Vibration driven motor

A vibration driven motor constituted by an elastic member and an electro-mechanical converting element connected to the elastic member is characterized in that the driving direction is changed by changing the frequency of a vibration produced by the electro-mechanical converting element. In this case, the driving direction preferably includes two orthogonal directions.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a vibration driven motor for obtaining a 
driving force by generating an elliptic motion in an elastic member. 
2. Related Background Art 
FIG. 4 is a view showing a conventional linear vibration driven motor. 
In the conventional linear vibration driven motor, a vibration member 102 
for applying a vibration is disposed at one end side of a rod-like elastic 
member 101, and a transformer 103 for controlling a vibration is disposed 
at the other end side thereof. Vibrators 102a and 103a are respectively 
coupled to the vibration member 102 and the transformer 103. An AC voltage 
is applied from an oscillator 102b to the vibrator 102a for applying a 
vibration to vibrate the rod-like elastic member 101, and this vibration 
becomes a progressive wave when it propagates through the rod-like elastic 
member 101. A movable member 104, which is in press contact with the 
rod-like elastic member 101, is driven by the progressive wave. 
The vibration of the rod-like elastic member 101 is transmitted to the 
vibrator 103a via the transformer 103 for controlling a vibration, and the 
vibrator 103a converts the vibration energy into electric energy. A load 
103b connected to the vibrator 103a consumes the electric energy, thereby 
absorbing the vibration. The transformer 103 for controlling a vibration 
suppresses reflection at the end face of the rod-like elastic member, 
thereby preventing generation of a standing wave in a characteristic mode 
of the rod-like elastic member 101. 
In the linear vibration driven motor shown in FIG. 4, the rod-like elastic 
member 101 must have a length corresponding to the moving range of the 
movable member 104, and the entire rod-like elastic member 101 must be 
vibrated, thus increasing the size of the apparatus. In addition, the 
transformer 103 for controlling a vibration is required to prevent 
generation of a standing wave in the characteristic mode. 
In order to solve the above-mentioned problems, various self-running 
vibration driven motors have been proposed. For example, a 
"hetero-degeneracy longitudinal L1--bending B4 mode plate motor" described 
in "222 Piezoelectric Linear Motors for Application to Driving a Light 
Pick-Up Element" in "Lecture Papers of 5th Electromagnetic Force 
Associated Dynamics Symposium" is known. 
FIGS. 5A to 5C are views showing a conventional hetero-degeneracy 
longitudinal L1--bending B4 mode plate motor, in which FIG. 5A is a front 
view, FIG. 5B is a side view, and FIG. 5C is a plan view. 
An elastic member 1 has a rectangular planar shape, and driving force 
output portions 1a and 1b as projecting portions are formed on one surface 
of the member 1. The driving force output portions 1a and 1b are arranged 
at antinode positions of a bending vibration B4 mode generated in the 
elastic member 1, and are pressed against an object such as a guide rail 4 
(see FIG. 7). 
Electro-mechanical converting elements 2a and 2b are elements for 
converting electric energy into mechanical energy, and are adhered on the 
other surface of the elastic member 1. The elements 2a and 2b generate a 
longitudinal vibration L1 mode and a bending vibration B4 mode in the 
elastic member 1. 
The operation principle of the motor shown in FIGS. 5A to 5C elucidated by 
the present inventor will be described below, and its problems will also 
be mentioned. 
FIG. 6 is a view for explaining the driving principle of the 
hetero-degeneracy longitudinal L1--bending B4 mode plate motor shown in 
FIGS. 5A to 5C. 
As shown in column (A) in FIG. 6, this vibration driven motor produces a 
compound vibration of bending and longitudinal vibrations by applying 
high-frequency voltages A and B to the two electro-mechanical converting 
elements 2a and 2b, thereby generating elliptic motions at the distal ends 
of the driving force output portions 1a and 1b, i.e., generating a driving 
force. 
Note that G indicates the ground. Assume that the two electro-mechanical 
converting elements 2a and 2b are polarized in polarities in the same 
directions, and the high-frequency voltages A and B have a time phase 
difference of .pi./2 therebetween. 
