JP3975666B2 - Object levitation device - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an object levitating apparatus that levitates an object using a radiation pressure such as a sound wave.
[0002]
[Prior art]
As an object levitating apparatus for levitating an object in the air, an object levitating apparatus for levitating an object on the surface of the vibrating body by the radiation pressure of the sound wave of the vibrating body vibrated by the excitation means is disclosed in JP-A-7-24415 and JP-A-7 -137824, JP-A-9-202425, and the like. In these devices, a flat vibrating body is used, and the surface of the object to be levitated facing the surface of the flat vibrating body is a flat surface, and the object is levitated by the radiation pressure of sound waves generated by the vibration of the vibrating body. There is also disclosed an object conveying apparatus that moves air that has been levitated by jetting air to the levitated object or generating a traveling wave with the vibrating body.
[0003]
Further, as a method of transporting an object in a levitated state, there is a method in which a trolley is equipped with the levitation device and the levitation device is moved.
Japanese Patent Application Laid-Open No. 9-169427 discloses a substrate transport apparatus for transporting an object having a relatively large flexibility, such as a glass substrate, and means for supporting and transporting the object in a contact state and bending of the object as a sound wave. There has been proposed a device in combination with a means for preventing radiation. In this apparatus, both ends of the object are supported by endless belts arranged in parallel, and the object is conveyed by the movement of the belt, and the diaphragm is emitted near the center of the object to prevent the object from being bent. The buoyancy is given by the energy of the pseudo standing wave node based on the sound wave. Since the resonance frequency of the diaphragm is about 20 kHz, the wavelength of the pseudo standing wave is about 20 mm, and one peak of levitation force exists at a position where the distance from the diaphragm is 10 to 20 mm.
[0004]
[Problems to be solved by the invention]
When the object to be levitated is a plate having a large area, it is preferable to apply a radiation pressure to the object with a plurality of diaphragms in order to levitate the object in a stable state. If the number of diaphragms is increased corresponding to the area of the object, the object can be prevented from bending and can be levitated in a stable state. However, as the number of diaphragms increases, the number of vibrators also increases and the cost increases. For this reason, it is conceivable that a diaphragm is disposed on the peripheral edge of the object to float and hold the object, and a diaphragm for preventing the object from bending is disposed in the center.
[0005]
As in the device disclosed in Japanese Patent Application Laid-Open No. 9-169427, the object is supported by the support member in the contact state, and the levitation force of the quasi-standing wave of the sound wave is used only for preventing the deflection. It is relatively difficult to position the diaphragm so that the position of the quasi-standing wave radiated from the diaphragm is located at a position corresponding to the bottom surface of the object. Easy to do.
[0006]
However, when the object is levitated and held completely in a non-contact state, it is difficult to levitate the object in a stable state unless the vibrators are excited with the same strength, and the bottom surface of the object and the surface of each vibrator The distance of fluctuates. In addition, it is difficult to make the resonance frequency of the vibration system including the vibration body constant due to manufacturing errors and assembly errors of each component constituting the vibration system. As a result, when an object having a large area and a large amount of deflection is levitated and held, simply providing a vibration-preventing vibration plate makes it easy for the object to come into contact with the vibration plate and scratch the object.
[0007]
The present invention has been made in view of the above problems, and its object is to suppress the bending of an object to a predetermined level or less when a plate-like object having a large area is levitated using a plurality of vibrating bodies. An object of the present invention is to provide an object levitation device capable of levitation in a stable state.
[0008]
[Means for Solving the Problems]
In order to achieve the above object, according to the first aspect of the present invention, an object levitation apparatus in which a plurality of vibrating bodies are excited by excitation means, and an object is levitated on the surface of the vibrating body by the radiation pressure of sound waves of the vibrating body. The distance between the surface of the vibration suppressing vibration body that plays a role of suppressing the bending of the object among the plurality of vibration bodies and the bottom surface of the object when the object is floated in a flat state without bending. , The wavelength λ of the pseudo standing wave of the sound wave generated from the deflection suppressing vibration body is set to be ½ or more, and each of the vibration bodies is vibrated so as to generate a standing wave, and the deflection suppression vibration The body is placed horizontally on the center side of the object, and the vibrator placed near the periphery of the object is such that the entire surface of the vibrator is against the bottom of the object so that the radiation pressure acting on the object is balanced in the horizontal direction of the object. Tilted inward In it is located.
