axis direction as shown by arrow T. 
According to the invention, electromotive forces are generated among the 
electrodes by vibration of the plane-normal vibration arm. A turning 
angular rate is detected by measuring this voltage. 
As shown in FIGS. 58 and 59, vibration arms 198A, 198B and 202 can be also 
manufactured by joining plate-shaped members 200A and 200B with each 
other. In this example, directions 194 and 199 of polarization of the 
plate-shaped members are inclined at a specified angle to the main faces, 
and the directions 194 and 199 are nearly equal to each other in 
plane-parallel direction component but are opposite to each other in 
plane-normal direction component. One electrode 190A is formed on one main 
face of each of the plane-normal vibration arms 198A and 198B, and the 
other electrode 190B is formed on the other main face. In the 
plane-parallel vibration arm 202, as shown in FIG. 59, three electrodes 
191A, 191B and 191C are formed on one main face, and the opposite 
electrodes 191D, 191E and 191F are formed on the other main face at 
positions, respectively, opposite to the electrodes 191A, 191B and 191C. 
For example, the middle plane-parallel vibration arm 202 is driven as shown 
by arrow Q, and the vibration arms 198A and 198B at both sides are 
resonated as shown by arrows P and R. In order to do so, for examle, the 
electrodes 191A, 191C, 191D and 191F of the plane-parallel vibration arm 
are grounded, and the electrodes 191B and 191E are connected to an 
alternating-current power source 192. In this state, for example, electric 
fields are generated from the electrodes 191A and 191C toward the 
electrode 191B as shown by arrows 201 in one layered part 200A, and 
electric fields are generated from the electrodes 191D and 191F toward the 
electrode 191E as shown by arrows 197 in the other layered part 200B. That 
is to say, the electric fields generated in one layered part and the 
electric fields generated in the other layered part are made reverse in 
direction to each other. In the same way after this, a turning angular 
rate is detected. 
Concrete experiment results are described in the following. The 
above-mentioned vibratory gyroscopes as shown in FIGS. 46 to 48 were made. 
A Z plate of quartz crystal was used as each plate-shaped member. A 
two-layered electrode of Cr and Au was used as a material for an 
electrode. An alternating electric field of 1 volt and 7.5 Hz in frequency 
was applied between the electrodes 163A and 163B, and a vibrator was 
turned, and then a relation between a turning angular rate and an output 
voltage from the electrodes 155A, 155B, 155C and 155D was measured. The 
result is shown in Table 1. A good linearity was found between an output 
voltage and a turning angular rate. 
TABLE 1 
______________________________________ 
Turning angular rate: (.degree./sec) 
-40 -30 -20 -10 0 
Output voltage: (mV) 
-5.01 -3.76 -2.52 
-1.30 0.10 
Turning angular rate: (.degree./sec) 
10 20 30 40 
Output voltage: (mV) 
1.26 2.51 3.74 5 
______________________________________ 
A sixth embodiment of the invention is described in the following. 
FIG. 60 shows a construction of an example of a vibrator of a vibratory 
gyroscope of the invention, 60(a) is a side view, 60(b) is a front view, 
and 60(c) is a plan view. This example shows a vibratory gyroscope of a 
vertical-arrangement type in which a drive vibration and a detection 
vibration are vertical. In an example shown in FIGS. 60(a) to 60(c), a 
tuning-fork vibrator 205 forming the vibratory gyroscope is composed of 
three arms 206, 207 and 208 arranged nearly in parallel with one another, 
and a base part 209 joining these three arms. Among the three arms the 
arms 206 and 208 at both sides form detection arms, and the middle arm 207 
forms a drive arm. As a material for the tuning-fork vibrator, it is 
preferable to use a piezoelectric material such as piezoceramic, quartz 
crystal, a single crystal of LiTaO.sub.3, LiNbO.sub.3 or the like, and 
particularly more preferable to use a single crystal of quartz, 
LiTaO.sub.3, LiNbO.sub.3 or the like. 
The tuning-fork vibrator 205 operates in the same way as a vibrator known 
up to now. That is to say, the drive arm 207 is first vibrated in the X-Z 
plane by means of an unillustrated driving means provided on the drive 
arm. And the left and right detection arms 206 and 208 are resonated in 
the same X-Y plane. When the vibrator is turned around the axis of 
symmetry Z of the tuning fork at a turning angular rate .omega. in this 
state, a Coriolis force f acts on each of the detection arms. Since the 
detection arms are vibrating in the X-Z plane, vibration in the Y-Z plane 
is excited in the detection arms. A turning angular rate is measured by 
detecting this vibration by means of an unillustrated detecting means 
provided on each of the detection arms. 
