Ceramic Motor

This invention relates to micro-motors and more particularly to piezoelectric motors.

The use of resonant piezoelectric ceramics to provide linear and rotational motion is well known. The major advantages of such systems is the capability of achieving very fine motion without the use of moving mechanical parts. In general such systems are limited to 1 micrometer of motion accuracy in open loop operation and 50 nanometers in closed loop operation. The velocity is limited to 5 to 10 mm/sec when the weight of a plate to be moved is 0.5 kg. Under these circumstances the force applied to the plate in the direction of motion is limited to about 5 N. It would be useful in many situations to achieve better resolution, higher velocities and greater motional drive force for such motors. Improved resolution would be especially useful if the ability to move at relatively high velocities was also preserved.

SU 693493 describes a piezoelectric motor comprising a flat rectangular piezoelectric plate having one electrode covering essentially all of one large face of the plate (the "back" face) and four electrodes each covering a quadrant of the front face. The back electrode is grounded and diagonal electrodes are electrically connected. Two ceramic pads are attached to one of the long edges of the plate and these pads are pressed against the object to be moved by a spring mechanism which presses against the other long edge.

The long and short directions have nearby resonant frequencies (for different mode orders) such that when one pair of connected electrodes is excited with an AC voltage to which the ceramic is responsive, the object moves in one direction, and when the other pair is excited the object moves in the other direction.

It is an object of some aspects of the present invention to provide a micromotor having higher speed, greater driving force and smaller minimum step size than micromotors of the prior art.

One aspect of the present invention comprises a thin rectangular piezoelectric ceramic having at least one electrode on one of the large faces thereof and a plurality of electrodes on the other large face. Preferably, a single spacer of hard material is attached to the center of the short edge of the piezoelectric ceramic and is pressed against a body. When at least some of the electrodes are electrified, as described below, movement of either the piezoelectric ceramic or the body along the length of the edge of the piezoelectric ceramic occurs.

In one embodiment of this aspect of the invention, the dimensions of the rectangular large face are preferably chosen such that the piezoelectric ceramic has closely spaced resonances for x and y (the dimensions of the large rectangular face of the piezoelectric ceramic), albeit in different modes. Preferably the resonances have overlapping response curves.

Excitation of the piezoelectric ceramic is achieved by connecting an AC voltage at a frequency at which both modes are excited to selected ones of the plurality of electrodes. In this embodiment, the resonant excitation is applied for at least some minimal period if a small displacement is required and can be applied for a longer period if greater displacement is required.

In a second embodiment of this aspect of the invention, the excitation is a non-resonant non-symmetrical pulse of voltage to certain of the plurality of electrodes. The present inventor has found that when such a pulse, for example, a triangular pulse having a relatively higher rise than fall time, is used, extremely small motion can be achieved.

In a third embodiment Of this aspect of the invention, the excitation is switched between resonant AC excitation for relatively large steps and pulsed, preferably triangular, excitation, when small steps are required.

A number of electrode configurations are possible in accordance with the invention. In one configuration, the plurality of electrodes comprise two rectangular electrodes, each covering half of one of the rectangular surfaces of the piezoelectric ceramic, and lying along the long direction of the large rectangular face of the ceramic.

A second preferred electrode configuration provides four electrodes which cover the four quarters of the large face of the piezoelectric ceramic. One, two or three of these electrodes can be excited, where the different modes of excitement (AC and Pulsed) and excitement configurations result in larger or small minimum step sizes for the movement caused by the motor.

Another aspect of the invention includes the use of a plurality of stacked piezoelectric ceramics, which have the same resonant frequencies, but which are preferably fabricated of different piezoelectric materials, one of which is substantially softer than the other. The ceramics having different hardnesses are driven by out of phase signals at the same frequency. In such a system, the harder material provides a high driving force during the part of the cycle in which it drives the body and the softer material provides a longer contact time but with a smaller force. This combination allows for a high starting drive to overcome inertia and static friction forces, combined with a smooth operation during movement.

There is therefore provided, in a preferred embodiment of the invention, a micromotor for moving a body comprising:

at least one rectangular piezoelectric plate having long and short edges and first and second faces, electrodes attached to the first and second faces and a ceramic spacer attached to the center of a first one, preferably a short one, of the edges and operative to be pressed against the body;

means for applying resilient force to the center of a second edge opposite the first edge, whereby the ceramic spacer is pressed against the body; and

means for electrifying at least some of the electrodes.