Column (A) in FIG. 6 shows time changes in two-phase high-frequency 
voltages A and B input to the vibration driven motor at times t1 to t9. 
The abscissa of column (A) represents the effective value of the 
high-frequency voltage. Column (B) shows the deformation state in the 
section of the vibration driven motor, i.e., time changes (t2 to t9) in 
bending vibration generated in the vibration driven motor. Column (C) 
shows the deformation state in the section of the vibration driven motor, 
i.e., time changes (t1 to t9) in longitudinal vibration generated in the 
vibration driven motor. Column (D) shows time changes (t1 to t9) in 
elliptic motion generated in the projecting portions 1a and 1b of the 
vibration driven motor. 
The operation of the vibration driven motor will be described below in 
units of time changes (t1 to t9). 
At time t1, as shown in column (A), the high-frequency voltage A generates 
a positive voltage, and similarly, the high-frequency voltage B generates 
a positive voltage having the same magnitude as that generated by the 
voltage A. As shown in column (B), bending vibrations produced by the 
high-frequency voltages A and B cancel each other, and mass points Y1 and 
Z1 have zero amplitudes. As shown in column (C), the high-frequency 
voltages A and B produce longitudinal vibrations in a direction to expand. 
Mass points Y2 and Z2 exhibit a maximum expansion to have a node X as the 
center, as indicated by an arrow in column (C). As a result, as shown in 
column (D), the two different types of vibrations are combined, so that 
the synthesis of motions of the mass points Y1 and Y2 becomes a motion of 
a mass point Y, and the synthesis of motions of the mass points Z1 and Z2 
becomes a motion of a mass point Z. 
At time t2, as shown in column (A), the high-frequency voltage B becomes 
zero, and the high-frequency voltage A generates a positive voltage. As 
shown in column (B), the high-frequency voltage A produces a bending 
motion, so that the mass point Y1 oscillates in the positive direction, 
and the mass point Z1 oscillates in the negative direction. As shown in 
column (C), the high-frequency voltage A produces a longitudinal 
vibration, and the mass points Y2 and Z2 contract to be smaller than those 
at time t1. As a result, as shown in column (D), the two different 
vibrations are combined, and the mass points Y and Z move clockwise from 
the positions at time t1. 
At time t3, as shown in column (A), the high-frequency voltage A generates 
a positive voltage, and similarly, the high-frequency voltage B generates 
a negative voltage having the same magnitude as that generated by the 
voltage A. As shown in column (B), bending motions produced by the 
high-frequency voltages A and B are synthesized and amplified. The mass 
point Y1 is amplified in the positive direction as compared to that at 
time t2, and exhibits a maximum positive amplitude value. The mass point 
Z1 is amplified in the negative direction as compared to that at time t2, 
and exhibits a maximum negative amplitude value. As shown in column (C), 
longitudinal vibrations produced by the high-frequency voltages A and B 
cancel each other, and the mass points Y2 and Z2 return to their initial 
positions. As a result, as shown in column (D), the two different types of 
vibrations are combined, and the mass points Y and Z move clockwise from 
the positions at time t2. 
At time t4, as shown in column (A), the high-frequency voltage A becomes 
zero, and the high-frequency voltage B generates a negative voltage. As 
shown in column (B), the high-frequency voltage B produces a bending 
motion. The amplitude of the mass point Y1 becomes smaller than that at 
time t3, and the amplitude of the mass point Z1 becomes smaller than that 
at time t3. As shown in column (C), the high-frequency voltage B produces 
a longitudinal vibration, and the mass points Y2 and Z2 contract. As a 
result, as shown in column (D), the two vibrations are combined, and the 
mass points Y and Z move clockwise from the positions at time t3. 