An important point in this invention is to fix a domain where movement of 
the vibrator is the least by supporting the tuning-fork vibrator at the 
small domain where there is locally a domain having the least detection 
vibration in case of supporting the above-mentioned tuning-fork vibrator 
to form a vibratory gyroscope. Thanks to this, a detection vibration can 
be effectively generated by a Coriolis force without damping, the Q value 
of the detection vibration can be made higher, and the sensitivity can be 
improved. Since the detection vibration generated by a Coriolis force is 
small in amplitude, this invention is particularly effective to improve 
the sensitivity. Concretely, in the example shown in FIGS. 60(a) to 60(c), 
the vibrator is supported at a domain 210 nearly in the middle part of the 
base part 209. 
A method for supporting the vibrator is not limited in particular, and any 
method known up to now as a method for adhering a piezoelectric member may 
be used. As an example, as shown in FIGS. 61(a) and 61(b), a specified 
hole 213 is provided at the nearly middle domain 210 of the base part 209 
in the direction of thickness, and the vibrator can be fixed on a base 
part 211 of the vibratory gyroscope by inserting an end part 214 
projecting from an arm 212 and perpendicularly to the longitudinal 
direction of the arm 212 projecting from the base part 211 into the hole 
213. Fixing the end part 214 and the hole 213 onto each other can be 
performed by applying metallization to the surface of the end part and/or 
the internal surface of the hole and then soldering or brazing, or by 
providing resin between the end part and the hole. Although the base part 
209 is supported on one surface of it in the example shown in FIGS. 61(a) 
and 61(b), the base part can be also supported on both surfaces of it. And 
it is possible also to provide a through hole instead of the hole 213, 
pass a supporting arm through the through hole, and fix both end parts of 
the supporting arm onto the base part 211 of the vibratory gyroscope. 
In the above-mentioned example, the reason why the nearly middle part 210 
of the main face of the base part 209 is assumed to be a small domain 
where there is locally a domain having the smallest detection vibration is 
as follows. The inventors first applied a natural mode analysis by means 
of a finite element analysis method to a vibrator 205 having the 
above-mentioned shape in order to examine whether or not there is a small 
domain where there is locally a domain having the smallest detection 
vibration in relation to the vibrator 205. And the vibration amplitudes at 
each domain of the tuning-fork vibrator in the X-Z plane (where a drive 
vibration is generated) and in the Y-Z plane (where a detection vibration 
is generated by a Coriolis force) in case of assuming that the vibrator 
has been cut along the X-Z plane have been obtained as distribution of the 
ratio of the vibration amplitude at each domain to the vibration amplitude 
at the maximum vibration amplitude point. FIG. 62 shows the result in the 
X-Z plane where a drive vibration is generated, and FIG. 63 shows the 
result in the Y-Z plane where a detection vibration is generated by a 
Coriolis force. 
In the example shown in FIGS. 62 and 63, the respective domains different 
in color from one another show domains each of whose colors represents the 
ratio of the vibration amplitude at a domain to the vibration amplitude at 
the maximum vibration amplitude point, and in this invention, an orange 
part is a small domain where there is locally a domain having the smallest 
vibration whose amplitude is less than one thousandth of the amplitude at 
the maximum vibration amplitude point. In this example, FIG. 62 shows the 
ratio in comparison with the maximum vibration amplitude point in a drive 
vibration (plane-parallel vibration), and FIG. 63 shows the ratio in 
comparison with the maximum vibration amplitude point in the detection 
vibration (plane-normal vibration), and from the result shown in FIG. 63, 
it has been confirmed that there is a small domain where there is locally 
a domain having the smallest detection vibration. And similarly to the 
example shown in FIG. 60, it has been founded that supporting the vibrator 
at the nearly middle domain 210 of the main faces at both sides of the 
base part 209 results in not only supporting the vibrator at a small 
domain where there is locally a domain having the smallest detection 
vibration known from FIG. 63 but also supporting the vibrator at a small 
domain where there is locally a domain having the smallest drive vibration 
known from FIG. 62, and therefore in this example, supporting the vibrator 
in this way results in supporting the tuning-fork vibrator at a domain 
where a small domain where there is locally a domain having the smallest 
detection vibration and a small domain where there is locally a domain 
having the smallest drive vibration coincide with each other. 
