Abstract:
An actuator is formed by using at least one flexure that is continuously flexible between a rigid connection to a stator and a rigid connection to a translator. The one or more continuously flexible flexures provide a long range of translator motion when combined with an electrostatic levitation arrangement. In selected embodiments, the flexures that are continuously flexible are straight beam flexures, so as to provide a high degree of stiffness. In other embodiments, the flexures are pre-bent to provide a longer switching throw from a relaxed state. Where the translator is required to be displaced in a generally straight-line direction, some off-axis displacement will occur, but is preferably accompanied by a stepping of a levitation voltage pattern. In another embodiment one and only one straight beam flexure is used and the levitator is caused to rotate about a rotational axis that is intersected by the one straight beam flexure.

Description:
TECHNICAL FIELD 
     The invention relates generally to actuators and more particularly to flexural arrangements for supporting a movable member for controlled long range motion relative to a stationary member. 
     BACKGROUND ART 
     In many micromachine applications that use actuators, design goals include providing a long range of translator motion along a particular axis, while retarding out-of-plane displacements and in-plane displacements that are perpendicular to the intended direction of travel. Electrostatic surface actuators for use in micromachine applications are known. Such actuators may be used in advanced data storage applications and optical telecommunications applications. U.S. Pat. No. 5,986,381 to Hoen et al., which is assigned to the assignee of the present invention, describes electrostatic actuators and voltage variation techniques for driving a translator relative to a stator. U.S. Pat. No. 5,378,954 to Higuchi et al. also describes electrostatic actuators. 
     All of the actuators displace one element (i.e., the translator) relative to another element (i.e., the stator) and require that the moving element be stabilized against motions in undesired directions. Rolling or sliding elements are most commonly used to directionally stabilize the translator. However, in micromachined actuators, bending flexures are preferred, since the surface contact associated with the rolling or sliding elements is particularly unpredictable and risky for extremely small devices. Nevertheless, bending flexures pose different problems, since their stiffness varies with displacement. For a unidirectional actuator, the bending flexures must stabilize the translator with respect to the out-of-plane motions and with respect to the in-plane motions perpendicular to the desired direction of travel. Supports that are rigid against out-of-plane displacements are particularly important for electrostatic surface actuators, because the force tending to attract the two surfaces is approximately the same as the force pushing the translator parallel to the stator. 
     FIG. 1 shows an example of one type of folded beam flexure  10  that is used in micromachined electrostatic actuator applications. The flexural device includes a rigid floating beam  12  having opposite sides connected to flexible beams  14  and  16 . The flexible beams  14  and  16  are anchored to supports  18  and  20  on a stationary member (not shown), such as a semiconductor substrate. In addition to the pair of flexible beams  14  and  16 , there is a second pair of flexible beams  22  and  24  connected to the rigid floating beam  12 . The second pair of flexible beams supports a second rigid beam  26 , which moves with the movable member of interest. 
     The folded beam flexure  10  of FIG. 1 produces generally straight-line motion along an x axis. However, as the second rigid beam  26  is displaced along the x axis, the flexible beams  14 ,  16 ,  22  and  24  become increasingly compliant to forces along the y axis. For many electrostatic actuators, such as comb drives and surface drives, the applied force in the desired direction of motion (i.e., along the x axis) is accompanied by an instability in the y axis direction. The maximum stable travel of the second rigidly floating beam  26  is thus limited to when the y axis force gradient exceeds the y axis stiffness of the flexible beams. 
     A second known flexural device  28  is shown in FIG.  2 . Here, the translator is connected directly to the rigid floating beam  12  that is connected to the stator (not shown) via the two flexible beams  14  and  16 . This device is better suited for maintaining stiffness along the y axis as the rigid beam is displaced. Unfortunately, motion of the rigid floating beam does not follow a straight line as it is displaced. This is not suitable for use in actuators that require straight-line motion. 
     FIG. 3 shows a third known flexural device  30  which uses micromachine flexible beams. A series of pre-bent flexible beams  32 ,  34 ,  36 ,  38 ,  40 ,  42 ,  44  and  46  is used to provide increased stiffness to motion along the y axis. The flexible beams  32 ,  34 ,  36  and  38  are anchored to supports  50  at one end and are connected to either a first rigid floating beam  48  or a second rigid floating beam  52  at the opposite ends. The supports  50  are locations on a stationary member, such as a semiconductor wafer. The flexible beams  40  and  42  connect the first rigid floating beam  48  to a third floating member  54 , while the flexible beams  44  and  46  connect the second rigid floating beam to the third floating member. 
     The flexible beams  32 ,  36 ,  42  and  44  are pre-bent in such a way that the ends opposite to the rigid floating beams  48  and  52  are offset in a “negative direction” along the x axis with respect to the connections to the rigid floating beams. On the other hand, the flexible beams  34 ,  38 ,  40  and  46  are pre-bent in such a way that the ends opposite to the rigid floating beams  48  and  52  are offset in a “positive direction” along the x axis with respect to the connections to the rigid floating beams. Because of the difference in pre-bent conditions, as one set of flexible beams softens with increased bending, the other set is straightening, thereby maintaining the y axis stiffness. More particularly, as the third floating member  54  which is connected to the translator moves in the positive x direction, the flexible beam  44  will begin to straighten, while the flexible beam  46  will become increasingly bent. This has the effect of causing the third floating member  54  to rotate in a clockwise direction. However, for the same motion, the flexible beam  40  will become increasingly bent and the flexible beam  42  will straighten, causing the third floating member to be urged in a counterclockwise rotation. The two rigid floating beams  48  and  52  are linked at their centers by a bending flexure  56  that acts as a torsional joint. Because each side of the third floating beam  54  is acted upon by offsetting rotational forces, the third floating beam  54  moves in a straight-line motion. 
     There are some concerns with the flexural device  30  of FIG.  3 . First, it does not efficiently use semiconductor wafer area, which is often times at a premium. Second, the flexural device  30  requires contacts to rigid supports  50  which are sometimes fully surrounded by the various beams. Thus, it may be difficult to fabricate the device using a single material layer without external supports, as is often preferred with deep reactive ion etching. 
     A more complete flexural system  58  that utilizes folded beam arrangements  60  and  62  is shown in FIGS. 4 and 5. Each of the folded beam arrangements  60  and  62  is identical to the one described with reference to FIG. 1, but with a translator  64  taking the place of the second rigid beam  26 . The system  58  is shown in a relaxed state in FIG.  4 . In this state, the flexible beams  14 ,  16 ,  22  and  24  are generally perpendicular to the floating rigid beams  12 . As noted above, the flexible beams  14  and  16  are anchored to supports  18  and  20 , respectively, on the stationary substrate  65 , which is represented by dashed lines. The flexible beams  22  and  24  are connected between the rigid floating beams  12  and the translator  64 . 
     Before any motion takes place in the x direction, the system  58  is very stiff to forces in the y direction. This is because the flexing beams  14 ,  16 ,  22  and  24  are straight beams and must buckle in order to allow motion in the y direction. However, the system is more susceptible to forces in the y direction after some displacement of the translator  64  has occurred from the condition shown in FIG. 4. A displaced translator  64  is represented in FIG.  5 . Electrostatic forces that urge the translator  64  laterally cause the two rigid floating beams  12  to move more closely together, as indicated by the difference between the dotted lines and the solid lines representing the rigid floating beams. Because of the displacement of the rigid floating beams relative to the anchored supports  18  and  20 , a lateral force Fy exerts a moment M as indicated in FIG.  5 . The two floating rigid beams are moved in the positive x direction, but the lower beam is also moved in the positive y direction, while the upper beam is moved in the negative y direction. 
     In the displaced condition of FIG. 5, the flexible beams  14 ,  16 ,  22  and  24  are curved. The system is now more susceptible to unwanted displacement in the y direction. 
     Similar to the in-plane stiffness, the out-of-plane stiffness (i.e., stiffness that is perpendicular to both the x and y axes) depends on the beam displacement. Considering a single one of the flexible beams  14 ,  16 ,  22  and  24 , the beam can be made extremely stiff with respect to out-of-plane (i.e., z axis) displacements by fabricating the beam with a large aspect ratio (α) equal to the thickness-to-width ratio (t/w). The beam allows displacements along the x axis by bending perpendicularly with respect to its narrow width, as measured along the x axis. Unfortunately, as the flexible beam is bent, the out-of-plane stiffness k z  is significantly reduced. It has been theorized that the k z  can be related to the in-plane stiffness k x  as follows: 
     
       
           k   x   /k   z =1/α 2   +A (δ x/L ) 2   Eq. 1 
       
     
     where A≈0.280 for aspect ratios greater than 10 and δx is the amount of displacement along the x axis. When the beam is not displaced, δx will be 0 and k z  will be much larger than k x . As the beam is displaced, the out-of-plane stiffness is reduced as the square of the displacement period. For a 40:1 aspect ratio beam, a lateral displacement of only 5% of the flexure length causes k z  to be reduced by approximately 50%. The stiffness reduction occurs until the bending beam can no longer counteract the out-of-plane force of the actuator drive. The available lateral travel is therefore limited by the reduction in k z  with lateral displacement. 
     As can be seen from Equation 1, it is possible to increase the lateral travel by increasing the lengths of the flexible beams. However, for many applications, it is important to locate the actuators as closely together as possible. Increasing the beam lengths requires the neighboring actuators to be spaced further apart. Therefore, it is more desirable to increase the range of lateral travel without increasing the beam lengths. 
     The above-identified patent to Hoen et al. describes a technique for offsetting the attractive force that is generated as a result of electrostatically driving the translator. FIG. 6 is a bottom view of a translator  66  which is supported at its four corners by folded beam flexures  68 ,  70 ,  72  and  74 . Referring specifically to the flexure  68 , the device includes outer flexible beams  76  and  78  that are anchored to the stator (not shown) and an inner flexible beam  80  that is connected to the translator. All three of the flexible beams have ends that connect to a floating rigid beam  82  of the type described above. The technique for at least partially offsetting the attractive force that is generated by interaction of translator drive electrodes  84  with the stator drive electrodes (not shown) is to include levitator electrodes  86  on both the translator and the stator. Only eight translator levitator electrodes are shown in FIG. 6, but typically a larger number of such electrodes are included. The electrical connections to the levitator electrodes are shown in FIG.  7 . An alternating pattern of voltage high and voltage low states is established along the levitator electrodes of the translator  66 . A corresponding alternating pattern is established along the levitator electrodes  88  of the stator  90 . Consequently, the translator is repulsed from the stator, providing levitation force. 
     For the purpose of clarity, the operation of the drive electrodes will be briefly described with reference to FIG.  8 . The voltage pattern along the drive electrodes  84  of the translator  66  is fixed. While not critical, the voltage pattern is preferably an alternating pattern of electrical high and electrical low. On the other hand, the voltage pattern along the drive electrodes  92  of the stator  90  is varied to induce the in-plane movement along the x axis. The applied voltages generally alternate, but include a “disruption” in the alternating pattern. In FIG. 8, the disruption occurs at electrodes  94  and  96 , since these adjacent electrodes are both tied to electrical high. By moving the disruption along the x axis, the translator  66  will be moved to a new equilibrium position, thereby providing the desired translator displacement. 
     As is clear from FIG. 8, the voltage patterns along the drive electrodes  84 ,  92 ,  94  and  96  will generate attractive forces. The levitator electrodes  86  and  88  of FIG. 7 are aligned parallel to the direction of travel, so that the relative electrode positions remain fixed as the translator  66  is displaced in a direction perpendicular to the drive electrodes. By placing the appropriate voltages on the levitator electrodes, it is possible to mitigate, and in some cases completely counteract, the attractive force produced by the drive electrodes. Thus, the levitator electrodes significantly ease the limits imposed on translator travel as a result of the previously described reductions in out-of-plane stiffness k z . 
     Unfortunately, the addition of the levitator electrodes  86  and  88  has the secondary effect of increasing the stiffness requirements with respect to in-plane displacements normal to the direction of travel, i.e., displacements along the y axis. The increase with regard to in-plane stiffness is apparent from FIG.  7 . The desired repulsive forces are achieved by aligning the high voltage electrodes  86  of the translator  66  with the high voltage electrodes  88  of the stator  90 . Without sufficient in-plane stiffness along the y axis, the desired alignment will be lost. 
     What is needed is an actuator that satisfies in-plane stiffness and out-of-plane stiffness requirements and provides a desired electrical relationship to enable a long range of motion without jeopardizing stability. 
     SUMMARY OF THE INVENTION 
     At least one flexure that is continuously flexible from a first end anchored to a stationary member to a second end fixed to a movable member may be combined with a levitation scheme to provide an actuator with a long range of motion. In the preferred embodiment, the flexures that are continuously flexible between their ends are of equal length and, at least in the most preferred embodiment, are straight beam flexures. Straight beam flexures are at least one order of magnitude stiffer than folded beam flexures. This greater stiffness enables longer ranges of travel. 
     In one preferred embodiment, the movable member is a translator of an electrostatic surface actuator which provides generally straight-line motion. The translator is supported by four straight beam flexures. The flexures are of equal length and extend in the same direction from a rigid connection to the translator. As the translator moves laterally along the x axis, each flexure bends, causing the translator to be displaced an amount δy in the y direction. This displacement is related to the lateral movement δx and the beam length L as follows: 
     
       
         δ y≅ 0.6 δx   2   /L   Eq. 2 
       
     
     Because the beams are the same length, the orientation of the translator does not change as it is displaced. Moreover, even though the beams are bent, the beams remain extremely stiff with respect to forces in the y direction. 
     Both the translator and the stator include arrays of drive electrodes and levitator electrodes. The drive electrodes are physically configured and electrically manipulated in the same manner described with reference to FIG.  9 . However, the levitator electrodes are configured in an unconventional manner. Preferably, the pitch of the levitator electrodes on the translator is different than the pitch of the levitator electrodes on the stator, with the pitch being defined as the average center-to-center distance between the electrodes. There may be 2n±1 electrodes in a repeating group of stator levitator electrodes for every 2n translator levitator electrodes. In this configuration, a strictly alternating voltage pattern is applied to the translator levitator electrodes, while a disruption in the alternating pattern is applied along the stator levitator electrodes. Unlike the drive electrodes, the voltage pattern along the stator levitator electrodes is selected so that most translator levitator electrodes are positioned in alignment with stator levitator electrodes biased at the same voltage. The levitator electrodes then produce a force pushing the translator away from the stator. In the most preferred embodiment, the translator pitch is smaller than eight times the distance g between the translator and stator. This pitch-to-distance arrangement provides both a large drive force and a large levitating force. 
     In this first embodiment, the drive electrodes are used to step the translator in the desired x direction of travel. As the translator is displaced in the x direction, the bending of the straight beams causes the actuator to also move in the y direction. The y displacement δy depends quadratically on the x displacement δx. Typically, the y displacement is parallel to the drive electrodes and is much smaller than the drive electrode length, so that the drive method is not affected by the displacement. However, the y displacement does cause the levitator electrodes to move relative to each other. To accommodate this movement, the voltage pattern on the stator levitator electrodes is preferably stepped, keeping the desired alignment of opposing voltages for the two arrays of levitator electrodes. 
     In a second embodiment, the translator is supported by four continuously flexible beams that are curved when in a relaxed condition. That is, the beams are pre-bent. This reduces the available travel in one direction along the x axis, but doubles the possible throw in the opposite direction, which may be desirable in some applications. The physical and operational arrangements of the drive electrodes and the levitator electrodes of the first embodiment apply equally to this second embodiment. One method of producing pre-curved beams is to use curved masks in the etching of the beams. 
     In a third embodiment, the translator is mounted for rotation about an axis that is intersected by the only straight beam flexure that is used to support the rotary translator. While not critical, the actuator is designed to rotate about an axis that is located at approximately 80% of the length of the straight beam flexure (i.e., 20% of the length as measured from the anchoring of the flexure to the stator). Folded beam flexures or other non-straight flexures are used to support the outer edge of the translator. In this embodiment, the drive electrodes extend along radial lines from the rotational axis, but are operated in the same manner as the straight-line embodiments described above. The levitator electrodes are curved and have a common center at the rotational axis. Also in this embodiment, the levitator electrodes do not require voltage pattern stepping, since the relative positions of the levitator electrodes of the two arrays remain fixed as the translator is moved. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a top view of a folded beam flexure in accordance with the prior art. 
     FIG. 2 is a top view of a second embodiment of a known flexural device. 
     FIG. 3 is a known flexural device that is designed to reduce a tendency to rotate as lateral movement is induced. 
     FIG. 4 is a top view of an actuator that uses folded beam techniques to support a translator, with the actuator being shown in a relaxed condition. 
     FIG. 5 is a top view of the actuator of FIG. 4 after the translator has been displaced. 
     FIG. 6 is a bottom view of a translator supported by four folded beam flexures, with the drive electrodes and the levitator electrodes being exposed on the bottom surface of the translator. 
     FIG. 7 is a representation of the voltage patterns for driving the levitator electrodes in accordance with the prior art. 
     FIG. 8 is a schematic representation of the voltage patterns along the drive electrodes of FIG. 6 in accordance with the prior art. 
     FIG. 9 is a top view of a surface drive translator having straight beam flexures in accordance with one embodiment of the invention. 
     FIG. 10 is a bottom view of the translator of FIG. 9, showing levitator electrodes and drive electrodes. 
     FIG. 11 is a side representation of connectivity to the levitator electrodes of the actuator of FIG.  9 . 
     FIG. 12 is a side representation of connectivity to the drive electrodes of the actuator of FIG.  9 . 
     FIG. 13 is a top view of a second embodiment of the invention. 
     FIG. 14 is a top view of a rotary translator in accordance with a third embodiment of the invention. 
    
    
     DETAILED DESCRIPTION 
     With reference to FIG. 9, a top view of an actuator  100  in accordance with the first embodiment of the invention includes four straight beam flexures  102 ,  104 ,  106  and  108  for supporting a translator  110  to be moved relative to a stator  112 . While not critical, the stator  112  may be a semiconductor wafer and the flexures and translator may be patterned materials that are fabricated using known micromachine fabrication techniques, such as reactive ion etching. 
     Each of the straight beam flexures  102 ,  104 ,  106  and  108  is formed of a material and has a sufficient width to allow the flexure to be easily bent. For micromachining applications, the widths (as measured along the x axis in FIG. 9) may be in the order of 1 μm to 3 μm. Each of the flexures is anchored at a first end to a support  114  on the stator  112 . The second ends of the flexures are connected to rigid arms  116 ,  118 ,  120  and  122  of the translator  110 . The arms  116  and  118  are configured as an inverted and backward “L” in order to provide sufficient distance for the flexures  102  and  104  to extend in the same direction and length as the other two flexures  106  and  108 . Since the arms  116  and  118  are rigid, the flexing operations from the supports  114  to the body of the translator  110  will be materially different than those of a folded beam flexure. 
     As previously noted, when a flexible beam is bent, the out-of-plane stiffness k z  is significantly reduced and is theoretically related to the in-plane stiffness k x  as follows: 
       k   x   /k   z =1/α 2   +A (δ x/L ) 2   Eq. 1 
     where A≈0.280 for aspect ratios greater than 10. Similar to the out-of-plane stiffness, the in-plane stiffness k y  that is perpendicular to the desired direction of travel depends on the beam displacement. The folded beam flexures of FIG. 5 have a large k y  when they are not displaced. Unfortunately, k y  is known to be rapidly reduced as displacement occurs. Researchers have shown that: 
     
       
           k   x   /k   y ≅( w/L ) 2 +(3/8)(δ x/L ) 2   Eq. 3 
       
     
     Comparing Eq. 1 to Eq. 3, k y  is initially larger than k z , but decreases more rapidly as the beams are displaced. For large aspect ratio folded beam flexures, the greatest available displacement is determined by the softening in k y . 
     Straight beam flexures offer an alternative means of support. The straight beam flexures exhibit less softening in k y  than the folded beam flexures. Modeling studies show that for a straight beam deflecting in the intended manner: 
     
       
           k   x   /k   y ≅( w/L ) 2 +(0.018)(δ x/L ) 2   Eq. 4 
       
     
     It follows that the straight beam flexures are more than 20 times stiffer than the folded beam flexures. The increased stiffness allows larger travel. 
     In the embodiment of FIG. 9, the four straight beam flexures  102 ,  104 ,  106  and  108  that support the translator  110  over the stator  112  will bend as the translator is caused to move along the x axis. The bending will cause the translator  110  to be displaced by an amount δy in the y direction. The displacement is related to the lateral movement δx and the beam length L by Eq. 2 given above as: 
     
       
           δy ≅0.6 δx   2   /L   Eq. 2 
       
     
     However, because the beams are of the same length, the orientation of the translator does not change as it is moved. As indicated by Eq. 4, even though the beam flexures  102 ,  104 ,  106  and  108  are bent, the beams are extremely stiff with respect to forces in the y direction. 
     The flexure design of FIG. 9 would not be suitable for a conventional comb drive, since the displacement in the y direction would cause the comb fingers that are attached to the translator to contact the comb fingers of the stator. An electrostatic surface drive is ideally suited for the flexure design. 
     Referring now to FIG. 10, the underside of the translator  110  is shown as including two sets of levitation electrodes  124  on opposite sides of drive electrodes  126 . The drive electrodes extend perpendicular to the direction of travel and to the levitator electrodes, but are parallel to the straight beam flexures  102 ,  104 ,  106  and  108 . The electrodes may be formed of a conductive material and may be formed using known techniques. A side view of the levitator electrodes  124  is shown in FIG.  11 . The stator  112  also includes levitator electrodes  128 . In FIG. 12, the drive electrodes  126  of the levitator are shown as being adjacent to drive electrodes  130  on the stator  112 . 
     The drive electrodes  126  and  130  of FIG. 12 are configured with voltage patterns that are similar or identical to those described with reference to FIG.  8 . There are 2n±1 drive electrodes  130  in a repeating group of stator drive electrodes for every group of 2n drive electrodes  126  on the translator  110 . A strictly alternating voltage pattern may be applied to the drive electrodes  126  on the translator  110 . In FIG. 12, the alternating pattern is established by connections to a voltage source  132 . While not critical, the spatially alternating pattern of applied voltages is shown as being a pattern in which a given electrode that is held at 12 volts has nearest neighboring electrodes that are held at 0 volts. A similar voltage pattern is applied to drive electrodes  130  on the stator  112 , but because the stator has an odd number of drive electrodes in each repeating group, there is always a disruption of the alternating pattern of voltages. In FIG. 12, the disruption occurs at the center of the illustrated drive electrodes  130 . The pattern is provided by a drive electrode controller  134 . To displace the translator  110 , the disruption (as well as the other disruptions along the voltage pattern) is moved in one direction or the other. To move the disruption, one of the electrodes in the same-voltage pair may be switched from 12 volts to 0 volts. The disruption would then be formed by a pair of adjacent electrodes that are both biased at 0 volts. By stepping the disruption to the right, the translator  110  is displaced to the left. The displacement step size is determined both by the electrode pitch along the translator and by the number of stator drive electrodes in one group (i.e., by the number=2n±1). Specifically, the displacement step size is the translator electrode pitch divided by the number of stator electrodes in a group. For example, if the translator pitch is one micron and the stator group size is seven, a single step of the voltage pattern causes the translator to move by 0.143 microns. However, this is not critical. 
     In contrast to the drive electrodes, the levitator electrode arrangement of FIG. 11 is inconsistent with the prior art levitator arrangements. The levitator electrodes  124  along the translator  110  continue to follow the alternating pattern, as applied by a voltage source  136 . However, the levitator electrodes  128  along the stator  112  are configured similarly to the drive electrodes  130  along the stator, except that the voltages that are applied to the stator levitator electrodes  128  are selected to oppose the voltages on the translator levitator electrodes  124 . This is shown schematically in FIG. 11, wherein the voltage pattern on the stator  112  is selected so that most translator levitator electrodes are positioned above stator levitator electrodes of the same voltage. As in FIG. 12, the filled electrodes represent electrodes that are at least temporarily at 0 volts, while the remaining electrodes represent a high voltage state at the electrodes. As a result of the combination of the support provided by the straight beam flexures and the voltage patterns shown in FIG. 11, the translator  110  is spaced apart from the stator  112  by a gap g. The pitches (as determined by an average center-to-center difference among electrodes in an array) for each of the four different arrays of electrodes  124 ,  126 , 128  and  130  of FIGS. 11 and 12 should be less than eight times the gap g in order to provide a large drive force and a large levitating force. 
     Referring now to FIGS. 9-12, the drive electrodes  126  and  130  are used to step the translator  110  in the desired direction of travel. As the translator is displaced in the x direction, the straight beam flexures  102 ,  104 ,  106  and  108  bend, causing the translator to move in the y direction as well. The y displacement δy depends quadratically on the displacement δx, as shown by Eq. 2. For most cases, the y displacement is parallel to the drive electrodes and is much smaller than the length of the drive electrodes, so that the drive operation is not affected by the displacement. However, the y displacement does cause the levitator electrodes to move relative to each other. In order to accommodate this movement, the voltage pattern along the levitator electrodes  128  on the stator  112  is stepped by a levitator electrode controller  138 . By periodically stepping the levitator electrodes  128 , the arrangement of opposing voltages may be maintained despite the y displacement. 
     FIG. 13 is a top view of another embodiment of the invention. This embodiment may be identical to the one described with reference to FIG. 9, but includes pre-bent beam flexures  140 ,  142 ,  144  and  146 . The flexures connect to stator supports  148  at a first end to rigid arms  150 ,  152 ,  154  and  156  at the opposite ends. The rigid arms are extensions from a translator  158  that is supported by the flexures in a position spaced apart from a stator, not shown. The translator  158  and the stator include drive electrodes and levitator electrodes (not shown) of the types described with reference to FIGS. 11 and 12. 
     The curvature of the pre-bent beam flexures  140 - 146  biases the translator  158  in the positive x direction. While this reduces the available travel in the positive x direction, it doubles the possible throw in the negative x direction. This may be beneficial in some applications. 
     A third embodiment of the invention is shown in FIG.  14 . In this embodiment, a translator  160  is allowed to rotate about an axis of rotation  162 . The embodiment includes one and only one straight beam flexure  164 . The flexure has a first end anchored to a support  166  on a stator  168 , which may be a semiconductor substrate. The outer edge of the rotatable translator  160  is shown as being supported by folded beam flexures  170  and  172 , but other types of flexures with a large lateral compliance may be used to support the outer edge of the translator. 
     The actuator of FIG. 14 is constructed such that the sole straight beam flexure  164  intersects the rotational axis  162 . In the preferred embodiment, the rotational axis is located at approximately 80% of the length of the straight beam flexure  164 , as measured from the translator  160 . 
     The translator  160  includes drive electrodes  174  and levitator electrodes  176 . While the electrodes  174  and  176  are visible in the top view of FIG. 14, it should be understood that the translator electrodes are on a surface of the translator that faces the surface of the stator  168  on which corresponding arrays of drive and levitator electrodes are formed. 
     The drive electrodes  174  are positioned in radial alignment with the rotational axis  162 . Drive electrodes on the stator  168  are similarly aligned. While not shown in FIG. 14, the electrodes on the stator may extend beyond the sides of the translator  160 , so that the electrodes are available when the translator is rotated into a position above those electrodes. The levitator electrodes  176  of the translator have a curvature that is based upon the rotation of the translator. The stator  168  also includes levitator electrodes. As with the drive electrodes, the levitator electrodes on the stator may extend beyond the edges of the translator, so that the distribution of forces remains intact as the translator is rotated. 
     In operation, the translator  160  is caused to rotate in the same manner that lateral displacement is induced in the embodiments described above. That is, local disruptions in the voltage pattern along the drive electrodes of the stator  168  are stepped in one direction in order to drive the translator  160  in the opposite direction. Regarding the levitator electrodes, it is not necessary to step the voltage pattern that is applied to the stator levitator electrodes, because the relative positions of the two arrays of levitator electrodes are maintained as the translator rotates about the rotational axis  162 . 
     Referring again to FIG. 9, another embodiment of the invention would provide two generally straight beam flexures that support one side of the translator  110  and would include a third straight beam flexure supporting the opposite side. The important factor in determining the support arrangement of the three flexures is that the bending of the three flexures should cause off-axis movement in the same direction. That is, the flexures should all provide movement in either the negative y direction or the positive y direction as the translator is moved in a particular direction. This provides a predictable y axis displacement, so that the voltage pattern along the levitator electrodes of the stator may be stepped accordingly.