At time t5, as shown in column (A), the high-frequency voltage A generates 
a negative voltage, and similarly, the high-frequency voltage B generates 
a negative voltage having the same magnitude as that generated by the 
voltage A. As shown in column (B), bending motions produced by the 
high-frequency voltages A and B cancel each other, and the mass points Y1 
and Z1 have zero amplitudes. As shown in column (C), the high-frequency 
voltages A and B produce longitudinal vibrations in a direction to 
contract. The mass points Y2 and Z2 exhibit a maximum contraction to have 
the node X as the center, as indicated by an arrow in column (C). As a 
result, as shown in column (D), the two different types of vibrations are 
combined, and the mass points Y and Z move clockwise from the positions at 
time t4. 
As the time elapses from t6 to t9, bending and longitudinal vibrations are 
produced in the same manner as in the above-mentioned principle, and as a 
result, as shown in column (D), the mass points Y and Z move clockwise and 
make elliptic motions. 
With the above-mentioned principle, the vibration driven motor obtains a 
driving force by producing elliptic motions at the distal ends of the 
driving force output portions 1a and 1b. Therefore, when the distal ends 
of the driving force output portions 1a and 1b are in press contact with 
an object 4, as shown in FIG. 7, the elastic member 1 moves relative to 
the object 4. 
However, the motor shown in FIGS. 5A to 5C can realize a driving operation 
in only one direction since the producing direction of the elliptic 
motions is determined depending on the size of the elastic member 1 and 
the adhered positions of the electro-mechanical converting elements 2a and 
2b. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a vibration driven 
motor which can solve the above-mentioned problems, and can realize a 
two-dimensional driving operation by a simple arrangement. 
In order to achieve the above object, according to the first aspect of the 
present invention, there is provided a vibration driven motor which 
comprises an elastic member and an electro-mechanical converting element 
connected to the elastic member, and the ultrasonic motor is characterized 
in that the driving direction is changed by changing the frequency of a 
vibration produced by the electro-mechanical converting element. In this 
case, the driving direction preferably includes two orthogonal directions. 
According to the second aspect of the present invention, there is provided 
a vibration driven motor which comprises an elastic member and an 
electro-mechanical converting element connected to the elastic member, and 
the ultrasonic motor is characterized in that the elastic member has a 
first direction motion mode of making a motion in a first direction by a 
first mode vibration and a second mode vibration when a first driving 
signal is input to the electro-mechanical converting element, and a second 
direction motion mode of making a motion in a second direction by a third 
mode vibration and a fourth mode vibration when a second driving signal is 
input to the electro-mechanical converting element. 
The elastic member preferably has a plurality of projecting portions, and 
the projecting portions are preferably aligned in a direction parallel to 
the first or second direction. 
The mode orders of the first, second, third, and fourth mode vibrations and 
the frequencies of the first and second driving signals are appropriately 
set on the basis of the material, area, shape, and thickness of the 
elastic member. In this case, the material, area, shape, and thickness of 
the elastic member are preferably set, so that the mode order of the 
second mode vibration does not coincide with that of the fourth mode 
vibration. Alternatively, when the mode order of the second mode vibration 
is set to be equal to that of the fourth mode vibration, the first and 
second driving signals are preferably set to have different frequencies. 
Furthermore, the first and third mode vibrations are preferably 
longitudinal vibrations, and the second and fourth mode vibrations are 
preferably bending vibrations. Alternatively, the first and third mode 
vibrations are preferably 1st-order longitudinal vibrations, the second 
mode vibration is preferably a 4th-order bending vibration, and the fourth 
mode vibration is preferably a 6th-order bending vibration. 
According to the third aspect of the present invention, there is provided a 
vibration driven motor which comprises an elastic member and an 
electro-mechanical converting element connected to the elastic member, and 
changes a driving direction by changing the frequency of a vibration 
produced by the electro-mechanical converting element, and the vibration 
driven motor is characterized in that the motor has a plurality of driving 
force output portions for outputting driving forces, and the driving force 
output portions are arranged commonly to respective driving directions. 