Taking the above-mentioned result into account, a result shown in Table 2 
can be obtained by measuring the Q value of a drive vibration in the X-Z 
plane, the Q value of a detection vibration in the Y-Z plane, and the 
sensitivity in relation to the example explained as a former example in 
FIG. 2 where the base part is fixed, the example where one axis is fixed, 
and the example where the vibrator is fixed as shown in FIG. 60 as the 
invention. From the result shown in Table 2, it has been found that both 
of the Q value of a drive vibration in the X-Z plane and the Q value of a 
detection vibration in the Y-Z plane are higher and the sensitivity also 
is higher in the examples of the invention in comparison with the former 
examples. 
TABLE 2 
______________________________________ 
Q of drive 
Q of detection 
Sensitivity 
vibration 
vibration (at 1 degree/sec) 
______________________________________ 
Base part fixed 
4000 3000 1.1 mV 
One axis fixed 
7000 8000 3.4 mV 
This embodiment 
30000 30000 10.8 mV 
______________________________________ 
Although the above-mentioned example shows an example of using three arms 
as a tuning-fork vibrator, it is a matter of course that the number of 
arms is not limited to three and the invention can be also applied to 
another number of arms such as four arms, five arms, or the like. Although 
the above-mentioned example shows an example of generating a drive 
vibration in the X-Z plane and a detection vibration in the Y-Z plane in 
FIG. 60, it is a matter of course that the invention can be also applied 
to a gyroscope in which the shape of a vibrator 1 is kept as it is and a 
relation between both vibrations is reverse, namely, a drive vibration is 
generated in the Y-Z plane and a detection vibration is generated in the 
X-Z plane. 
Although the above-mentioned example explains an example of a vibratory 
gyroscope of a vertical-arrangement type in which a drive mode vibration 
and a detection mode vibration are vertical, the invention can be 
preferably applied to a vibratory gyroscope of a horizontal-arrangement 
type in which a drive mode vibration and a detection mode vibration are 
horizontal in the same plane. An example in which a finite element 
analysis was applied to a vibratory gyroscope of a horizontal-arrangement 
type in the same way as the above-mentioned example is described in the 
following. 
FIG. 64 shows an example of the result of applying a natural mode analysis 
by means of a finite element analysis method to a detection mode vibration 
in a vibrator composed of a T-shaped arm and a base part. Since this 
vibrator was described in FIGS. 3 to 5, the description at that time is 
quoted. In FIG. 64 also, vibrations in the respective domains are 
classified by color according to the ratio of the amplitude of vibration 
at each domain to that at the maximum vibration amplitude point in the 
same way as FIGS. 62 and 63. In the example shown in FIG. 64 also, it has 
been confirmed that there is a small domain where there is locally a 
domain having the smallest detection vibration in the middle of the base 
part. Actually, a result shown in Table 3 can be obtained by measuring the 
Q value of a drive vibration, the Q value of a detection vibration in the 
same plane as the drive vibration, and the sensitivity in relation to the 
example explained in FIG. 2 where the base part is fixed and the example 
where the vibrator shown in FIG. 64 is supported at a small domain where 
there is locally a domain having the smallest detection vibration as the 
invention. From the result shown in Table 3, it has been found that the Q 
value of a drive vibration is made slightly higher and the Q value of a 
detection vibration is made extraordinarily higher and the sensitivity 
also is made higher in the example of the invention in comparison with the 
former examples. 
TABLE 3 
______________________________________ 
Q of drive 
Q of detection 
Sensitivity 
vibration 
vibration (at 1 degree/sec) 
______________________________________ 
Base part fixed 
3000 200 0.1 mV 
Node fixed 5000 3000 1.1 mV 
(this embodiment) 
______________________________________ 
FIG. 65 shows an example of the result of applying a natural mode analysis 
by means of a finite element analysis method to a detection mode vibration 
in a vibrator composed of a Y-shaped arm and a base part. Since this 
vibrator was described in FIGS. 24, 25 and 27, the description at that 
time is quoted. In FIG. 65 also, in the same way as the example shown in 
FIG. 64, it has been confirmed that there is a small domain where there is 
locally a domain having the smallest detection vibration in the middle of 
the base part. By actually measuring the Q value of a drive vibration, the 
Q value of a detection vibration in the same plane as the drive vibration, 
and the sensitivity in relation to the example explained in FIG. 2 where 
the base part is fixed and the vibrator shown in FIG. 6, in the same way 
as the vibrator shown in FIG. 64, it has been found that the Q value of a 
drive vibration is made slightly higher and the Q value of a detection 
vibration is made extraordinarily higher and furthermore the sensitivity 
also is made higher in the example of the invention in comparison with the 
former examples. 