There is further provided, in a preferred embodiment of the invention, a micromotor for moving a body comprising:

at least one rectangular piezoelectric plate having long and short edges and first and second faces and having electrodes attached to the first and second faces;

means for resiliently urging one of the edges or one or more extensions of the edge against the body; and

means for electrifying at least some of the electrodes with asymmetric unipolar pulsed excitation.

There is further provided, in a preferred embodiment of the invention, a micromotor for moving a body comprising:

at least one rectangular piezoelectric plate having long and short edges and first and second faces and having electrodes attached to the first and second faces;

means for resiliently urging one of the edges or one or more extensions of the edge against the body; and

means for selectively electrifying at least some of the electrodes with asymmetric unipolar pulsed excitation or AC excitation.

There is further provided, in a preferred embodiment of the invention, a micromotor for moving a body comprising:

at plurality of rectangular piezoelectric plates having long and short edges and first and second fades and having electrodes attached to the first and second faces;

means for resiliently urging one of the edges or one or more extensions of the edge of each of the plurality of plates against the body; and

means for electrifying at least some of the electrodes on each of the piezoelectric plates.

Preferably, at least one of the plurality of plates is formed of a relatively harder piezoelectric material and at least one of the plurality of plates is formed of a relatively softer piezoelectric material.

In a preferred embodiment of the invention, the means for electrifying is operative to electrify the softer and harder materials out of phase with each other.

In a preferred embodiment of the invention, the electrodes comprise a plurality of electrodes on the first face of the piezoelectric plate and at least one electrode on the second face. Preferably, the plurality of electrodes comprise an electrode in each quadrant of the first face.

The present invention will be understood and appreciated more fully from the following detailed description, taken in conjunction with the drawings in which:

FIG. 1A is a simplified view of a piezoelectric ceramic element useful in a motor in accordance with a preferred embodiment of the present invention;

FIGS. 1B and 1C show a first excitation configuration (1C), in accordance with a preferred embodiment of the invention, for the element of FIG. 1 together with mode plots (1B) for that configuration;

FIGS. 1D and 1E show a second excitation configuration (1E), in accordance with a preferred embodiment of the invention, for the element of FIG. 1 together with mode plots (1D) for that configuration;

FIG. 2 shows resonance curves for two closely spaced resonant modes of the element of FIG. 1, in accordance with a preferred embodiment of the invention;

FIG. 3 shows a representation of a bi-morphological movement of a piezoelectric element useful in a motor in accordance with a preferred embodiment of the invention;

FIG. 4 is a voltage pulse which, when applied to electrodes on the element shown in FIG. 3, caused controlled motion of a body in contact with the element;

FIG. 5 is a partially schematic, partially block diagram of a motor for achieving controlled motion in accordance with a preferred embodiment of the invention;

FIG. 6 is a schematic drawing of a tandem configuration of piezoelectric ceramic elements useful in a motor in accordance with a preferred embodiment of the invention;

FIG. 7 is a schematic drawing of a tandem/parallel configuration of piezoelectric ceramic elements useful in a motor in accordance with a preferred embodiment of the invention;

FIG. 8A is a schematic drawing of a piezoelectric ceramic element configured and adapted for x-y motion in accordance with a preferred embodiment of the invention;

FIG. 8B is a schematic drawing of two piezoelectric ceramic elements configured and adapted for x-y motion in accordance with an alternative preferred embodiment of the invention;

FIG. 8C is a schematic partial drawing of an x-y table utilizing the embodiment of FIG. 8B;

FIG. 9 shows the use of piezoelectric ceramic elements in accordance with a preferred embodiment of the invention configured to rotate a cylinder or a sphere; and

FIG. 10 shows an alternative electrode shape for a piezoelectric ceramic in accordance with a preferred embodiment of the invention.

Reference is made to FIG. 1A which shows one large face of a relatively thin rectangular piezoelectric ceramic 10 for use in a motor in accordance with a preferred embodiment of the invention. Four electrodes 14, 16, 18 and 20 are plated or otherwise attached onto the face (hereinafter, "the first face") of the piezoelectric ceramic to form a checkerboard pattern of rectangles, each substantially covering one-quarter of the first face. The opposite face of the piezoelectric ceramic (hereinafter "the second face") is substantially fully covered with a single electrode (not shown). Diagonally located electrodes (14 and 20; 16 and 18) are electrically connected by wires 22 and 24 preferably placed near the junction of the four electrodes. The electrode on the second face is preferably grounded. Alternatively, the electrodes can be connected by printed circuit techniques similar to those used to form the electrodes.

