Abstract:
An actuator using a piezoelectric element. The actuator includes: the piezoelectric element, which is capacitive; an inductor; and a resistor. The piezoelectric element, the inductor and the resistor are serially arranged so as to define a serial circuit. When a suitable voltage is supplied to the serial circuit, a saw-tooth waveform voltage is applied to the piezoelectric element so that the piezoelectric element extends at a speed and compresses at a different speed repeatedly.

Description:
[0001]    This application is based upon application No. 2002-202750 filed in Japan, the contents of which are hereby incorporated by reference.  
         BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The present invention relates to a drive mechanism, a drive method and a circuit employed therein. More specifically, the present invention relates to the circuit suitable for applying a saw-tooth waveform of a voltage to a capacitive load, the drive mechanism provided with the circuit, and the drive method employing the circuit.  
           [0004]    2. Description of the Related Arts  
           [0005]    Conventionally, there have been two manners of running a drive mechanism in which a saw-tooth waveform of voltage is applied to a piezoelectric element.  
           [0006]    Referring to FIGS. 1A through 1C, the first manner of running the drive mechanism will be explained. As shown in FIG. 1A, a waveform generator W, specifically a digital-analog transducer therein, for example, of 8 bits and 1-5 volts type, generates a voltage having a saw-tooth waveform. The voltage having the saw-tooth waveform is amplified, for example, up to 1-10 volts, by an amplifier M, and then is applied to a piezoelectric element X in order to running the drive mechanism. By adjusting the waveform generator W, a waveform of forward direction as shown in FIG. 1B and a waveform of backward direction as shown in FIG. 2C can be generated.  
           [0007]    [0007]FIGS. 2, 3A and  3 B show a second manner of running the drive mechanism. FIG. 2 shows a circuit for applying a power-supply voltage V to a piezoelectric element X. The circuit includes constant current circuits A, D and switching circuits B, C. The waveform of forward direction or the waveform of backward direction are generated by actuating the constant current circuit A and the switching circuit B alternately, or by actuating the constant current circuit D and the switching circuit C alternately.  
           [0008]    For example, the circuit is constituted as shown in FIG. 3A. When control signals are input to terminals “a”, “b”, “c” and “d” of the circuit, the waveform of forward direction or the waveform of backward direction is generated, as shown in FIG. 3B.  
           [0009]    Specifically, when the terminal “a” is supplied with Hi input, the voltage applied to a piezoelectric element X gradually increases through the constant current circuit A as shown by the reference numeral  10  in FIG. 3B. Next, when the terminal “b” is supplied with Hi input, the piezoelectric element X is grounded through the switch circuit B, so that the voltage applied to the piezoelectric element X rapidly decreases as shown by the reference numeral  12  in FIG. 3B. Thus, the waveform of forward direction is generated.  
           [0010]    In the mean time, when the terminal “c” is supplied with Hi input, the piezoelectric element X is connected to the power supply voltage V through the switch circuit C, so that the voltage applied to the piezoelectric element X rapidly increases as shown by the reference numeral  14  in FIG. 3B. Then, when the terminal “d” is supplied with Hi input, the voltage applied to the piezoelectric element X gradually decreases through the constant current circuit D as shown by the reference numeral  16  in FIG. 3B. Therefore, the waveform of backward direction is generated.  
           [0011]    In the first manner, the waveform generator W and the power amplifier M are needed. In the second manner, the constant current circuits A, D and the switch circuits B, C are needed. Thus, the construction of the circuit is complex and introduces high cost. Additionally, the waveform includes high-order harmonic waves, which are not needed, and causes undesirable influence upon the drive mechanism.  
         SUMMARY OF THE INVENTION  
         [0012]    Accordingly, it is an object of the present invention to provide a drive mechanism, a drive method and a circuit employing a simple construction, in which a voltage having a saw-tooth waveform to be applied can be generated.  
           [0013]    In order to achieve the above object, according to one aspect of the present invention, there is provided a drive mechanism, comprising: an electromechanical transducer operating as a capacitor and having a pair of terminals; an inductive element operating as an inductor and having a pair of terminals; and a resistive element operating as a resistor and having a pair of terminals, wherein the electromechanical transducer, the inductive element and the resistive element are connected by terminals thereof in series so as to constitute a series resonance circuit, and wherein a voltage having a saw-tooth waveform applied to the electromechanical transducer causes the electromechanical transducer to expand at a first velocity and to contract at a second velocity, different from the first velocity.  