When a natural mode analysis by means of a finite element analysis method 
has been also applied to a drive mode vibration in a vibrator having a 
T-shaped arm shown in FIG. 64 and a vibrator having a Y-shaped arm shown 
in FIG. 65, it has been found that the small domain where there is locally 
a domain having the smallest detection mode vibration and the small domain 
where there is locally a domain having the smallest drive mode vibration 
do not coincide with each other. 
FIGS. 66 and 67 show the result of applying a natural mode analysis by 
means of a finite element analysis method to a vibrator having the 
opposite Y-shaped arms joined with the joint of two base parts. Since this 
vibrator was described in FIGS. 28 and 29, the description at that time is 
quoted. An example shown in FIG. 66 is a result in relation to a drive 
mode vibration, and an example shown in FIG. 67 is a result in relation to 
a detection mode vibration. From the example shown in FIG. 66, in the same 
way as the examples shown in FIGS. 64 and 65, it has been confirmed that 
there is a small domain where there is locally a domain having the 
smallest detection vibration at the respective middle points of both base 
parts and an intersecting point of the opposite Y-shaped arms and the 
joint of the two base parts. From the example shown in FIG. 67, it has 
been confirmed that there is a small domain where there is locally a 
domain having the smallest drive vibration also in a drive mode vibration. 
In the example shown in FIG. 66, it has been founded that supporting the 
vibrator at the respective middle points of both base parts and an 
intersecting point of the opposite Y-shaped arms and the joint of the two 
base parts results in also supporting the vibrate or at the small domain 
where there is locally a domain having the smallest drive mode vibration 
as known from FIG. 67, and therefore in this example, it results in 
supporting the vibrator at the domain where the small domain where there 
is locally a domain having the smallest detection vibration and the small 
domain where there is locally a domain having the smallest drive vibration 
coincide with each other. 
When the Q value of a drive vibration, the Q value of a detection vibration 
in the same plane as the drive vibration, and the sensitivity have been 
actually measured in relation to the example explained in FIG. 2 where the 
base part is fixed and the example where the vibrator is supported at the 
small domains at each of which there is locally a domain having the 
smallest detection vibration like the invention, namely, at the respective 
middle points of both base parts and an intersecting point of the opposite 
Y-shaped arms and the joint of the two base parts, the results shown in 
Tables 4 and 5 have been able to be obtained. Hereupon, the result of 
Table 3 shows an example of supporting the vibrator at the intersecting 
point of the opposite Y-shaped arms and the joint of the two base parts, 
and the result of Table 4 shows an example of supporting the vibrator at 
the respective two middle points of both base parts. From the results 
shown in Tables 4 and 5, it has been found that the Q value of a drive 
vibration is made slightly higher and the Q value of a detection vibration 
is made extraordinarily higher, and furthermore the sensitivity is made 
higher in any of the examples of the invention in comparison with the 
former examples. 
TABLE 4 
______________________________________ 
Q of drive 
Q of detection 
Sensitivity 
vibration 
vibration (at 1 degree/sec) 
______________________________________ 
Base part fixed 
4000 300 0.2 mV 
Node fixed 5000 3000 1.3 mV 
(this embodiment) 
______________________________________ 
TABLE 5 
______________________________________ 
Q of drive 
Q of detection 
Sensitivity 
vibration 
vibration (at 1 degree/sec) 
______________________________________ 
Base part fixed 
4000 300 0.2 mV 
Node fixed 5000 4000 1.5 mV 
(this embodiment) 
______________________________________ 
Comparing Table 2 showing the result of a vibratory gyroscope of a 
vertical-arrangement type and Tables 3 to 5 each of which shows the result 
of a vibratory gyroscope of a horizontal-arrangement type with each other 
among the examples of the invention, it has been found that in any example 
of the invention the Q value of a detection mode vibration is made one 
digit or so higher and the invention is more effective to a vibratory 
gyroscope of a horizontal-arrangement type having naturally a small Q 
value of the detection mode vibration. 