A relatively hard ceramic spacer 26 is attached, for example with cement, to a short edge 28 of piezoelectric ceramic 10, preferably at the center of the edge.

Piezoelectric ceramic 10 has a large number of resonances. In particular, the dimensions of piezoelectric ceramic 10 are chosen such that resonances for .DELTA.x and .DELTA.y are closely spaced and have overlapping excitation curves as shown in FIG. 2. In particular, the resonances which are preferred in accordance with the present invention are a one-half (1/2) mode resonance for .DELTA.y and a one and one-half (11/2) mode resonance for .DELTA.x as shown in FIGS. 1B and 1D. However, other resonances can be used depending on the dimensions of ceramic 10.

When piezoelectric ceramic 10 is excited by a frequency within the band indicated as .omega..sub.o in FIG. 2, both the .DELTA.x and .DELTA.y resonances will be excited. FIG. 1C shows one configuration for electrifying certain electrodes thereby exciting the two resonances. In this configuration, in which electrodes 16 and 18 are electrified and electrodes 14 and 20 are left floating (or less preferably, grounded), the mode amplitudes are shown in FIG. 1B. Excitation in this configuration causes .DELTA.x to be negative when .DELTA.y is positive, resulting in leftward movement of a body 30 which is pressed against piezoelectric ceramic 10 if piezoelectric ceramic 10 is constrained from movement. While the surface of body 30 is shown as being curved, such as the surface of a cylinder which is to be rotated, it can also be flat when linear motion is desired.

For the excitation configuration shown in FIG. 1E in which electrodes 14 and 20 are electrified and 16 and 18 are left floating (or less preferably, grounded), the .DELTA.y mode is the same, but the .DELTA.x mode is reversed in phase, causing movement to the right.

In a preferred embodiment of the invention, piezoelectric ceramic 10 is constrained from movement by a pair of fixed supports 32 and 34 and two spring loaded supports 36 and 38. Supports 32-38 contact piezoelectric ceramic 10 at points of zero movement in the x direction along a pair of long edges 40 and 42 of the ceramic. These supports are designed to slide in the y direction.

Such spring loading is provided to reduce the effects of wear and to provide a degree of shock protection for the piezoelectric ceramic.

A spring loaded support 44 is preferably pressed against the middle of a second short edge 43 of piezoelectric ceramic 10 opposite short edge 28. Support 44 supplies pressure between ceramic 26 and body 30 which causes the motion of ceramic 26 to be transmitted to body 30. It should be understood that spring loaded support 44 has a much slower time response than frequency at which piezoelectric ceramic 10 is excited. Thus, the face of ceramic 26 which is pressed against body 30 actually moves away from the body during part of the cycle when ceramic 26 is moving opposite the direction of motion applied to body 30.

In a preferred embodiment of the invention, the dimensions of piezoelectric ceramic 10 are 20 mm.times.10 mm with a thickness of between 2 and 5 mm when PZT piezoelectric material manufactured by Morgan Matroc Inc. is used. For this configuration, 30-500 volts of AC may be used to excite piezoelectric ceramic 10, depending on the speed desired, the weight of body 30 (and/or the pressure of spring 44) and the power required. Such a device operates at a frequency in the range of 20-100 kHz, has an efficiency of up to 60%, a minimum step size in the range of 10 nanometers (nm) and a maximum velocity of about 15-30 mm/sec. These are nominal ranges only and may vary depending on the material Used for piezoelectric ceramic 10, the dimensions, the resonant mode which is selected and other factors.

In practice the larger dimension of the ceramic can be between 20 mm and 80 mm and the smaller dimension can be between 3 mm and 20 mm. For example a very long and thin device (e.g., 3 mm.times.80 mm) would result in a motor with a very high speed.

In the embodiments described above in conjunction with FIGS. 1 and 2, excitation of piezoelectric ceramic 10 in FIG. 1A is by an AC voltage near the resonances of the piezoelectric ceramic. In the method depicted in FIGS. 3 and 4, the excitation is by a pulsed unipolar voltage. In this pulsed excitation embodiment of the invention, electrodes 12, 14, 16 and 18 are not connected together in a fixed manner as in the embodiment of FIG. 1, but are connected in different ways, depending on the minimum step required, as described below.