[0009]
Therefore, in the present invention, the object is levitated on the surface of the vibrating body by the radiation pressure of the sound wave from the plurality of vibrating bodies excited by the excitation means. Deflection of an object held in a floating state is suppressed by the radiation pressure of a sound wave from another vibration body by the radiation pressure of the sound wave generated from the vibration body for bending suppression. In addition to the near field (several tens of μm to several hundreds of μm) that is very close to the vibrating body, the levitation force of the sound wave generated from the vibrating body is determined by the distance from the surface of the vibrating body for suppressing bending as the wavelength of the pseudo standing wave. The levitation force increases at a position n times 1/2 of λ (n is a natural number). Since the distance is ½ or more of the wavelength λ of the quasi-standing wave, the bending of the object is normally suppressed at a portion that is n / 2 times the wavelength λ, and the object at the portion for some reason. Even if the levitation fails and the deflection becomes large, the object is levitated by the levitation force in the near field of the vibrating body, and the bending is suppressed without contacting the vibrating body.
In the present invention, the object is held in a floating state at a predetermined position by the balance of the radiation pressure of the sound wave based on the standing wave generated from each vibrating body. Also, due to the action of the air flow generated between the vibrating body arranged near the periphery of the object and the object, the object has a horizontal force inward, and the object has a small horizontal external force. To the extent that it acts, the object stays in a stable state at a predetermined position.
[0010]
According to a second aspect of the present invention, in the first aspect of the present invention, the distance is n / 2 times the wavelength λ (n is a natural number). Therefore, in the present invention, from the initial state, the bottom surface of the object exists at a position that is a natural number multiple of a half wavelength, which is the position where the buoyancy of the pseudo standing wave generated from the bending suppressing vibration body is large, The bending of the object is easily suppressed effectively.
[0011]
In the invention described in claim 3, in the invention described in claim 2, the n is 1 or 2. The levitation force due to the pseudo standing wave generated from the vibrating body becomes large at a portion that is n / 2 times (n is a natural number) of the wavelength λ. The magnitude of the levitation force depends on the wavelength λ of the pseudo standing wave. Is larger than when the wavelength λ is the same, and when the distance is n / 2 (n is a natural number of 3 or more), the levitation force is significantly smaller than when the wavelength λ is the same. Therefore, by making the distance equal to ½ of the wavelength λ of the quasi-standing wave or the wavelength λ, the distance is easily levitated and held in a stable state in which bending is suppressed.
[0012]
According to a fourth aspect of the present invention, in the invention according to any one of the first to third aspects, the vibrating body disposed near the periphery of the object faces four corners of the rectangular plate-shaped object. The vibrating body for suppressing deflection is disposed at an equal distance from the four vibrating bodies disposed near the periphery of the object .
[0014]
According to a fifth aspect of the invention, in the invention according to any one of the first to fourth aspects, the edges of the vibrators arranged near the periphery of the object are aligned with the edges of the object. Is arranged .
According to a sixth aspect of the present invention, in the invention according to any one of the first to fifth aspects, each vibrating body disposed near the periphery of the object forms a surface of each vibrating body and a horizontal plane. The angle is inclined to 3 ° or less.
[0016]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an embodiment in which the present invention is embodied in an object levitating apparatus suitable for levitating and holding a rectangular flat plate will be described with reference to FIGS. 1 and 2. FIG. 1A is a schematic plan view of the object levitation apparatus.
[0017]
As shown in FIG. 1A, the object levitation apparatus 1 includes a plurality (five in this embodiment) of vibrating bodies 2a to 2d, 3 formed in a rectangular plate shape. Each vibrating body 2a-2d, 3 is formed in the same magnitude | size. The four vibrating bodies 2a to 2d are arranged at positions corresponding to the four corners of the rectangular plate-like object 4 (illustrated by chain lines), and the four bending suppressing vibrating bodies 3 that play a role of suppressing the bending of the object are four. It arrange | positions in the position of equidistant from the vibrating bodies 2a-2d. A horn 5 that constitutes an excitation means is fastened to each of the vibrators 2a to 2d, 3 by a screw (not shown) at the tip thereof. The horn 5 is formed in a shape in which a cylindrical portion is continuous at the upper part of the truncated cone, and is attached in a state orthogonal to the vibrating bodies 2 a to 2 d and 3 at the center of the vibrating bodies 2 a to 2 d and 3.
[0018]
As shown in FIG.1 (b), the surface of the vibrating body 3 is arrange | positioned horizontally. Each pair of vibrating bodies 2 a, 2 c, 2 b, 2 d arranged along the longitudinal direction of the object 4 (the left-right direction in FIGS. 1A and 1B) has a surface that is relative to the bottom surface of the object 4. It arrange | positions so that the radiation pressure which acts on the object 4 may be balanced in the state inclined toward the inner side. The angle θ formed with the horizontal plane of each of the vibrating bodies 2a to 2d varies depending on the mass of the object 4, the area of the vibrating bodies 2a to 2d, etc., but is, for example, approximately 1 °, usually 3 ° or less. .
[0019]
As shown in FIG. 1B, each horn 5 is fixed to the vibrator 6 on the surface opposite to the surface to which the vibrators 2a to 2d, 3 are fastened. The front end surface of the horn 5 is formed in a plane perpendicular to the axial direction of the vibrator 6, and the angle θ between the horizontal plane and the vibrating bodies 2 a to 2 d, 3 is the central axis of the horn 5 and the vibrator 6 with respect to the vertical direction. It is arranged in a state inclined at the same angle.
[0020]
A so-called Langevin-type vibrator is used as the vibrator 6 for driving the vibrators 2a to 2d, 3, and a pair of ring-shaped piezoelectric elements 7a, 7b and a ring-shaped electrode disposed between the piezoelectric elements 7a, 7b. The plate 8 and the metal blocks 9a and 9b arranged at positions where they abut against the outer surfaces of the piezo elements 7a and 7b are fastened and fixed by bolts (not shown). The bolt is screwed into a screw hole (not shown) formed in the metal block 9a from the metal block 9b side. Both metal blocks 9a and 9b are in a state of being electrically connected to each other via bolts.
[0021]
As shown in FIG. 1 (b), the object levitation apparatus 1 is attached on a carriage 10 via a support bracket 11. Each vibrator 6 is fixed to the support bracket 11 so that the vibrators 2a to 2d, 3 are at a predetermined angle θ or horizontal.
[0022]
The bending suppression vibrator 3 has a distance D between the surface thereof and the bottom surface of the object 4 when the object 4 is floated in a flat state without bending. The quasi-standing wave is disposed so as to be 1/2 or more of the wavelength λ. In this embodiment, the distance D is arranged so as to be twice the half of the wavelength λ, that is, a size corresponding to one wavelength.
[0023]
As shown in FIGS. 1A and 1B, the vibrators 6 that excite the vibrators 2 a to 2 d and 3 are connected to different oscillators 12. As shown in FIG. 1B, the electrode plate 8 is connected to the oscillator 12 via the wiring 13a, and the ground terminal of the oscillator 12 is connected to the metal block 9b via the wiring 13b. The horn 5, the vibrator 6, and the oscillator 12 constitute excitation means for exciting the vibrating bodies 2 a to 2 d and 3.
[0024]
Next, the operation of the apparatus configured as described above will be described.
The object levitation apparatus 1 is conveyed to the target position by the movement of the carriage 10 while holding the plate-like object 4 to be conveyed in a levitated state.
[0025]
As shown in FIGS. 1A and 1B, the object 4 is placed on the vibrating bodies 2a to 2d and 3 so that the edges 4a are aligned with the outer edges 14 of the vibrating bodies 2a to 2d. . In this state, by driving the oscillator 12, the vibrator 6 is excited at a predetermined resonance frequency (for example, around 20 kHz), the horn 5 is vibrated longitudinally, and the vibrators 2 a to 2 d and 3 are excited via the horn 5. Performs flexural vibration. When the vibrating bodies 2a to 2d and 3 perform flexural vibration, sound waves (standing waves) are generated from the vibrating bodies 2a to 2d and 3. The object 4 is levitated from the surfaces of the vibrating bodies 2a to 2d and 3 by the radiation pressure of the sound waves emitted from the vibrating bodies 2a to 2d and 3.
[0026]
Radiation pressure acts obliquely on the object 4 from the vibrating bodies 2a, 2b, 2c, and 2d inclined inward from each other, and the object 4 floats in a state where the horizontal component forces facing each other are balanced. Each vibrating body 2 a to 2 d applies a levitation force in the near field to the object 4.
[0027]
On the other hand, the bending suppressing vibration body 3 is vibrated so that a levitation force is applied to the object 4 at a distance equal to the wavelength λ of the pseudo standing wave of the sound wave generated from the bending suppressing vibration body 3. If the bending of the object 4 is prevented by the levitation force at the one-wavelength resonance portion of the pseudo standing wave generated from the bending suppressing vibration body 3, the object 4 will vibrate as shown in the solid line in FIG. When the distance D from the surface of the body 3 is twice the half of the wavelength λ of the quasi-standing wave, it is levitated and held in a substantially horizontal state without bending. When the levitation of the quasi-standing wave at the one-wavelength resonance part fails for some reason, the object 4 is a vibrating body for suppressing deflection as shown by a chain line A in FIG. It is levitated and held in a bent state until the distance D from the surface 3 becomes a position half the wavelength λ of the pseudo standing wave. If the levitation at a distance of λ / 2 fails for some reason, the object 4 has a distance D from the surface of the vibration suppressing vibration body 3 of λ / 2 as shown by a chain line B in FIG. The bending force of the object 4 is prevented by the levitation force of a much smaller near field.
[0028]
When the edge 14 of the vibrating bodies 2a to 2d and the edge 4a of the object 4 are aligned, the object 4 that is about to protrude from the edge 14 of the vibrating bodies 2a to 2d is radiated by the vibrating bodies 2a to 2d. The object 4 is pulled back inward by the action of the sound wave, so that the object 4 is held in a stable state at a predetermined position.
[0029]
This embodiment has the following effects.
(1) The distance D between the surface of the bending suppression vibrating body 3 and the bottom surface of the object 4 when the object 4 is floated in a flat state without bending is a sound wave generated from the bending suppression vibrating body 3. The pseudo standing wave has a wavelength λ of ½ or more. Therefore, normally, the object 4 can be levitated at a portion of n / 2 times (n is a natural number) of the wavelength λ of the pseudo standing wave to suppress the deflection of the object 4, and the object 4 at the portion can be suppressed for some reason. Even if the levitation fails and the flexure increases, the object 4 is levitated by the levitation force in the near field of the flexure suppressing vibration body 3, and the flexure is suppressed without contacting the vibrator 3.
[0030]
(2) Since the distance D is n / 2 times the wavelength λ (n is a natural number), and n = 2 in this embodiment, the object 4 is levitated by the pseudo standing wave generated from the vibration suppressing vibration body 3. There are three places where a large levitation force acts: a place where the distance from the vibration suppressing vibration body 3 is equal to the wavelength λ, a half of the wavelength λ, and a near field far away from the place. The vibrations 2a to 2d and 3 do not come into contact with the object 4 and the bending is effectively suppressed.
[0031]
(3) Since each of the vibrating bodies 2a to 2d, 3 is vibrated so as to generate a standing wave, the structure is simplified compared to a configuration that generates a traveling wave.
(4) Since the vibrating bodies 2a to 2d arranged at positions corresponding to the four corners of the object 4 are arranged in a state inclined at a predetermined angle θ with respect to the horizontal plane, the vibrating bodies 2a to 2d are arranged horizontally. As a result, the effect of holding the object 4 in a predetermined position is improved, and the edges of the vibrating bodies 2a to 2d are difficult to contact the object 4 even if the object 4 is bent.
[0032]
(5) The object levitation device 1 is mounted on the carriage 10. Therefore, the object 4 can be reliably conveyed to a predetermined position in a floating state by the movement of the carriage 10.
(6) The object 4 to be levitated has a flat bottom surface and has a straight edge 4a. When the vibrating bodies 2a to 2d hold the object 4 in the levitated state, the outer edge 14 thereof is a straight line of the object 4. It is arranged so as to extend along the edge 4a in the vicinity of the edge 4a. Therefore, the object 4 can be held in a stable state at a predetermined position.
[0033]
The embodiment is not limited to the above, and may be configured as follows, for example.
The distance between the surface of the bending suppression vibrating body 3 and the bottom surface of the object 4 in a state where the object 4 is levitated in a flat state without bending is a pseudo constant of the sound wave generated from the bending suppression vibrating body 3. The wavelength is not limited to the same as the wavelength λ of the existing wave, and may be not less than ½ of the wavelength λ.
[0034]
The bending suppressing vibration body 3 may be disposed at positions corresponding to the four corners of the object 4. That is, when the specific gravity is applied to one of the four corners compared to the other three due to the material of the object 4, if the bending suppressing vibration body 3 is disposed at the corresponding position, the bending is suppressed for some reason. Even if levitation fails at a distance of wavelength λ from the surface of the vibrating body 3 for use, levitation at a distance of λ / 2 or near field becomes possible and stable levitation is performed.
[0035]
O As shown in FIG. 3, you may comprise the bending suppression vibration body 3 so that raising / lowering is possible by an raising / lowering means. For example, the support bracket 11 is fixed to the rod 15a of the actuator 15 as the lifting means. As the actuator 15, an actuator that can be controlled by an electric signal, such as an electric cylinder or a linear actuator, is used. In this case, depending on the thickness and specific gravity of the object 4, the distance can be easily changed to a position where the distance is the same as the wavelength λ and a position where the distance is ½ of the wavelength λ.
[0036]
○ The object levitation device is not limited to the one that holds the object 4 in a levitated state at a predetermined position, and includes a plurality of vibrating vibrators that are formed to be long and are arranged in parallel to be excited so as to generate traveling waves. It may be provided. For example, as shown in FIG. 4, a bending suppressing vibration body 17 that generates a standing wave is disposed between the vibration bodies 16 a and 16 b as a pair of conveying vibration bodies. The vibrator 6 that excites the horn 18a fastened to one end of each of the vibrating bodies 16a and 16b is connected to an oscillator 19 respectively. The vibrator 6 for exciting the horn 18b fastened to the other end of each of the vibrating bodies 16a and 16b is connected to a load circuit 20 including a resistor R and a coil L, respectively. A horn 18c is fastened to the center of the bending suppressing vibration body 17, and each horn 18c is fixed to a vibrator (none of which is shown) connected to an oscillator.
[0037]
In the apparatus of this embodiment, when the vibrator 6 connected to the oscillator 19 is excited, the vibrating bodies 16a and 16b are bent and vibrated via the horns 18a and 18b, and the object 4 is levitated from the vibrating bodies 16a and 16b. . The vibrations of the vibrating bodies 16 a and 16 b are transmitted to the vibrator 6 connected to the load circuit 20, and the vibration energy, which is mechanical energy, is converted into electric energy by the piezoelectric elements 7 a and 7 b constituting the vibrator 6. This electrical energy is converted into Joule heat by the resistance R of the load circuit 20 and is dissipated. Therefore, the vibration wave generated in each of the vibrating bodies 16a and 16b becomes a traveling wave traveling in one direction, and the object 4 is conveyed in a floating state from the side corresponding to the vibrator 6 on the side connected to the oscillator 19 to the other side. The The conveyance is stopped by stopping the driving of the oscillator 19. The bending of the object 4 conveyed in a levitated state by the traveling waves generated from both the vibrating bodies 16a and 16b is suppressed by the bending suppressing vibrating body 17 disposed between the both vibrating bodies 16a and 16b.
[0038]
O The vibrating bodies 16a and 16b for conveyance may be disposed in an inclined state toward the inside. In this case, the stability of the object 4 is improved.
In the object levitation apparatus 1 that levitates and holds the rectangular object 4 at a predetermined position, the arrangement positions of the vibrators 2a to 2d are not limited to the positions corresponding to the four corners of the object 4, but correspond to the centers of the sides. You may arrange in a position. Further, the number of the vibrating bodies 2a to 2d is not limited to four, and may be changed as appropriate depending on the size of the object 4, and the arrangement position may be changed as appropriate. The number of the bending suppressing vibrating bodies 3 is one. Not only the number but also the number of the objects 4 may be changed as appropriate depending on the size of the object 4, and the arrangement position may be changed as appropriate.
[0039]
The resonance frequency for exciting the vibrator 6 is not limited to around 20 kHz, and may be a higher frequency. For example, it may be around 40 kHz. The levitation force due to the sound pressure becomes stronger at higher frequencies, and the number of positions where the levitation force becomes stronger, that is, λ × ((), even if the distance from the bending suppressing vibration bodies 3 and 17 to the bottom surface of the horizontal object 4 is the same. The value of n in (n / 2) increases.
[0040]
The shape of the object 4 to be levitated and held is not limited to a rectangle such as a rectangle, but may be an arbitrary shape such as a triangle, another polygon, or a circle.
○ Instead of the configuration in which the vibrating bodies 2a to 2d are arranged in a state inclined at a predetermined angle θ with respect to the horizontal plane, all the vibrating bodies 2a to 2d may be arranged horizontally.
[0041]
A part of the edge 14 of each of the vibrating bodies 2a to 2d may not correspond to the edge 4a of the object 4, and the object 4 may be applied to a size that protrudes from the edge 14.
The fixing of the vibrating bodies 2a to 2d, 3, 16a, 16b, 17 to the horns 5, 18a, 18b is not limited to fastening with screws, and an adhesive may be used, or may be fixed by brazing or welding.
[0042]
The vibrator 6 is not limited to the Langevin type vibrator, and other vibrators may be used.
Inventions (technical ideas) other than the claims described from the embodiments will be described below.
[0043]
(1) Before Symbol conveying vibrator provided two, are disposed in an inclined state so as to be directed inwardly to each other.
(2) pre-Symbol object has a rectangular shape, the vibrator at a position corresponding to the four corners of at least the object is located.
[0044]
【The invention's effect】
As described in detail above, according to the invention described in each claim , when a plate-like object having a large area is levitated using a plurality of vibrating bodies, the object is prevented from being bent below a predetermined level and stabilized. Can be levitated in the state.
[Brief description of the drawings]
FIG. 1A is a schematic plan view of an object levitation apparatus according to an embodiment, and FIG. 1B is a schematic front view of the object levitation apparatus mounted on a carriage.
FIG. 2 is a schematic diagram showing the relationship between the bending of an object and the vibration suppressing vibration body.
FIG. 3 is a schematic front view of an object levitation apparatus according to another embodiment.
FIG. 4 is a schematic perspective view of another embodiment.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Object levitation apparatus, 2a-2d ... Vibrating body, 3,17 ... Deflection suppressing vibrating body, 4 ... Object, 5, 18a, 18b ... Horn which comprises excitation means, 6 ... Similarly vibrator, 12, 19 ... Similarly, an oscillator, 16 ... a vibrating body for conveyance, D ... a distance.

Claims (6)

In an object levitation apparatus that excites a plurality of vibrators with an excitation means and floats an object on the surface of the vibrator by the radiation pressure of sound waves of the vibrator,
The distance between the surface of the bending-suppressing vibrating body that plays a role of suppressing the bending of the object among the plurality of vibrating bodies and the bottom surface of the object in a state where the object is levitated in a flat state without bending, More than ½ of the wavelength λ of the pseudo standing wave of the sound wave generated from the vibration suppressing vibration body ,
Each vibrator is vibrated so as to generate a standing wave, and the bending restraining vibrator is disposed horizontally on the center side of the object, and the vibrator disposed near the periphery of the object acts on the object. An object levitation device in which the entire surface of the vibrating body is disposed in an inwardly inclined state with respect to the bottom surface of the object so that the radiation pressure is balanced in the horizontal direction of the object.   The object levitation apparatus according to claim 1, wherein the distance is n / 2 times the wavelength λ (n is a natural number).   The object levitation apparatus according to claim 2, wherein n is 1 or 2. 4. The vibrating body disposed near the periphery of the object is disposed at a position facing the four corners of the rectangular plate-shaped object, and the vibration suppressing vibration body includes four vibrations disposed near the periphery of the object. The object levitation apparatus according to any one of claims 1 to 3, wherein the object levitation apparatus is disposed at an equal distance from the body . The object levitation apparatus according to any one of claims 1 to 4 , wherein an edge of each vibrating body arranged near the periphery of the object is arranged so as to align with an edge of the object.   The object levitation according to any one of claims 1 to 5, wherein each vibrating body arranged near the periphery of the object is inclined at an angle of 3 ° or less with the surface of each vibrating body and a horizontal plane. apparatus.

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