A seventh embodiment of the invention is described in the following. 
FIG. 68 shows a construction of an example of a vibratory gyroscope 255 
using a piezoelectric member already proposed by the applicants. In an 
example shown in FIG. 68, a vibratory gyroscope is provided with a 
tuning-fork vibrator 234 formed by joining a pair of vibration arms 232a 
and 232b with bending-vibration pieces in the X-Y plane, a base part 236 
for fixing this tuning-fork vibrator on an external fixing member 235 in 
the X-Y plane, electrodes 237A, 237B, 237C and 237D which are provided on 
the tuning-fork vibration pieces 232a and 232b and are used for driving 
the tuning-fork vibration pieces, and electrodes 238A, 238B, 238C and 238D 
used for obtaining an angular speed from vibration of the base part 236. 
In the vibratory gyroscope having the a construction shown in FIG. 68, the 
tuning-fork vibration pieces 232a and 232b are vibrated in the X-Y plane 
so as to be exactly reverse in phase to each other by means of the 
electrodes 237A to 237D in a turning system with the Z axis as the central 
axis. When a turning angular rate .omega. acts around the Z axis in this 
state, a Coriolis force makes forces F1 and F2 which are reverse in phase 
to each other act on the tuning-fork vibration pieces along the Y axis. As 
the result, moments M1 and M2 in the same direction act on both ends of 
the bending-vibration pieces of the tuning-fork vibrator 234. A turning 
angular rate .omega. can be measured by detecting deformation of the base 
part caused by the moments M1 and M2 by means of the electrodes 238A to 
238D. 
In the vibratory gyroscope 255 having the construction shown in FIG. 68 
which acts in this way, for example, in case of using a single crystal of 
lithium tantalate (LiTaO.sub.3) as a piezoelectric material and cutting it 
along the 130.degree. Y crystal face, driving and detection are performed 
as described in the following. As seen from a sectional view of a part 
having the electrodes 237A to 237D of the tuning-fork vibration piece 
shown as an example in FIG. 69, the electrodes 237A to 237D are formed on 
end parts of both main faces of each of the tuning-fork vibration pieces 
so that each two of the electrodes can form a pair. And in FIG. 69, it is 
possible to contract the right side of each tuning-fork vibration piece 
and extend the left side by applying voltages reverse in phase to each 
other, respectively, to a pair of electrodes 237A and 237B and a pair of 
electrodes 237C and 237D. Thus, it is possible to give a drive vibration 
from left to right to the vibration pieces 232a and 232b in FIG. 69 by 
applying alternating voltages reverse in phase to each other to the pair 
of electrodes 237A and 237B and the pair of electrodes 237C and 237D. And 
a turning angular rate .omega. can be obtained by performing the 
above-mentioned operation in the reverse manner. 
A former vibratory gyroscope 255 having the above-mentioned construction 
can act with no problem in an ordinary angular speed measurement. In case 
of performing an angular speed detection of high accuracy as demanded in 
recent years, however, as shown in FIG. 70, in each of the tuning-fork 
vibration pieces and the base part an electric field E1 is applied to each 
pair of the pair of electrodes 237A (238A) and 237B (238B) and the pair of 
electrodes 237C (238C) and 237D (238D), and additionally to this, there is 
a horizontal-leakage electric field E2, although it is very weak, and 
since unnecessary displacements are generated in the tuning-fork vibration 
pieces and the base part due to this leakage electric field, there is a 
problem that this leakage electric field causes noises. Therefore, it has 
been impossible to perform an angular speed detection of high accuracy. 
FIG. 71 shows composition of an example of a vibratory gyroscope using a 
piezoelectric member of the invention. In an example shown in FIG. 71, a 
vibratory gyroscope 215 is provided with a tuning-fork 218 formed by 
joining a pair of tuning-fork vibration pieces 216a and 216b with 
bending-vibration pieces 256a and 256b in the X-Y plane, a base part 220 
for fixing this tuning-fork vibrator 218 on an external fixing member 219 
in the X-Y plane, electrodes 221A, 221B, 221C and 221D which are provided 
on the tuning-fork vibration pieces and are used for driving the 
tuning-fork vibration pieces, and electrodes 223A, 223B, 223C and 223D 
used for obtaining an angular speed from vibration of the base part 220. 