The principle by which the pulsed method operates is shown in FIG. 3. In this figure, electrodes 14 and 18 are excited by a positive DC voltage and electrodes 16 and 20 are excited by a negative DC voltage with respect to the electrode on the second side of piezoelectric ceramic 10. Under this excitation the left side of piezoelectric ceramic 10 becomes longer than the right side (shown greatly exaggerated in FIG. 3 ) and ceramic 26 moves to the right. Of course when the voltage is removed, the ceramic will move back to its original position.

However, the present inventor has found that, if a non-symmetrical voltage pulse, such as that shown in FIG. 4, is applied to the electrodes, then, during the return to zero, the inertia of body 30 will cause the body not to return with ceramic 26 to the starting position. Preferably the fall time of the pulse should be at least four times as long as the rise time. A total pulse time of 10 to 50 milliseconds is preferred, but the exact times will depend on the mass which is moved by the piezoelectric ceramic and on the force of spring 44. The minimum step for this configuration will depend on the pulse voltage and can vary from 2-6 nm for peak voltages of 30-100 volts, with a larger minimum step for greater masses due to the increased inertia of the mass. Velocities of 1-2 mm/sec of body 30 can be achieved with this configuration. Reversing the polarity of the excitation or applying a pulse having slow rise time and a fast fall time results in travel in the opposite direction.

Other configurations of excitation of the electrodes with such pulsed voltages yield other minimum step values. For example, excitation of electrode 14 with a positive pulse and electrode 16 with a negative pulse (while grounding electrodes 18 and 20, will result in a minimum step of about 2-5 nm. Excitation of electrodes 18 and 20 with respective positive and negative pulses (while preferably allowing 14 and 16 to float) will result in a minimum step of 5-8 nm. A similar value of minimum step is achieved when electrodes 14 and 18 are pulsed with one polarity and electrode 20 is pulsed with the opposite polarity (electrode 16 is floating). Alternatively, the electrodes which are indicated above as floating can be grounded, however, this will result in a lower efficiency.

In a particularly useful differential mode, electrodes 14 and 20 are pulsed positive and electrodes 16 and 18 are grounded or are pulsed negative. In this mode very small minimum movements can be achieved in the range of 0.1-2 nm. The diagonal electrodes may be pulsed with voltages of the same or differing amplitudes.

While the pulsed excitation is preferably utilized with the configuration shown in FIG. 8, it is also useful when applied to configurations of the prior art such as that of SU 693494 described above, where each of the electrodes is separately excitable.

In a preferred embodiment of a motor according to the invention, piezoelectric ceramic 10 is first excited by an AC voltage as described in conjunction with FIGS. 1 and 2 to produce fast movement to the vicinity of a target position and is then excited by pulsed voltages as described in conjunction with FIGS. 3 and 4. One preferred embodiment of a motor system including provision for such excitation is shown in block diagram form in FIG. 5.

As shown in FIG. 5, a control system 50 comprises a microcontroller 52 which controls the energizing of a pair of regulated power supplies 54 and 56 respectively and four switch/modulator circuits 58, 60, 62 and 64. Each of the switch modulators is connected to one of electrodes 14, 16, 18 or 20. The electrode on the second face is connected to ground, preferably via a tuning inductor 66.

Microcontroller 52 preferably receives position signals from a position indicator 68, which indicates the position of body 30 and provides feedback to microcontroller 52. Microcontroller 52 also preferably receives position (or movement ) and, optionally, velocity commands from a user interface 70.

In operation, microcontroller 52 receives a position command from user interface 70 and compares it to the actual position indicated by indicator 68. If the command is a movement command, the position is only noted for later comparison.

Microcontroller 52 notes the amount of movement which is required and based on predetermined optimization criteria, decides if the AC or pulsed mode is appropriate and in which direction the body most move. Appropriate signals are sent to the switch/modulators so that they produce either AC or pulsed voltages (or no voltage or ground) to each of the electrodes such that piezoelectric ceramic 10 operates in an appropriate excitation configuration as described above. When the remaining distance to be traveled is reduced below an appropriate level, microcontroller 52 switches to a high resolution, low speed mode utilizing appropriate pulsed excitation as described above in conjunction with FIGS. 3 and 4. Several changes in excitation regime may be appropriate when high position accuracies are desired. When body 30 arrives at the target destination, the excitation of the electrodes is terminated.