According to the fourth aspect of the present invention, there is provided 
a vibration driven motor which comprises an elastic member and an 
electro-mechanical converting element connected to the elastic member, 
produces a motion in a first direction by a first mode vibration and a 
second mode vibration generated in the elastic member in response to a 
first driving signal input to the electro-mechanical converting element, 
and produces a motion in a second direction by a third mode vibration and 
a fourth mode vibration generated in the elastic member in response to a 
second driving signal input to the electro-mechanical converting element, 
and the vibration driven motor is characterized in that a driving force 
output portion in the first direction and a driving force output portion 
in the second direction are arranged at intersections between antinode 
positions of the second and fourth mode vibrations so as to be commonly 
used in the two directions. 
The first and third mode vibrations are preferably longitudinal vibrations, 
and the second and fourth mode vibrations are preferably bending 
vibrations. In this case, the second and fourth mode vibrations preferably 
have different mode orders. Alternatively, the first and third mode 
vibrations are preferably 1st-order longitudinal vibrations, the second 
mode vibration is preferably a 4th-order bending vibration, and the fourth 
mode vibration is preferably a 6th-order bending vibration. 
According to the fifth aspect of the present invention, there is provided a 
vibration driven motor which comprises an elastic member and a plurality 
of electro-mechanical converting elements connected to the elastic member, 
and changes a driving direction by changing the frequencies of vibrations 
produced by the electro-mechanical converting elements, and the vibration 
driven motor is characterized in that the plurality of electro-mechanical 
converting elements are divided into groups in correspondence with driving 
directions, and output predetermined driving vibrations in units of 
groups. 
The driving directions are preferably directions in which the 
electro-mechanical converting elements are disposed. Alternatively, when 
the electro-mechanical converting elements are divided into groups, the 
boundary line between adjacent groups is preferably substantially 
perpendicular to the corresponding driving direction. 
According to the sixth aspect of the present invention, there is provided a 
vibration driven motor which comprises an elastic member, and first to 
fourth electro-mechanical converting elements connected to the elastic 
member, and changes a driving direction by changing the frequencies of 
vibrations produced by the electro-mechanical converting elements, and the 
vibration driven motor is characterized in that the motor forms a first 
group by electrically connecting the first and second electro-mechanical 
converting elements, and a second group by electrically connecting the 
third and fourth electro-mechanical converting elements, in response to a 
first control signal for instructing a motion in a first direction, and 
applies first driving signals having different phases to the first and 
second groups to generate first and second mode signals so as to produce 
the motion in the first direction; and the motor forms a third group by 
electrically connecting the first and third electro-mechanical converting 
elements, and a fourth group by electrically connecting the second and 
fourth electro-mechanical converting elements, in response to a second 
control signal for instructing a motion in a second direction, and applies 
second driving signals having different phases to the third and fourth 
groups to generate third and fourth mode signals so as to produce the 
motion in the second direction. 
The first and third mode vibrations are preferably longitudinal vibrations, 
and the second and fourth mode vibrations are preferably bending 
vibrations. In this case, the second and fourth mode vibrations preferably 
have different mode orders. Alternatively, the first and third mode 
vibrations are preferably 1st-order longitudinal vibrations, the second 
mode vibration is preferably a 4th-order bending vibration, and the fourth 
mode vibration is preferably a 6th-order bending vibration. 
In addition, the elastic member preferably comprises a non-polarized 
piezoelectric element. 
According to the seventh aspect of the present invention, there is provided 
a vibration driven motor comprising: an elastic member; first to fourth 
electro-mechanical converting elements connected to the elastic member; a 
driving signal generation unit for generating a driving signal; a driving 
direction instruction unit; a grouping unit for, when the driving 
direction instruction unit instructs a first direction, forming a first 
group by electrically connecting the first and second electro-mechanical 
converting elements and a second group by electrically connecting the 
third and fourth electro-mechanical converting elements, and for, when the 
driving direction instruction unit instructs a second direction, forming a 
third group by electrically connecting the first and third 
electro-mechanical converting elements and a fourth group by electrically 
connecting the second and fourth electro-mechanical converting elements; 
and an input frequency instruction unit for, when the grouping unit forms 
the first and second groups, controlling the driving signal generation 
unit to apply first driving signals having different phases to the first 
and second groups, and for, when the grouping unit forms the third and 
fourth groups, controlling the driving signal generation unit to apply 
second driving signals having different phases to the third and fourth 
groups, and the vibration driven motor is characterized in that the 
elastic member makes a motion in the first direction by first and second 
mode vibrations produced upon application of the first driving signals, 
and makes a motion in the second direction by third and fourth vibrations 
produced upon application of the second driving signals. 