The tuning-fork vibration pieces, the bending-vibration pieces, the base 
part, and the fixing member which form the vibratory gyroscope are formed 
out of a piezoelectric material in one body, and concretely, are formed 
out of piezoceramic such as PZT or the like, or a piezoelectric single 
crystal of quartz, lithium tantalate or the like. 
The composition of the vibratory gyroscope 215 is the same as that of the 
above-mentioned former vibratory gyroscope. An important point in the 
vibratory gyroscope of the invention shown in FIG. 71 is that through 
holes 222a, 222b and 224 passing through both main faces are provided, 
respectively, between a pair of electrodes 221A (223A) and 221B (223B) and 
between a pair of electrodes 221C (223C) and 221D (223D) in the 
tuning-fork vibration pieces 216a and 216b and the base part 220. Although 
the through holes 222a, 222b and 224 are not limited in size in 
particular, it is preferable to make each through hole equal to or longer 
than the longitudinal length of each electrode, provide each through hole 
in a range of 1/3 to 2/3 of the arm length from the arm base, and form the 
piezoelectric member out of a 130.degree. Y plate of lithium tantalate 
(LiTaO.sub.3). 
The vibratory gyroscope of the invention shown in FIG. 71 also acts in the 
same way as the above-mentioned former example and vibrates the 
tuning-fork vibration pieces in the X-Y plane exactly reverse in phase to 
each other by means of the electrodes 221A to 221D in a turning system 
with the Z axis as the central axis. When a turning angular rate .omega. 
acts around the Z axis in this state, a Coriolis force makes forces F1 and 
F2 which are reverse in phase to each other along the Y axis act on the 
tuning-fork vibration pieces. As the result, moments M1 and M2 in the same 
direction act on both ends of the bending-vibration pieces of the 
tuning-fork vibrator 218. A turning angular rate .omega. can be measured 
by detecting deformation of the base part caused by the moments M1 and M2 
by means of the electrodes 223A to 223D. 
In an example of the invention, a sectional view of a part of the 
tuning-fork vibration piece 216a having the through hole 222a is shown in 
FIG. 72, and in case of making the tuning-fork vibration piece 216a 
drive-vibrate by applying alternating voltages reverse in phase to each 
other, respectively, to the pair of electrodes 221A and 221B and the pair 
of electrodes 221C and 221D, since even when there is a horizontal-leakage 
electric field directed from one pair of electrodes to the other pair of 
electrodes there is no piezoelectric member in the through hole 222a, no 
unnecessary displacement is generated in the tuning-fork vibration piece. 
And since a vibratory gyroscope of the invention comprising arms having 
through holes can reduce the arms in rigidity by forming the through holes 
in the arms, it can obtain a drive vibration and a detection vibration in 
high efficiency. As the result, the invention can perform a high-accuracy 
angular speed detection. 
FIG. 73 shows a construction of another example of a vibratory gyroscope 
using a piezoelectric member of the invention. In an example shown in FIG. 
73, the same symbols are given to the same members as those of FIG. 71, 
and description of them is omitted. Differently from the example shown in 
FIG. 71, the example shown in FIG. 73 uses a quartz crystal having the a 
axis of a triad axis of symmetry in a specified plane as a piezoelectric 
material. In the example shown in FIG. 73, therefore, as seen from a 
sectional view of a part of the tuning-fork vibration piece 216a having 
the through hole 222a as an example in FIG. 74, a pair of electrodes 221A 
and 221B and a pair of electrodes 221C and 221D are formed, respectively, 
on the outside faces and the inside faces facing the through hole 222a 
(222b) of each of the tuning-fork vibration pieces. In this example also, 
since there is no quartz crystal as a piezoelectric material in the 
through hole 222a (222b), unnecessary displacement can be removed. 
Although in the above-mentioned example a vibratory gyroscope comprising a 
tuning-fork 218 formed by joining a pair of tuning-fork vibration pieces 
216a and 216b with bending-vibration pieces 256a and 256b in the X-Y 
plane, a base part 220 for fixing this tuning-fork vibrator 218 on an 
external fixing member 219 in the X-Y plane, electrodes 221A to 221D which 
are provided on the tuning-fork vibration pieces and are used for driving 
the tuning-fork vibration pieces, and electrodes 223A to 223D used for 
obtaining an angular speed from vibration of the base part 220 has been 
described as an example, it is a matter of course that any vibratory 
gyroscope having another composition using an arm composed of a 
piezoelectric material as a vibrator can obtain an effect of the 
invention.