Inductor 66 is used to tune the electrical resonance of piezoelectric ceramic 10 and its associated wiring to the same frequency as the mechanical resonances of piezoelectric ceramic 10. Since the electrical circuit consists largely of the capacitance formed by the electrodes on the first and second faces of piezoelectric ceramic 10, it is appropriate to add an inductor, such as inductor 66 to "tune-out" this capacitance and improve the efficiency of the system.

While motion control of the system has been described with respect to a closed loop system, open loop operation is possible, at lower accuracy. For closed loop operation, it is believed that the system can achieve accuracies better than about 0.5 nm. For open loop operation, the amount of movement can be estimated fairly closely and the position can be controlled to within about 0.1% to 1% of the total amount of motion.

In a preferred embodiment of a motor in accordance with the invention, a plurality of piezoelectric ceramics can be configured to increase the power of the motor and to reduce any variability which exists between different units. One such configuration, shown in FIG. 6, includes two piezoelectric ceramics 10 and 10' in a tandem configuration, i.e., one in which the two ceramics are mounted in tandem in the direction of motion induced by piezoelectric ceramics 10 and 10'. The two piezoelectric ceramics can be driven by a common control system such as control system 50 shown in FIG. 5 or by separate control systems. For clarity, the control systems and electrical connections are not shown in FIG. 6.

As shown in FIG. 6, a spacer unit 74 located intermediate piezoelectric ceramics 10 and 10', supports and separates the piezoelectric ceramics. Four spring loaded side supports 76 and two spring loaded end supports 78 support the pair of piezoelectric ceramics in much the same way as described above with respect to the embodiment of FIG. 1. In practice piezoelectric ceramics 10 and 10' are also constrained from moving perpendicular to the face of the piezoelectric ceramics, preferably by extensions of spacer unit 74 and spring loaded supports 76 and 78. Such constraints are shown in FIG. 7.

FIG. 7 shows six piezoelectric ceramics configured in a 2 by 3 unit tandem/parallel configuration. Due to pictorial constraints, the spring loaded supports and the mechanism for pressing spacer unit 74 against the piezoelectric ceramics are not shown, however, the preferred support mechanism is that shown in FIG. 6.

In a preferred embodiment of a motor in accordance with the invention, the piezoelectric ceramics used in the embodiments shown in FIGS. 6 and 7 are not all the same. In this embodiment of the invention, one or more of the piezoelectric ceramics is made from a relatively hard material such as PZT-8 (manufactured by Morgan Matroc Inc.) and one or more of the piezoelectric ceramics is made from a softer material such PZT-5H (manufactured by Morgan Matroc). The two types of materials can be physically configured such that they have the same x and y dimensions and the same resonances and resonant frequencies can be obtained by adjusting the thickness of the various piezoelectric ceramics. When the softer piezoelectric ceramic is electrified, the amplitude of the resonance is greater in both .DELTA.x and .DELTA.y and the portion (time) of the period during which ceramic 26 contacts the body is greater than for the harder piezoelectric ceramic. However, by its nature, the amount of motive force which the softer piezoelectric ceramic applies is lower and the unevenness of the motion is also lower.

In a preferred embodiment of the invention, where both types of piezoelectric ceramic are used, as described in the previous paragraph, the harder piezoelectric ceramic is operative to overcome static friction and other inertial forces and the softer piezoelectric ceramic is operative to give a smoother, more accurate, motion with smoother stops and starts than when only a hard piezoelectric ceramic is used.

In a preferred embodiment of the invention, the two types of ceramic are excited out of phase with each other (180.degree. phase difference). In this way, the two types of piezoelectric ceramic act in an essentially independent manner (at different parts of the excitation cycle) and there is a minimum of friction due to the differing motions of the two types of piezoelectric ceramic. In a preferred embodiment of the invention, the phase reversal is achieved by using ceramics with reversed polarization directions for the two ceramics. Alternatively, the voltages can be applied out of phase.

X-Y motion having all of the advantages of the present invention is also possible.

One configuration for producing X-Y motion is shown in FIG. 8A. An integral X-shaped section 90 is formed of piezoelectric ceramic material and has front and back electrodes formed on the larger flat internal faces of the section. The internal faces which are not shown (and which oppose the faces which are fully or partially shown) are supplied with a single electrode running the entire face. These single electrodes are grounded, in accordance with a preferred embodiment of the invention, and the electrodes which are shown are activated in accordance with the schemes previously described. To construct an X-Y table with such a device would only require holding the ceramic as described above in accordance with FIGS. 1 and 7 and adding a flat table contacting ceramic 26. A number of such x-shaped sections 90 of the same or different ceramics may be used in a parallel-tandem configuration as described above with respect to FIGS. 6 and 7.