           [0014]    In the configuration, the electromechanical transducer (for example, electrostatic actuator, piezoelectric transducer, electrostriction transducer, magnetostriction transducer, and so on) changes the electrical energy (for example, electric voltage, electric current, electric field, electric charge, static electricity, magnetic field) supplied thereto into the mechanical energy (for example, transformation or strain such as prolonging, compressing, expanding, contracting, bending, twisting).  
           [0015]    In the configuration, the transfer function of the series resonance circuit, which is a serial RLC circuit, includes a second-order lag element, and therefore a suitable waveform of the voltage applied to the series resonance circuit causes the saw-tooth or slant waveform of the voltage applied to the electromechanical transducer.  
           [0016]    According to the configuration, it is possible to make parts of the circuit for generating a voltage applied to the electromechanical transducer less than that of conventional drive mechanisms. Thus, the voltage having the saw-tooth waveform applied to the electromechanical transducer can be generated, employing a simple construction.  
           [0017]    As an embodiment, a voltage having a square waveform applied to the series resonance circuit generates the voltage having the saw-tooth waveform applied to the electromechanical transducer.  
           [0018]    In the configuration, it is easy to apply the voltage having the square waveform so as to generate the voltage having the saw-tooth waveform applied to the electromechanical transducer.  
           [0019]    As an embodiment, one of the terminals of the electromechanical transducer is connected to ground. The other of the terminals of the electromechanical transducer is connected to one of the terminals of the resistive element. The other of the terminals of the resistive element is connected to one of the terminals of the inductive element. The voltage having the square waveform applied to the other of the terminals of the inductive element generates the voltage having the saw-tooth waveform applied to the other of the terminals of the electromechanical transducer.  
           [0020]    As an embodiment, an inequality of  
           0.4 ×fr&lt;fd&lt; 1.0 ×fr   (1)  
           [0021]    is satisfied, where fd is a frequency of the voltage having the square waveform applied to the series resonance circuit, and where fr is a resonance frequency of the series resonance circuit.  
           [0022]    Preferably, an inequality of  
           0.6 ×fr&lt;fd&lt; 0.8 ×fr   (2)  
           [0023]    is satisfied.  
           [0024]    As an embodiment, one of inequalities of  
           0.05&lt;Du&lt;0.48 and 0.52&lt;Du&lt;0.95   (3)  
           [0025]    is satisfied, where Du is a duty ratio of the voltage having the square waveform applied to the series resonance circuit.  
           [0026]    Preferably, one of inequalities of  
           0.15&lt;Du&lt;0.40 and 0.60&lt;Du&lt;0.85  (4)  
           [0027]    is satisfied.  
           [0028]    More preferably, one of inequalities of  
           0.25&lt;Du&lt;0.35 and 0.65&lt;Du&lt;0.75  (5)  
           [0029]    is satisfied.  
           [0030]    As an embodiment, an inequality of  
           (1/15 )×( L/C ) 1/2   &lt;R &lt;( L/C ) 1/2   (6)  
           [0031]    is satisfied, where C is a capacitance of the electromechanical transducer, where L is an inductance of the inductive element, and where R is a resistance of the resistive element.  
           [0032]    Preferably, an inequality of  
           (1/10 )×( L/C ) 1/2   &lt;R &lt;(1/1.5 )×( L/C ) 1/2   (7)  
           [0033]    is satisfied.  
           [0034]    As an embodiment, the electromechanical transducer has a pair of ends in an expanding and contracting direction. The drive mechanism further comprises a drive member fixed to one of the ends of the electromechanical transducer; and a driven member which contacts frictionally with the drive member under a predetermined frictional force exerting therebetween. The voltage having the saw-tooth waveform applied to the electromechanical transducer causes the electromechanical transducer to expand at the first velocity and to contract at the second velocity, different from the first velocity, so as to move the driven member along with the drive member relatively.  
           [0035]    According to the above embodiments, it is possible to generate a suitable waveform of the voltage applied to the electromechanical transducer for running the drive mechanism.  
           [0036]    In order to achieve the above object, according to another aspect of the present invention, there is provided a drive method for running a drive mechanism which comprises: an electromechanical transducer operating as a capacitor and having a pair of terminals; an inductive element operating as an inductor and having a pair of terminals; and a resistive element operating as a resistor and having a pair of terminals, wherein the electromechanical transducer, the inductive element and the resistive element are connected by terminals thereof in series so as to constitute a series resonance circuit, the driving method comprising: a first step of applying a voltage to the series resonance circuit so as to generate a voltage having a saw-tooth waveform applied to the electromechanical transducer; and a second step of expanding the electromechanical transducer at a first velocity and contracting at a second velocity, different from the first velocity, by the voltage having the saw-tooth waveform applied to the electromechanical transducer generated at the first step.  
           [0037]    In the configuration, the electromechanical transducer (for example, electrostatic actuator, piezoelectric transducer, electrostriction transducer, magnetostriction transducer, and so on) changes the electrical energy (for example, electric voltage, electric current, electric field, electric charge, static electricity, magnetic field) supplied thereto into the mechanical energy (for example, transformation or strain such as prolonging, compressing, expanding, contracting, bending, twisting).  
           [0038]    In the configuration, the transfer function of the series resonance circuit, which is a serial RLC circuit, includes a second-order lag element, and therefore a suitable waveform of the voltage applied to the series resonance circuit causes the saw-tooth or slant waveform of the voltage applied to the electromechanical transducer.  
           [0039]    According to the configuration, it is possible to make parts of the circuit for generating a voltage applied to the electromechanical transducer less than that of conventional drive mechanisms. Thus, the voltage having the saw-tooth waveform applied to the electromechanical transducer can be generated, employing a simple construction.  
           [0040]    As an embodiment, the voltage having a square waveform is applied to the series resonance circuit to perform the first step.  
           [0041]    In the configuration, it is easy to apply the voltage having the square waveform so as to generate the voltage having the saw-tooth waveform on the electromechanical transducer.  
           [0042]    As an embodiment, one of the terminals of the electromechanical transducer is connected to ground. The other of the terminals of the electromechanical transducer is connected to one of the terminals of the resistive element. The other of the terminals of the resistive element is connected to one of the terminals of the inductive element. The voltage having the square waveform is applied to the other of the terminals of the inductive element so as to generate the voltage having the saw-tooth waveform applied to the other of the terminals of the electromechanical transducer to perform the first step.  
           [0043]    As an embodiment, an inequality of  
           0.4 ×fr&lt;fd&lt; 1.0 ×fr   (1′)  
           [0044]    is satisfied, where fd is a frequency of the voltage having the square waveform applied to the series resonance circuit, and where fr is a resonance frequency of the series resonance circuit.  
           [0045]    Preferably, an inequality of  
           0.6 ×fr&lt;fd&lt; 0.8 ×fr   (2′)  
           [0046]    is satisfied.  
           [0047]    As an embodiment, one of inequalities of  
           0.05&lt;Du&lt;0.48 and 0.52&lt;Du&lt;0.95  (3′)  
           [0048]    is satisfied, where Du is a duty ratio of the voltage having the square waveform applied to the series resonance circuit.  
           [0049]    Preferably, one of inequalities of  
           0.15&lt;Du&lt;0.40 and 0.60&lt;Du&lt;0.85  (4′)  
           [0050]    is satisfied.  
           [0051]    More preferably, one of inequalities of  
           0.25&lt;Du&lt;0.35 and 0.65&lt;Du&lt;0.75  (5′)  
           [0052]    is satisfied.  
           [0053]    As an embodiment, an inequality of  
           (1/15 )×( L/C )  1/2   &lt;R &lt;( L/C ) 1/2   (6′)  
           [0054]    is satisfied, where C is a capacitance of the electromechanical transducer, where L is an inductance of the inductive element, and where R is a resistance of the resistive element.  
           [0055]    Preferably, an inequality of  
           (1/10 )×( L/C ) 1/2   &lt;R &lt;(1/1.5 )×( L/C ) 1/2   (7′)  
           [0056]    is satisfied.  
           [0057]    As an embodiment, the electromechanical transducer have a pair of ends in an expanding and contracting direction. The drive mechanism further comprises: a drive member fixed to one of the ends of the electromechanical transducer; and a driven member which contacts frictionally with the drive member under a predetermined frictional force exerting therebetween. The second step of expanding the electromechanical transducer at the first velocity and contracting at the second velocity, different from the first velocity, is carried out so as to move the driven member along with the drive member.  
           [0058]    According to the above embodiments, it is possible to generate a suitable waveform of the voltage applied to the electromechanical transducer for running the drive mechanism.  
           [0059]    In order to achieve the above object, according to still another aspect of the present invention, there is provided a circuit for generating a voltage having a saw-tooth waveform, comprising: an capacitance element operating as a capacitor and having a pair of terminals; an inductive element operating as an inductor and having a pair of terminals; and a resistive element operating as a resistor and having a pair of terminals, wherein the capacitance element, the inductive element and the resistive element are connected by terminals thereof in series so as to constitute a series resonance circuit, and wherein a voltage having a square waveform applied to the series resonance circuit generates the voltage having the saw-tooth waveform applied to the capacitance element.  
           [0060]    In the configuration, the transfer function of the series resonance circuit, which is a serial RLC circuit, includes a second-order lag element, and therefore a suitable waveform of the voltage applied to the series resonance circuit generates the saw-tooth or slant waveform of the voltage applied to the capacitive element.  
           [0061]    According to the configuration, it is possible to make parts of the circuit for generating a voltage applied to the capacitive element less than that of conventional drive mechanisms. Thus, the voltage having the saw-tooth waveform applied to the capacitive element can be generated, employing a simple construction.  
           [0062]    As an embodiment, one of the terminals of the capacitance element is connected to ground. The other of the terminals of the capacitance element is connected to one of the terminals of the resistive element. The other of the terminals of the resistive element is connected to one of the terminals of the inductive element. The voltage having the square waveform applied to the other of the terminals of the inductive element generates the voltage having the saw-tooth waveform applied to the other of the terminals of the capacitance element.  
           [0063]    As an embodiment, an inequality of  
           0.4 ×fr&lt;fd&lt; 1.0 ×fr   (1″)  
           [0064]    is satisfied, where fd is a frequency of the voltage having the square waveform applied to the series resonance circuit, and where fr is a resonance frequency of the series resonance circuit.  
           [0065]    Preferably, an inequality of  
           0.6 ×fr&lt;fd&lt; 0.8 ×fr   (2″)  
           [0066]    is satisfied.  
           [0067]    As an embodiment, one of inequalities of  
           0.05&lt;Du&lt;0.48 and 0.52&lt;Du&lt;0.95  (3″)  
           [0068]    is satisfied, where Du is a duty ratio of the voltage having the square waveform applied to the series resonance circuit.  
           [0069]    Preferably, one of inequalities of  
           0.15&lt;Du&lt;0.40 and 0.60&lt;Du&lt;0.85  (4″)  
           [0070]    is satisfied.  
           [0071]    More preferably, one of inequalities of  
           0.25&lt;Du&lt;0.35 and 0.65&lt;Du&lt;0.75  (5″)  
           [0072]    is satisfied.  
           [0073]    As an embodiment, an inequality of  
           (1/15 )×( L/C ) 1/2   &lt;R &lt;( L/C ) 1/2   (6″)  
           [0074]    is satisfied, where C is a capacitance of the electromechanical transducer, where L is an inductance of the inductive element, and where R is a resistance of the resistive element.  
           [0075]    Preferably, an inequality of  
           (1/10 )×( L/C ) 1/2   &lt;R &lt;(1/1.5 )×( L/C ) 1/2   (7″)  
           [0076]    is satisfied.  
           [0077]    According to the above embodiments, it is possible to generate a suitable waveform of the voltage applied to the capacitive element for actuating the capacitive element. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0078]    This and other objects and features of the present invention will become clear from the following description taken in conjunction with the preferred embodiment thereof with reference to the accompanying drawings.  
         [0079]    [0079]FIG. 1A is a schematic illustration showing a first conventional manner of running a drive mechanism.  
         [0080]    [0080]FIGS. 1B and 1C are waveform charts showing waveforms generated by the first conventional manner as shown in FIG. 1A.  
         [0081]    [0081]FIG. 2 is a circuit diagram showing a second conventional manner of running the drive mechanism.  
         [0082]    [0082]FIG. 3A is a detail circuit diagram of FIG. 2.  
         [0083]    [0083]FIG. 3B is a set of timing charts as to the circuit diagram of FIG. 3A.  
         [0084]    [0084]FIGS. 4A through 4C are schematic illustrations of a driving mechanism according to an embodiment of the present invention.  
         [0085]    [0085]FIG. 4D is a waveform chart of a voltage applied to a piezoelectric element in the driving mechanism as shown in FIGS. 4A through 4C.  
         [0086]    [0086]FIG. 5A is a schematic exploded view of the drive mechanism according to the embodiment of the present invention.  
         [0087]    [0087]FIG. 5B is a perspective view of the drive mechanism.  
         [0088]    [0088]FIG. 6A is a schematic circuit diagram of a series resonance circuit arranged in the drive mechanism.  
         [0089]    [0089]FIGS. 6B and 6C are transfer characteristic graphs of the series resonance circuit.  
         [0090]    [0090]FIG. 6D is a waveform chart of a voltage at a capacitive element.  
         [0091]    [0091]FIG. 7 is a detail circuit diagram including the series resonance circuit.  
         [0092]    [0092]FIGS. 8A through 8F are a set of timing charts as to the detail circuit diagram as shown in FIG. 7.  
         [0093]    [0093]FIGS. 9A through 9E are waveform charts of a voltage at a piezoelectric element.  
         [0094]    [0094]FIGS. 10A through 10G are waveform charts of a voltage at the piezoelectric element.  
         [0095]    [0095]FIGS. 11A through 11G are waveform charts of a voltage at the piezoelectric element.  
         [0096]    [0096]FIG. 12 is a graph showing a relationship between the velocity of a moving body and a frequency.  
         [0097]    [0097]FIG. 13 is a graph showing a relationship between the velocity of a moving body and a duty ratio.  
         [0098]    [0098]FIG. 14 is a graph showing a relationship between the velocity of a moving body and a resistance of the resistive element. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0099]    Before the description of the preferred embodiment according to the present invention proceeds, it is to be noted that like or corresponding parts are designated by like reference numerals or characters throughout the accompanying drawings.  
         [0100]    A detailed description is made below upon a drive mechanism of the preferred embodiment, with reference to FIG. 4 through FIG. 14.  
         [0101]    [0101]FIGS. 4A through 4D show the operation principal of the drive mechanism.  
         [0102]    As shown in FIGS. 4A through 4C, one end of a piezoelectric element in an extending and contracting direction is connected to a fixed member. The other end of the piezoelectric element in the same direction is connected to a drive member. The drive member moves in forward direction and backward direction, when the piezoelectric element extends or contacts. A moving body is engaged with the drive member by a frictional force.  
         [0103]    The moving body is driven when a voltage having a saw-tooth waveform is applied to the piezoelectric element so as to cause the piezoelectric element to extend at a first velocity, and to contract at a second velocity, different from the first velocity. FIGS. 4A, 4B and  4 C show respective states at points of time indicated by the reference characters A, B and C in FIG. 4D.  
         [0104]    When the voltage gradually increases during a section A-B as shown in FIG. 4D, the piezoelectric element relatively slowly extends so that the state as shown in FIG. 1A changes into the state as shown in FIG. 4B. At the time, the moving body slides little, or it does not slide with respect to the drive member, and therefore the moving body moves together with the drive member substantially.  
         [0105]    Secondly, when the voltage abruptly decreases during a section B-C as shown in FIG. 4D, the piezoelectric element contracts relatively fast so that the drive member returns to an initial position. At the time, the moving body stays at the present position substantially, and the moving body slides with respect to the drive member. Therefore, only the drive member returns to the initial position. AS the result, the moving body moves from the initial position as shown in FIG. 4A to a forward position as shown in FIG. 4C.  
         [0106]    Repeating such a cycle, the moving body moves along the drive member in a forward direction.  
         [0107]    In the mean time, the moving body moves in a backward direction, when a waveform having a rapidly increasing part and a gradually decreasing part is applied to the piezoelectric element.  
         [0108]    [0108]FIG. 5A and 5B show a specific construction of the drive mechanism  20  according to the embodiment of the present invention. FIG. 5A is an exploded view of the drive mechanism  20 , and FIG. 5B is a perspective view of its assembled drive mechanism  20 .  
         [0109]    The drive mechanism  20  comprises a fixed member  24 , a piezoelectric element  22 , a drive rod  26  and a driven unit  28 . The fixed member  24  is fixed to a stationary member of an unshown apparatus (for example, a base of an XY-table). The piezoelectric element  22  is, for example, of a laminated type. The drive rod  26  is slidably supported by the fixed member  24 . The drive unit  28  is connected to a driven part (not shown) such as a stage in the XY-table. One end of the piezoelectric element  22  in an extending and contracting direction is fixed to an end of the fixed member  24 , and the other end of the piezoelectric element  22  in the extending and contracting direction is fixed to an end of the drive rod  26 . The drive unit  28 , including a slider  28   c , a contact member  28   b , and a spring plate  28   a , is engaged with the drive rod  26  by a frictional force so as to be able to slide along the drive rod  26 . When the voltage having the saw-tooth waveform is applied to the piezoelectric element  22  of the drive mechanism  20  so as to cause the drive rod  26  to vibrate axially, the drive unit  28  moves along the drive rod  26  in a desired direction.  
         [0110]    That is, the piezoelectric element  22  performs as an electromechanical transducer, a drive rod  26  performs as a drive member, and the drive unit  28  performs as a moving body or an engaging member.  
         [0111]    Referring to FIGS. 6A through 6C, a circuit for generating a voltage to drive the drive mechanism  20  will be explained.  
         [0112]    As shown in FIG. 6A, a capacitive load X (corresponding to the piezoelectric element  22  of the drive mechanism  20 ), a resistive element R, and a inductive element L are connected in series so as to constitute a series resonance circuit P. Specifically, one terminal of the capacitive load X is grounded and the other terminal thereof, a voltage of which is designated as Vd, is connected to one terminal of the resistive element R. The other terminal of the resistive element R is connected to one terminal of the inductive element L. A voltage supplied to the series resonance circuit P, or to the other terminal of the inductive element L is designated as Vp.  
         [0113]    [0113]FIGS. 6B and 6C show the transfer characteristic from Vp to Vd in the series resonance circuit P. The reference character fr in the figures designates a resonance frequency of the series resonance circuit P.  
         [0114]    [0114]FIG. 6D shows an example of a waveform of the voltage Vd at the capacitive load X, when a square waveform of the voltage Vp, or the voltage Vp having a square waveform, is applied to the series resonance circuit P. At the time, the frequency of the voltage Vp is shown by the reference character fd in FIGS. 6B and 6C. Such a frequency fd is 0.7 times resonance frequency fr (fd=0.7×fr), and the duty ratio of the square waveform of the voltage Vp is 0.3.  
         [0115]    Expressing the waveform of the voltage Vp by Fourier series, the gain of the secondary wave is about half of that of the primary wave, and the phase of the secondary wave delays or lags with respect to the primary wave, according to the transfer characteristic as shown in FIGS. 6B and 6C. The gain of the tertiary wave or high-order wave is attenuated significantly. Thus, supplying the square waveform of the voltage Vp, the waveform of the voltage Vd between the terminals of the capacitive load X is consisted nearly of the primary wave and the secondary wave, and has a saw-tooth waveform as shown in FIG. 6D.  
         [0116]    [0116]FIG. 7 shows a circuit of the drive mechanism  20 .  
         [0117]    The circuit comprises four switching elements Q 1 , Q 2 , Q 3  and Q 4 , the inductive element L, and the resistive element R, which are arranged to apply the voltage between the terminals of the capacitive load X (or the piezoelectric element  22 ).  
         [0118]    Each of the switching elements Q 1 , Q 2 , Q 3  and Q 4  is MOSFET (metal oxide semiconductor field effect transistor), and gates thereof are connected to terminals Sc 1 , Sc 2 , Sc 3  and Sc 4  of a control circuit K. The switching elements Q 1  and Q 3  are of the p channel type, and the switching elements Q 2  and Q 4  are of the n channel type.  
         [0119]    A source of the switching elements Q 1  and a source of the switching elements Q 3  are connected by a connecting point “a” to a power source Vcc. A drain of the switching elements Q 1  is connected to a drain of the switching elements Q 2  through a connecting point “c”. A drain of the switching elements Q 3  is connected to a drain of the switching elements Q 4  through a connecting point “d”. A source of the switching elements Q 2  and a source of the switching elements Q 4  are connected by a connecting point “b” to ground.  
         [0120]    The capacitive load X is connected in series with the inductive element L and a resistive element R between the connecting points “c” and “d” so as to constitute the resonance circuit therebetween.  
         [0121]    [0121]FIGS. 8A through 8F are a set of timing charts, which show operation of the control circuit K. FIGS. 8A through 8D show respective voltages at the terminals Sc 1 -Sc 4  of the control circuit K, that is, respective voltages of the gates of the switching elements Q 1 -Q 4 . FIG. 8E shows a voltage Vp of the resonance circuit P. FIG. 8F shows a voltage Vd between the terminals of the capacitive load X.  
         [0122]    Low signal of the terminals Sc 1 , Sc 3 , indicated by reference numerals  11 ,  13 , causes the switching elements Q 1 , Q 3  to be on, that is, to become conductive, since the switching elements Q 1 , Q 3  are the p channel type of FET. High signal of the terminals Sc 2 , Sc 4 , indicated by reference numerals  12 ,  14 , causes the switching elements Q 2 , Q 4  to be on, that is, to become conductive, since the switching elements Q 2 , Q 4  are the n channel type of FET.  
         [0123]    The control circuit K repeats a cycle consisting of periods T1 and T2.  
         [0124]    During the period T1, the terminals Sc 1 , Sc 2  are in the state of low signal, and the terminals Sc 3 , Sc 4  are in the state of high signal, so that the switching elements Q 2 , Q 3  are off or in an open state and the switching elements Q 1 , Q 4  are on or in a close state. Thereby, the connecting point “c”, or one end of the resonance circuit P is connected by the switching element Q 1  to the source power Vcc, and the connecting point “d”, or the other end of the resonance circuit P is connected by the switching element Q 4  to the ground. Thus, the voltage Vp across the resonance circuit P is +Vcc as shown by the reference numeral  15  in FIG. 8E. A positive direction of the voltage Vp is indicated by a direction of an arrow in FIG. 7.  
         [0125]    During the period T2, the terminals Sc 1 , Sc 2  are in the state of high signal, and the terminals Sc 3 , Sc 4  are in the state of low signal, so that the switching elements Q 1 , Q 4  are off or in an open state and that the switching elements Q 2 , Q 3  are on or in a close state. Thereby, the connecting point “c” is connected by the switching element Q 2  to the ground, and the connecting point “d” is connected by the switching element Q 3  to the power source Vcc. Thus, the voltage Vp across the resonance circuit P is −Vcc as shown by the reference numeral  16  in FIG. 8E.  
         [0126]    As shown in FIG. 8E, the waveform of the voltage Vp across the resonance circuit P is square. Corresponding to such a square waveform, the waveform of the voltage Vd at the capacitive load X is, for example, in the general shape of saw-tooth as shown in FIG. 8F.  
         [0127]    Referring to FIGS.  9 - 14 , the frequency fd and the duty ratio Du of the square waveform of the voltage Vp applied to the series resonance circuit P, and the values of the elements in the series resonance circuit P will be explained.  
         [0128]    First, the frequency fd of the square waveform of the voltage Vp applied to the series resonance circuit P will be explained, referring to FIGS. 9 and 12.  
         [0129]    [0129]FIG. 9A through 9E show a set of waveforms of the voltage Vd at the capacitive load X (or the piezoelectric element  22 ) for the variation of the frequency fd, that is, from 0.3 to 1.1 times resonance frequency fr, on condition that the duty ratio of the square waveform of the voltage Vp is 0.3 (Du=0.3), the inductance of the inductive element L is 100 micro-henries (L=100 μ H), the resistance of the resistive element R is 23 ohms (R=23 Ω), the capacitance of the capacitive load X (or the piezoelectric element  22 ) is 30 nano-farads (C=30 nF), concerning the circuit as shown in FIG. 7. FIG. 12 shows the velocity of the moving body or the drive unit  28  of the drive mechanism  20  in such a state. The reference character fr indicates the resonance frequency of the resonance circuit P, hereinafter.  
         [0130]    Referring to FIG. 12, the moving body moves fastest when the frequency fd is 0.7 time resonance frequency fr. It is because the difference between the sliding amount of the moving body during the expanding time of the capacitive element X (or the piezoelectric element  22 ) and that during the compressing time thereof is maximum. When the frequency fd is equal to the resonance frequency fr, it is not possible to move the moving body. At the time, the waveform of the voltage Vd is nearly a sine curve, and therefore there is no or little difference between the sliding amount of the moving body during the expanding time of the capacitive element X (or the piezoelectric element  22 ) and that during the compressing time thereof. When the frequency fd is not greater than 0.4 times resonance frequency fr, it is not possible to move the moving body. FIG. 12 provides a practical or preferable range of the frequency fd from 0.6 to 0.8 times resonance frequency fr.  
         [0131]    As a result, the preferable range of the frequency fd can be expressed in an inequality form as:  
         0.4 ×fr&lt;fd&lt; 1.0 ×fr   (8)  
         [0132]    The more preferable range thereof can be expressed in an inequality form as:  
         0.6 ×fr&lt;fd&lt; 0.8 ×fr   (9)  
         [0133]    Second, the duty ratio Du of the square waveform of the voltage Vp applied to the series resonance circuit P will be explained, referring to FIGS. 10 and 13.  
         [0134]    [0134]FIG. 10A through 10G show a set of waveforms of the voltage Vd at the capacitive load X (or the piezoelectric element  22 ) for the variation of the duty ratio Du, that is, from 0.05 to 0.95, on condition that the frequency fd is 0.7 times resonance frequency fr (fd=0.7×fr), the inductance of the inductive element L is 100 micro-henries (L=100 μH), the resistance of the resistive element R is 23 ohms (R=23 Ω), and the capacitance of the capacitive load X (or the piezoelectric element  22 ) is 30 nano-farads (C=30 nF), concerning the circuit shown in FIG. 7. FIG. 13 shows the velocity of the moving body or the drive unit  28  in the drive mechanism  20  in such a state.  
         [0135]    Referring to FIG. 13, the velocity of the moving body in forward direction is maximum when the duty ratio Du is 0.3, and the velocity of the moving body in backward direction is maximum when the duty ratio Du is 0.7. When the duty ratio Du is near to 0.5, that is, not less than 0.48 and not greater than 0.52 (0.48≦Du≦0.52), the waveform of the voltage Vd is nearly a sine curve as shown in FIG. 10D. Therefore, it is not possible to move the moving body. When the duty ratio Du is 0.05 or 0.95 (Du=0.05, 0.95), the voltage Vd is damped so significantly as shown in FIG. 10A or  10 G, that it is not possible to move the moving body. Referring to FIG. 13, a practical range of the duty ratio Du is 0.15-0.40 and 0.60-0.85, more preferably, 0.25-0.35 and 0.65-0.75.  
         [0136]    Therefore, the preferable range of the duty ratio Du can be expressed in an inequality form as:  
         0.05&lt;Du&lt;0.95  (10)  
         [0137]    The more preferable range thereof can be expressed in an inequality form as:  
         0.15&lt;Du&lt;0.4, 0.6&lt;Du&lt;0.85  (11)  
         [0138]    The further more preferable range thereof can be expressed in inequality form as:  
         0.25&lt;Du&lt;0.35, 0.65&lt;Du&lt;0.75  (12)  
         [0139]    Finally, the values of the elements in the series resonance circuit P will be explained, referring to FIGS. 11 and 14.  
         [0140]    The frequency of the voltage at the capacitive load X (or the piezoelectric element) equals the frequency fd of the square waveform of the voltage Vp applied to the series resonance circuit P, and can be expressed in a form of coefficient times resonance frequency fr of the series resonance circuit P, as described in the above inequalitys (8) and (9). The resonance frequency fr is determined by the inductance L of the inductive element L and the capacitance C of the capacitive load X in the series resonance circuit P. Therefor, the resistance R is varied, on the condition that the inductance L and capacitance C are constant, hereinafter.  
         [0141]    [0141]FIGS. 11A through 11G show a set of waveforms of the voltage Vd at the capacitive element (or the piezoelectric element  22 ) for the variation of the resistance R, that is, from 1/20 times of the squarer root of ( L divided by C) to 1/0.5 times thereof, on condition that the frequency fd of the voltage Vp is 0.7 time of the resonance frequency fr (fd=0.7×fr), the duty ratio Du of the square waveform of the voltage Vp is 0.3 (Du=0.3), the inductance L of the inductive element L is 100 micro-henries (L=100 μ H), the capacitance C of the capacitive load X (or the piezoelectric element  22 ) is 30 nano-Farad (C=30 nF), concerning the circuit as shown in FIG. 7. FIG. 14 shows the velocity of the moving body in such a state.  
         [0142]    Referring to FIG. 14, the velocity of the moving body is maximum when the resistance R is 1/2.5 times of the squarer root of ( L divided by C), that is, R=(1/2.5)×{square root}{square root over ( )}(L/C). It is not possible to move the moving body, when the resistance R is 1/20 times of the squarer root of ( L divided by C), and 1/0.5 times thereof, that is, R=(1/20)×{square root}{square root over ( )}(L/C), and R=(1/0.5)×{square root}{square root over ( )}(L/C). It is possible to move the moving body, when the resistance R is (1/15) and 1 times of the squarer root of ( L divided by C), that is, R=(1/50)×{square root}{square root over ( )}(L/C) and R=°{square root over ( )}(L/C). A practical range of the resistance R is (1/10)−(1/1.5) times squarer root of (L divided by C).  
         [0143]    Therefore, it is preferable that the values of the elements in the series resonance circuit P meet an inequality as follows:  
         (1/15)×( L/C ) 1/2   &lt;R &lt;( L/C ) 1/2   (13)  
         [0144]    More preferably, the values meet an inequality as follows:  
         (1/10)×( L/C ) 1/2   &lt;R &lt;(1/1.5)×( L/C ) 1/2   (14)  
         [0145]    As described above, FIGS.  9 - 12  show that the drive mechanism  20  can be driven when the voltage having the saw-tooth waveform Vd is applied to the capacitive load X (or the piezoelectric element  22 ). The saw-tooth waveform of the voltage Vd is generated by the circuit as shown FIGS. 7 and 8. The circuit includes the series resonance circuit P, and is constructed simply.  
         [0146]    Although the present invention has been fully described about the preferred embodiment thereof with reference to the accompanying drawings, it is to be noted that various changes and modifications are also apparent to those skilled in the art.  
         [0147]    For example, the present invention can be applied not only to the above element-fixed type of the drive mechanism employing electromechanical transducer, but various other types thereof such as a drive member fixed type, a moving body or engaging member fixed type, self-propelled type.  
         [0148]    The circuit which generates the voltage having the saw-tooth waveform according to the present invention can be used not only for the drive mechanisms, but also for the other apparatus or devices, for example, a micro-pomp described in Japanese Laid-Open Patent Publication No. 2001-322099.