The above and other objects, features and advantages of the present 
invention will be explained hereinafter and may be better understood by 
reference to the drawings and the descriptive matter which follows.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIGS. 1A, 1B, 1C, and 1D are respectively a plan view, a side view, a front 
view, and a bottom view illustrating a main body of an embodiment of a 
vibration driven motor according to the present invention by a 
trigonometric method. 
The vibration driven motor of this embodiment comprises an elastic member 
1, electro-mechanical converting elements 2a to 2d forming a matrix having 
rows and columns, and sliding members 3a to 3d, and the like. 
The elastic member 1 is a planar member, and consists of a metal such as 
stainless steel, an aluminum alloy, or the like; a plastic material; or 
the like. In this embodiment, assume that the elastic member 1 has a 
thickness H, a length Wx, and a width Wy. 
The four electro-mechanical converting elements 2a to 2d are adhered on the 
upper surface of the elastic member 1, and the four sliding members 3a to 
3d are adhered on the lower surface thereof. 
The electro-mechanical converting elements 2a to 2d are elements for 
converting electric energy into mechanical energy, and comprise, e.g., 
piezoelectric elements such as PZT, electrostrictive elements such as PMN, 
or the like. 
The sliding members 3a to 3d are portions contacting an object (not shown), 
and are arranged at driving force output portions of the elastic member 1. 
Each of the sliding members 3a to 3d consists of an ethylene tetrafluoride 
resin (e.g., Teflon: the trade name of a product available from Du Pont 
Corp.), a plastic material containing molybdenum disulfide, or the like. 
When frequency voltages are applied to the electro-mechanical converting 
elements 2a to 2d, the vibration driven motor makes elliptic motions at 
the adhered positions of the sliding members 3a to 3d on the elastic 
member 1, and makes a motion relative to the object (not shown) since the 
sliding portions 3a to 3d are in press contact with the object. 
FIG. 2 is a block diagram showing a driving circuit of the embodiment of 
the vibration driven motor according to the present invention. 
Referring to FIG. 2, the driving circuit includes an input frequency 
instruction unit 11, an oscillator 12, a phase shift instruction unit 13, 
a phase shifter 14, amplifiers 15 and 16, an X-Y direction instruction 
unit 17, and analog switches 18 to 21. 
In this vibration driven motor, when the object is to be moved in the (+) 
direction of the (X) direction, the X-Y direction instruction unit 17 sets 
the (X) direction. The analog switches 18 and 20 are turned on, and the 
analog switches 19 and 21 are turned off to form a group consisting of the 
electro-mechanical converting elements 2a and 2c and a group consisting of 
the electro-mechanical converting elements 2b and 2d. 
Then, the phase shift instruction unit 13 sets the (+) direction, and the 
phase shifter 14 sets a phase shift of +.pi./2. In this state, when the 
X-Y direction instruction unit 17 instructs the driving operation in the 
(X) direction to the input frequency instruction unit 11, the input 
frequency instruction unit 11 instructs the oscillator 12 to generate a 
first frequency signal. 
When the oscillator 12 outputs the first frequency signal, the signal is 
amplified by the amplifier 16, and the amplified signal is input to the 
electro-mechanical converting elements 2b and 2d. Also, the phase of the 
first frequency signal is shifted by +.pi./2 by the phase shifter 14, and 
this signal is then amplified by the amplifier 15. The amplified signal is 
input to the electro-mechanical converting elements 2a and 2c. 
In this manner, a 1st-order longitudinal vibration and a 6th-order bending 
vibration are produced in the elastic member 1, and these two different 
vibrations degenerate to produce elliptic motions at the adhered positions 
of the sliding members 3a to 3d on the elastic member 1, thereby producing 
a motion in the (+) direction of the (X) direction relative to the object. 
On the other hand, in this vibration driven motor, when the object is to be 
moved in the (-) direction of the (X) direction, the X-Y direction 
instruction unit 17 sets the (X) direction. The analog switches 18 and 20 
are turned on, and the analog switches 19 and 21 are turned off to form a 
group consisting of the electro-mechanical converting elements 2a and 2c 
and a group consisting of the electro-mechanical converting elements 2b 
and 2d. 
Then, the phase shift instruction unit 13 sets the (-) direction, and the 
phase shifter 14 sets a phase shift of -.pi./2. In this state, when the 
X-Y direction instruction unit 17 instructs the driving operation in the 
(X) direction to the input frequency instruction unit 11, the input 
frequency instruction unit 11 instructs the oscillator 12 to generate a 
first frequency signal. 
When the oscillator 12 outputs the first frequency signal, the signal is 
amplified by the amplifier 16, and the amplified signal is input to the 
electro-mechanical converting elements 2b and 2d. Also, the phase of the 
first frequency signal is shifted by -.pi./2 by the phase shifter 14, and 
this signal is then amplified by the amplifier 15. The amplified signal is 
input to the electro-mechanical converting elements 2a and 2c. 
In this manner, a 1st-order longitudinal vibration and a 6th-order bending 
vibration are produced in the elastic member 1, and these two different 
vibrations degenerate to produce elliptic motions at the adhered positions 
of the sliding members 3a to 3d on the elastic member 1, thereby producing 
a motion in the (-) direction of the (X) direction relative to the object. 
Furthermore, in this vibration driven motor, when the object is to be moved 
in the (+) direction of the (Y) direction, the X-Y direction instruction 
unit 17 sets the (Y) direction. The analog switches 19 and 21 are turned 
on, and the analog switches 18 and 20 are turned off to form a group 
consisting of the electro-mechanical converting elements 2a and 2b and a 
group consisting of the electro-mechanical converting elements 2c and 2d. 
Then, the phase shift instruction unit 13 sets the (+) direction, and the 
phase shifter 14 sets a phase shift of +.pi./2. In this state, when the 
X-Y direction instruction unit 17 instructs the driving operation in the 
(Y) direction to the input frequency instruction unit 11, the input 
frequency instruction unit 11 instructs the oscillator 12 to generate a 
second frequency signal. 
When the oscillator 12 outputs the second frequency signal, the signal is 
amplified by the amplifier 16, and the amplified signal is input to the 
electro-mechanical converting elements 2c and 2d. Also, the phase of the 
second frequency signal is shifted by +.pi./2 by the phase shifter 14, and 
this signal is then amplified by the amplifier 15. The amplified signal is 
input to the electro-mechanical converting elements 2a and 2b. 
In this manner, a 1st-order longitudinal vibration and a 4th-order bending 
vibration are produced in the elastic member 1, and these two different 
vibrations degenerate to produce elliptic motions at the adhered positions 
of the sliding members 3a to 3d on the elastic member 1, thereby producing 
a motion in the (+) direction of the (Y) direction relative to the object. 
Finally, in this vibration driven motor, when the object is to be moved in 
the (-) direction of the (Y) direction, the X-Y direction instruction unit 
17 sets the (Y) direction. The analog switches 19 and 21 are turned on, 
and the analog switches 18 and 20 are turned off to form a group 
consisting of the electro-mechanical converting elements 2a and 2b and a 
group consisting of the electro-mechanical converting elements 2c and 2d. 
Then, the phase shift instruction unit 13 sets the (-) direction, and the 
phase shifter 14 sets a phase shift of -.pi./2. In this state, when the 
X-Y direction instruction unit 17 instructs the driving operation in the 
(Y) direction to the input frequency instruction unit 11, the input 
frequency instruction unit 11 instructs the oscillator 12 to generate a 
second frequency signal. 
When the oscillator 12 outputs the second frequency signal, the signal is 
amplified by the amplifier 16, and the amplified signal is input to the 
electro-mechanical converting elements 2c and 2d. Also, the phase of the 
second frequency signal is shifted by -.pi./2 by the phase shifter 14, and 
this signal is then amplified by the amplifier 15. The amplified signal is 
input to the electro-mechanical converting elements 2a and 2b. 
In this manner, a 1st-order longitudinal vibration and a 4th-order bending 
vibration are produced in the elastic member 1, and these two different 
vibrations degenerate to produce elliptic motions at the adhered positions 
of the sliding members 3a to 3d on the elastic member 1, thereby producing 
a motion in the (-) direction of the (Y) direction relative to the object. 
FIG. 3 is a view for explaining the principle of driving the embodiment of 
the vibration driven motor of the present invention in the X and Y 
directions. 
If the length Wx of the elastic member 1 is set to satisfy: 
EQU Wx=32..pi..H/(12).sup.1/2 
then, the resonance frequency, .OMEGA.L1X, of the 1st-order longitudinal 
vibration is given by: 
##EQU1## 
where E is the longitudinal elastic coefficient of the elastic member 1, 
and .rho. is the density of the elastic member 1. 
The resonance frequency, .OMEGA.B6X, of the 6th-order bending vibration is 
given by: 
##EQU2## 
where I is the geometrical moment of inertia of the elastic member 1, and 
A is the sectional area of the elastic member 1. As is understood from 
these equations, the 1st-order longitudinal vibration and the 6th-order 
bending vibration match and degenerate. 
Therefore, when a frequency of (12.E/.rho.).sup.1/2 !/(64.H) is input, the 
vibration driven motor is driven in the X direction (in the right-and-left 
direction of the plane of the drawing of FIG. 3). 
Next, if the width Wy of the elastic member 1 is set to satisfy: 
EQU Wy=72..pi..H/(12).sup.1/2 
then, the resonance frequency, .OMEGA.L1Y, of the 1st-order longitudinal 
vibration is given by: 
##EQU3## 
where E is the longitudinal elastic coefficient of the elastic member 1, 
and .rho. is the density of the elastic member 1. 
The resonance frequency, .OMEGA.B4Y, of the 4th-order bending vibration is 
given by: 
##EQU4## 
where I is the geometrical moment of inertia of the elastic member 1, and 
A is the sectional area of the elastic member 1. As is understood from 
these equations, the 1st-order longitudinal vibration and the 4th-order 
bending vibration match and degenerate. 
Therefore, when a frequency of (12.E/.rho.).sup.1/2 !/(144.H) is input, 
the vibration driven motor is driven in the Y direction (the up-and-down 
direction of the plane of the drawing of FIG. 3). 
Of course, since the input frequency (12.E/.rho.).sup.1/2 !/(64.H) for 
driving the motor in the X direction is different from the input frequency 
(12.E/.rho.).sup.1/2 !/(144.H) for driving the motor in the Y direction, 
one of the driving operation in the X direction and the driving operation 
in the Y direction can be selected. 
Strictly speaking, the resonance frequencies must be calculated in 
consideration of the influences of the electro-mechanical converting 
elements 2a to 2d and the sliding members 3a to 3d. However, since these 
calculations are considerably complicated, a description thereof will be 
omitted herein. 
In this embodiment, as shown in FIG. 3, the sliding members 3a to 3d are 
disposed at the intersection positions between the antinode positions of 
the 4th-order bending vibration (corresponding to a vibration in the third 
mode), B4, and the 6th-order bending vibration (corresponding to a 
vibration in the fourth mode), B6, to commonly use relative motion output 
portions in the X direction (corresponding to the first direction) and 
relative motion output portions in the Y direction (corresponding to the 
second direction). 
Having described preferred embodiments of the present invention, it is to 
be understood that any variations will occur to those skilled in the art 
within the scope of the appended claims.