FIG. 8B shows a second, simpler to visualize, but less compact configuration in which two piezoelectric ceramics such as those shown in FIG. 1 are cemented together to achieve x motion at one end and y motion at the other end.

An x-y table 100 constructed in accordance with a preferred embodiment of the present invention and using the configuration of FIG. 8B is shown in simplified form in FIG. 8C. Table 100 comprises two piezoelectric ceramics 10 in the configuration of FIG. 8B sandwiched between a fixed base 102 and a top 104. Supports 106, 108, 110, 112, 114 and 116, 118 and 120 are similar in form and function to supports 32, 34, 36 and 38 of FIG. 1. All of supports 106-120 are mounted together on a fixture (not shown for clarity of presentation) but are not attached to base 102. However, sliders which allow for sliding movement in the x-direction (shown by arrows 122) between the fixture and base 102 are preferably provided and are attached to the fixture.

A set of sliders 124, 126 and 128 are provided for allowing motion of top 104 with respect to the fixture in the y direction shown by arrows 130. Preferably sliders 124-128 are attached to the fixture.

In summary, the fixture includes supports for the upper and lower piezoelectric ceramics 10 and sliders which allow sliding motion of the fixture with respect to base 102 in the x direction and of top 104 with respect to the fixture in the y direction.

In operation, activation of the lower piezoelectric ceramic causes it to move in the x direction. Since top 104 is constrained by the fixture from movement in the x direction with respect to the fixture, top 104 moves by the same amount as the fixture in the x direction. Thus, activation of the lower piezoelectric ceramic causes x motion of top 104. When the upper piezoelectric ceramic is activated, top 104 moves in the y direction with respect to the fixture. Since the fixture is constrained from any movement in the y direction with respect to the base, top 104 moves with respect to base 102.

Selective activation of the upper and lower piezoelectric ceramics results in x-y motion of top 104 with respect to base 102, having all of the advantages of the embodiments for linear motion shown above with respect to the embodiments of FIGS. 1-7.

Furthermore, tandem and series arrangements of piezoelectric ceramics of differing or the same hardness will result in similar improvements to those described, with respect to FIGS. 6 and 7, for such tandem arrangements with respect to linear motion devices.

Use of piezoelectric ceramics in accordance with the present invention to achieve rotational motion is shown in FIG. 9, in which a tandem configuration of piezoelectric ceramics 150 similar to that shown in FIG. 6 is adapted to conform with and rotate a cylinder 152. In such a configuration, the surfaces of ceramic spacers 26 would preferably have a concave shape conforming with the surface of cylinder 152. A single piezoelectric ceramic similar to that shown in FIG. 1 can also be used in place of configuration 150.

When circular motion and three-axis positioning of a sphere are required, a configuration such as that of FIG. 9 would be used modified by providing three orthogonally placed ceramic structures similar to configuration 150 to revolve and position the sphere. If only rotation (and not three-axis positioning) is required, two orthogonal drivers would be sufficient. In this embodiment, the outer surface of ceramic 26 would be shaped to conform with the surface of the sphere.

Utilizing the present invention, an improved combination of velocity, accuracy, and driving force is possible. By utilizing only a single ceramic pad 26, greater force can be employed to push the ceramic against body 30 over the prior art which is subject to cracking when excessive force is used. Use of tandem ceramics unexpectedly results in a large increase in driving force and velocity. In general, both higher velocities and higher driving force can be simultaneously achieved in the present invention for the same volume of piezoelectric ceramic.

The present inventor has also found that, when rectangular electrodes are used as shown in the above embodiments, the motion is not completely linear, i.e., due to the rotational nature of the motion of ceramic 26, only one part of the ceramic will touch body 30 during operation. Linearity can be improved by shaping the electrodes as, for example, shown in FIG. 10, where 14', 16', 18' and 20' are linearizing versions of the unprimed electrodes shown in the previous figures. While a sinusoidal variation is shown in FIG. 10, other electrode configurations are also possible to improve the linearity of the device.

It will be appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and described herein. Rather the scope of the present invention is defined only by the claims which follow: