Endless zip actuation

Abstract

Aspects of this disclosure relates to configuration, operation, and manufacture of an electrostatic motor. The electrostatic motor includes at least one rotor and at least one stator, where at least one of which is flexible and at least one of which, usually the stator, includes a set of electrodes. Voltages applied to the electrodes produces electrostatic attraction between associated regions of the rotor and stator. The electrostatic attraction causes contact between the rotor and stator in at least two regions, causing a gap to be formed between the rotor and stator, known as a "bubble". By causing a proper sequence of voltages to be applied to the electrodes, the bubble to rotates relative to the rotor and / or the stator, where a full rotation of the bubble causes a partial rotation of the rotor relative to the stator. The bubble rotates around the stator without limit.

Description

ENDLESS ZIP ACTUATIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of, and priority to, U.S. Provisional Patent Application No. 63 / 649,160 filed on May 17, 2024, the content of which is expressly incorporated herein by reference in its entirety for any and all non-limiting purposes.FIELD

[0002] The present disclosure relates to devices and methods for electrostatic actuation.BACKGROUND

[0003] Currrently many methods of converting electrical energy to mechanical work are performed. One common method is via use of a direct current (DC) electromagnetic motor. For example, a DC motor converts electrical power input to mechanical motion through rotation of a shaft, which then can be used to drive some mechanical system, such as a joint of a robot. Typically, however, a DC motor often produces its peak power output at speeds and / or torques that are poorly suited for many applications, such as many robotic applications and haptic interfaces. For example, the DC motor may produce its peak power output at speeds that are too high and / or with torques that are too low to be abple to perform the desired action. A common solution to this problem is to add a reduction element, such as a gearbox, to the output of the motor. An ideal (e.g., a lossless) reduction will reduce speed and increase torque by a factor known as the gear ratio. This approach, however, has drawbacks since real- world systems are never lossless. Reduction elements, such as the aforementioned gearboxes, are usually inefficient, heavy, difficult to backdrive, and / or may compromise control bandwidth. As such, need has been recognized for an approach to actuation that is intrinsically suited to these high torque, low speed applications without the many drawbacks of the approach of using a DC motor with a reduction element.RELATED ART

[0004] Related devices and / or methods may be discussed in the following references, US 4,395,650, US 4,922,164, US 5,237,234, US 5,965,968, US 2006 / 0214535 Al, US 9,479,085, US 2020 / 0112269 Al, US 11,486,421, Campolo, Domenico, Metin Sitti, and Ronald S. Fearing. "Efficient charge recovery method for driving piezoelectricactuators with quasi- square waves." IEEE transactions on ultrasonics, ferroelectrics, and. frequency control 50, no. 3 (2003): 237-244. Karpelson, Michael, Gu-Yeon Wei, and Robert J. Wood. "A review of actuation and power electronics options for flappingwing robotic insects." In 2008 IEEE international conference on robotics and automation, pp. 779-786. IEEE, 2008. Ludois, Daniel C., Kevin J. Frankforter, Baoyun Ge, Aditya N. Ghule, Peter Killeen, and Ryan P. Knippel. "Macroscale electrostatic rotating machines and drives: A review and multiplicative gain performance strategy." IEEE Journal of Emerging and Selected Topics in Power Electronics 10, no. 1 (2020): 14-34. Xu, Lizhong, Lei Qin, and Cuirong Zhu. "Electromechanical integrated electrostatic harmonic actuator." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and. Control Engineering 221, no. 3 (2007): 487-495.SUMMARY

[0005] The present disclosure describes a class of electrostatic actuators that are well-suited to robotic and haptic interface applications as well as other applications that require high torque-to-weight ratios, low operating speeds, and high controllability, including high control bandwidth, high accelerations, and backdrivability. One aspect described in the present disclosure concerns concentric rotor and stator components where at least one of which is flexible and at least one of which, usually the stator, includes a set of a plurality of electrodes. Voltages applied to the electrodes produce electrostatic attraction between certain regions of the rotor and stator, which then causes contact between the rotor and stator in those regions. Contact does not occur in at least one other region where voltages are not applied (or a different voltage is applied), thus causing a gap to be formed between the rotor and stator. This gap may be referred to as a “bubble”. By causing a proper sequence of voltages to be applied to the electrodes (e.g., a voltage pattern of different voltage potentials applied to the electrodes and that changes over time), the bubble rotates about an axis of rotation relative to the rotor and / or stator, and that a full rotation of the bubble will cause only a partial rotation of the rotor relative to the stator. As the bubble rotates, the leading edge is said to “unzip” (i.e., the rotor and stator lose contact at this edge) while the trailing edge is said to “zip” (the rotor and stator make contact at this edge). Another aspect described in the present disclosure is that the zipping and unzipping edges can rotate around the stator without limit.

[0006] Another aspect described in the present disclosure is that the contact between rotor and stator, as caused by electrostatic attraction, will bend or deform at least one of the rotor and stator. In some cases, prior to being so deformed, the stator is a flat disk while the rotor is saddle-shaped. In some cases, the stator is cone-shaped while the rotor is a flat disk. In some cases, a saddle-shaped rotor is sandwiched between two disk-shaped stators. In some cases, both the rotor and stator are cylindrical.

[0007] Another aspect described in the present disclosure is that rotor / stator sets may be stacked together to increase one or both of torque and speed.

[0008] Another aspect described in the present disclosure is that electrostatic contact between the rotor and stator may be turned off, which enables the motor to be freely backdriven. Alternatively, electrostatic attraction between the rotor and stator may be activated without causing the bubble to move, enabling the motor to act as a brake.

[0009] Another aspect described in the present disclosure is that either unipolar or bipolar voltages may be applied to the electrodes. Additionally, to improve motor efficiency, electrostatic energy may be recaptured by converting it to magnetic energy stored in one or more inductors. Efficiency may be also be increased by associating one or more inductors with each stator electrode and driving the one or more inductors at a resonant frequency.

[0010] Another aspect described in the present disclosure is that the rotor may be electrically floating yet held close to ground (e.g., zero volts (V)) potential by pairs of stator electrodes being activated at (approximately) equal and opposite voltages.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Aspects of the disclosure may be implemented in certain parts, steps, and embodiments that will be described in detail in the following description and illustrated in the accompanying drawings in which like reference numerals indicate similar elements. It will be appreciated with the benefit of this disclosure that the steps illustrated in the accompanying figures may be performed in other than the recited order and that one or more of the steps may be optional. It will also be appreciated with the benefit of this disclosure that one or more components illustrated in the accompanying figures may be positioned in other than the disclosed arrangement and that one or more of the components illustrated may be optional, in which:

[0012] FIG. 1A shows an exploded view of an electrostatic motor with a deformed rotor exhibiting a single bubble and a flat, disk- shaped stator including six electrodes, according to aspects of the disclosure;

[0013] FIG. IB shows a perspective view of the electrostatic motor of 1A with the rotor in contact with the stator except in the region of the single bubble, according to aspects of the present disclosure;

[0014] FIG. 2 shows a section view of an electrostatic motor with a plurality of rotor-stator pairs stacked axially and operating in parallel, according to aspects of the present disclosure;

[0015] FIG. 3 shows a cylindrical electrostatic motor with six adjacent stator electrodes and two bubbles in the rotor, according to aspects of the present disclosure;

[0016] FIG. 4 shows an electrostatic motor with a saddle-shaped rotor sandwiched between two flat, disk-shaped stators, according to aspects of the present disclosure;

[0017] FIG. 5 shows a scheme for applying bipolar voltages to each of six electrodes for the electrostatic motor of FIG. 1, and also illustrates the progression of the bubble as time advances, according to aspects of the present disclosure; and

[0018] FIG. 6 shows a scheme for applying bipolar sinusoidal voltages to the stator electrodes as well as the rotor and using beating to create a time-varying pattern of excitation that drives the bubble from electrode to electrode, according to aspects of the present disclosure.DETAILED DESCRIPTION

[0019] The detailed description below refers to the accompanying figures, which are an integral part of this document. Similar symbols in the figures typically denote similar components unless the context dictates otherwise. The illustrative configurations discussed in the detailed description, figures, and claims are not intended to impose limitations. Alternate configurations can be employed, and modifications can be made without deviating from the scope of the subject matter presented in this document. It is evident that the aspects of the present disclosure, as broadly outlined herein and depicted in the figures, can be organized, substituted, amalgamated, isolated, andconfigured in numerous diverse arrangements — all of which are explicitly considered in this context.

[0020] As explained above, the actuation technologies (where “actuation” refers to the combination of a prime mover and transmission) available for robotics, haptic interface, and many other applications suffer a number of limitations, such a low torque output, low efficiency, low or no backdrivability, high weight, and / or a combination of high compliance and slow response. Aspects of the present disclosure describe a new class of electrostatic actuators that improve on the extant technologies in multiple ways including providing high torque output, high efficiency, high backdrivability, low weight, and / or a combination of low compliance and fast response.

[0021] FIG. 1 illustrates the geometry and function of an illustrative electrostatic motor. Here, the stator 102 is a flat disk (e.g., between 100 nm to 3 mm thick, although other thicknesses are possible) that has patterned on it, a number of adjacent sector-shaped stator electrodes 103 (e.g., six wedge shaped segments). The stator substrate may be made from any of a number of inelastic materials including metals, ceramics, and polymers (e.g., polyimide) and the like. In this example, six stator electrodes 103 are shown distributed about the axis of rotation, but the number may be as few as three or as many as desired. In some cases, the electrodes may be covered with a thin (e.g. 10 nm to 10 micron) coating of dielectric material. The dielectric material may have a high relative permittivity, and may (or may not) have weakly conducting or semiconducting properties. The thickness of the dielectric divided by its relative permittivity is preferably less than 1 micron, although other values may be used. The dielectric may have a breakdown strength in excess of 100 MV / m, although lower values may be used.

[0022] In some cases, the rotor 101 is a flexible disk that is not flat and not stretchable (e.g., it can bend, while having high in-plane stiffness). The rotor 101 may be made, for instance, from biaxially-oriented polyethylene terephthalate (BoPET), and may be thin (e.g., 100 microns, although thinner or thicker disks will also work). The flexible disk of the rotor 101 may be electrically conducting, or may be a dielectric coated with a conductive or semiconductive layer. The conductive part of the disk may optionally be insulated with a thin (e.g. 10 nm to 10 micron) coating of a dielectric material. The dielectric may have a high relative permittivity, and may or may not have weaklyconducting or semiconducting properties. The thickness of the dielectric divided by its relative permittivity may be less than 1 micron, although other values may be used. The dielectric may have a breakdown strength in excess of 100 MV / m, although lower values may be used.

[0023] The geometry of the flexible disk of the rotor 101 may be visualized via an illustrative manufacturing process, described as follows. Start with a flat circular disk. A single radial cut is made from the outer edge of the flat circular disk to the center. The cut is forced open, creating a wedge or sector-shaped gap, and this sector is then filled with the same material that the disk is made from. The resulting shape is not flat, nor is it possible to flatten the shape to a plane without in-plane deformation. In the absence of any external forces (e.g., arising from contact with the stator), the rotor 101 will take on a saddle shape, as shown in FIG. 1A. Because of the additional sector, the length of a closed path in which every point is a distance r from the center of the disk is (2n + 9)r, where 9 is the sector angle. It is important to note that a saddle-shaped rotor 101 need not be manufactured by the process described here for visualization purposes, but may be made in other ways, such as casting, molding, or by plastically deforming a flat sheet, and the like.

[0024] The extra path length of 9r, as compared to the circumference of a circle, is integral to the function of the actuator. To illustrate this, consider what happens when the rotor 101 is placed on top of the stator 102 as shown in FIG. IB, and a potential difference is established between the rotor 101 and the electrodes of the stator 102. This potential difference may cause electrostatic attraction between the rotor 101 and the stator electrodes 103. If the attraction is strong enough, the rotor 101 will flatten itself against the stator 102. However, because the rotor 101 is not a flat disk, it will not be able to flatten completely. If, additionally, one stator electrode of the stator electrodes 103 is set to the same potential as the rotor, no attraction will occur in that region, and the rotor 101 will exhibit a “bubble” 104. For the purposes of exposition, assume that the rotor potential is ground, and that the stator set to that potential is “off.” In practice, however, all that is required to cause a bubble 104 is that the one stator electrode of the stator electrodes 103 and rotor 101 are at approximately the same potential, while other electrodes of the stator electrodes 103 are at a different potential. Note that the rotor 101 and stator 102 need to be (at least approximately) coaxial and close enough forelectrostatic attraction to occur (e.g., less than 1 mm), but otherwise no alignment is needed. Now, if the enabled stator electrode of the stator electrodes 103 is switched from “off’ to “on” while a neighboring stator electrode, previously “on”, is turned “off’, then the bubble 104 will move until it aligns with the new “off’ electrode. The bubble movement will result from the leading edge peeling from the newly “off’ electrode, while the trailing edge “zips” down along the newly “on” electrode. Note that, while the bubble 104 moves by the entire angular width of the stator electrode, there may be very little particle motion of the rotor 101. Nonetheless, as the stator electrodes 103 are sequenced and the bubble 104 continues to travel around the stator 102, the rotor 101 will advance (i.e., rotate with respect to the stator 102) by a very small amount. In the absence of slip, after one complete rotation of the bubble 104, the rotor 101 will have rotated around axis 105 by the sector angle 9.

[0025] In some cases, 9 = n / 100 radians (1.8 degrees), thus requiring n = 2n / 9 = 200 revolutions of the bubble 104 to cause one revolution of the rotor 101. The parameter n is referred to as the reduction ratio. In a standard gearbox transmission, the reduction ratio relates an input speed to an output speed. For instance, a motor spinning at 2000 revolutions per minute (rpm) coupled to a gearbox having a 200: 1 reduction will produce an output speed of 10 rpm. Here, the reduction ratio is similar, but it relates the rotational speed of the bubble 104 to that of the output. When the bubble 104 rotates at 2000 rpm, no physical object is actually spinning at 2000 rpm. Instead, segments of the rotor 101 are moving in and out of contact with the stator 102 at a particular rate, e.g., 2000 times per minute. Because the amplitude of this motion is typically quite small (e.g., less than 1 millimeter), and because the inertia of the rotor 101 may also be quite small, this can lead to a great reduction in kinetic energy storage. One implication of this is that the electrostatic motor will be capable of very high bandwidth operation.

[0026] With a conventional gearbox, the reduction ratio also applies to torques. For instance, an ideal 200:1 gearbox would produce an output torque 200 times greater than the torque input from the motor. In practice, this value is reduced by frictional losses. Here, the reduction ratio also applies to torque, but the relationship is more complicated because no well-defined input torque exists. We may however, define an effective input torque as the gradient of electrostatic potential energy with respect to angular movement of the bubble 104. Given an applied voltage V, a stator insulator with thickness dtandrelative permittivity , and a toroid-shaped rotor having inner radius and outer radius r2, the effective input torque is approximately:

[0027] Where e0is the permittivity of free space. Ideally, the output torque will be a factor of n greater than this. In practice, both the input and output torques will be somewhat lower due to limitations in the electrostatic potential energy and various losses, both electrical and mechanical. As equation 1 indicates, the torque scales with the square of the applied voltage. The voltage, however, cannot be increased without limit: if it is too high, electrostatic breakdown will occur in the gap between the rotor 101 and stator 102 (e.g., in the bubble 104), or across a dielectric layer (which may be on the rotor 101, the stator 102, or both). As mentioned previously, dielectric layers should be chosen to exhibit high breakdown strength. If the bubble 104 is filled with a gas such as air, its breakdown strength will tend to follow Paschen’s Law, which establishes an air gap width at which the breakdown strength is minimized. For gaps smaller than this minimum width, breakdown due to ionization is thwarted and larger field strengths may be accommodated. In very narrow air gaps, such as found near the edge of the bubble 104, breakdown is often due to field emission. In some cases, both the rotor 101 and the stator electrodes 103 are coated with one or more layers of dielectric or semiconductor material to reduce emissions, and surface finishes are very smooth. Similarly, the material filling the gap, which may be air or some other material, should have a high breakdown strength. The gap may be filled with air, with a gas such as sulfur hexafluoride or octafluorocyclobutane, with a dielectric fluid such as silicone oil, or it may be evacuated (e.g., a vacuum). Because the bubble 104 may move at high speed, a material filling the bubble 104 may have a low viscosity to reduce losses.

[0028] The torque produced by the electrostatic motor may also be affected by the number of bubbles in the rotor 101. For instance, it may be desirable to have two diametrically opposed bubbles, both rotating at the same speed (e.g., bubbles 303 and 304 of FIG. 3 in a cylindrical geometry). This would have the beneficial effect of nulling out any radial forces, leaving pure moments about the motor’s axis of rotation. It would also double the torque output (and the electrical current input).

[0029] Additionally, the number of stator electrodes 103, nE, may be modified. At least three stator electrodes 103 are needed for continuous movement (with two electrodes, oscillatory movement is possible); however, the maximum number of stator electrodes 103 is unlimited. The number of stator electrodes 103 will affect the number of bubbles that may be created, and it will affect the supporting electronics, as discussed further below. The number of stator electrodes 103 will also affect the shape and torque generation of individual bubbles.

[0030] An advantage of aspects of this disclosure, compared to electromagnetic motors, is that both the stator 102 and rotor 101 may be thin. One consequence of this is that multiple rotor-stator segments (e.g., rotor-stator segments 203) may be stacked, as illustrated in FIG. 2. With this stacking configuration, which can be termed “parallel,” the torque on the output shaft 204 common to the device (relative to a stator housing, such as the housing 205) is the sum of the segment torques, while all rotor-stator segments 203 must have the same angular velocity. A “series” stacking configuration is also possible. In it, the stator of each additional rotor- stator segment of the rotor- stator segments 203 would be mounted to the rotor of the previous rotor-stator segment. As such, the output angular velocity would be the sum of the segment angular velocities, while all rotorstator segments 203 would support the same torque. Combinations of serial and parallel stacking are also possible. When stacking multiple rotor-stator segments 203, the bubbles may all be aligned, or they may be displaced angularly relative to one another. For instance, the bubble locations may be skewed relative to one another in a parallel configuration, which may help to ensure smooth torque production.

[0031] In a housed configuration, such as shown in FIG. 2, the stator disks may be placed under tension when mounted to the housing 205. This may help the stator segments to support high torques, even if they are very thin. In a related way, the output shaft 204 may be mounted to the housing 205 via bearings (e.g., radial ball bearings) and the rotor segments may be mounted to this output shaft 204. This arrangement will ensure smooth rotation of the output shaft 204 even though the rotor segments may be very thin.

[0032] Multiple other geometries are possible without changing the basic operation. For instance, a rotor 401 may be sandwiched between two stators 402, as shown in FIG. 4 so that the rotor 401 is driven from both sides, doubling the torque output. Given thesaddle-shaped rotor 401 contemplated here, the sandwich configuration will naturally result in two bubbles on each stator of the two stators 402. Thus, there will be a doubling of torque due to nb= 2 on each stator, and another doubling of torque due to the use of two stators 402. In this configuration, the two stators 402 may be flat or, optionally, slightly conical with the two cones facing away from one another.

[0033] Another geometry of interest, shown in FIG. 2, is one in which the rotor 201 is a thin, flat disk, while the stator 202 is a shallow cone. This geometry will also produce one or more bubbles in the rotor when it is pulled down against the stator via electrostatic attraction. As shown in FIG. 2, this geometry also allows for stacking. Yet another geometry, shown in FIG. 3, is one in the stator 302 is a cylinder and the rotor 301 is a thin cylinder having an inner diameter larger than the stator’ s outer diameter. One or more bubbles (303, 304) will be produced when the rotor 301 is pulled into contact with the stator 302.

[0034] Other design considerations are the surface compliance and texture. For instance, the surface of either the rotor 101 or the stator 102 or both may be made from a relatively compliant material (e.g., a material with elastic modulus of 50 kPa, although lower or higher values may be used). Compliance will help increase adhesion under the influence of an electrostatic field. Additionally, the surface of either the rotor 101 or stator 102 may be textured, embossed, etched, perforated, or otherwise patterned. One reason to do this is to enable air between the rotor 101 and stator 102 to escape rather than get pushed along when zipping occurs. Texturing may also impact adhesion. Surfaces may be patterned at a longer length scale (e.g., 100 microns, although other values may be used) while very smooth at shorter length scales (e.g., RMS roughness values less than 100 nm, although other values may be used). Smooth surfaces may help to avoid dielectric breakdown, as discussed above.

[0035] In some cases, the electrostatic motors contemplated here may be controlled by switching voltage from one electrode to the next, thereby causing the bubble 104 to move. The switches may be high voltage MOSFETs, IGBTs, or any of a number of devices known in the art. The switches may be sequenced and timed using either open loop or closed loop techniques. For the purposes of illustration, consider the motor of FIG. 1 with one bubble 104 and six stator electrodes 103. The voltages may be switched on and off as shown in FIG. 5. Each of the six voltage traces (e.g. 501) corresponds tothe voltage applied to one of the six stator electrodes 103. The switching period Tcdetermines the rate at which the bubble 104 rotates. A potential weakness of this approach, however, is that voltage will be switched even if the bubble 104 has not completely moved from one electrode to the next. This weakness may be addressed by including sensors 110 that measure the state of the bubble 104 or otherwise identify a locaton of the bubble 104 relative to each stator electrode, and switching only when a bubble 104 is fully rotated. Sensor-based switching is commonly used with brushless DC motors, for example by using Hall effect devices to sense the rotation of the rotor. The presently described actuator differs, however, since it is bubble rotation, not rotor rotation, that needs to be sensed. This may be accomplished in a number of ways, for instance by measuring the capacitance between the rotor 101 and each electrode of the stator electrodes 103. This capacitance will depend strongly on the bubble location. For example, the capacitance of the rotor 101 relative to a drive electrode (or a sense electrode aligned with the drive electrode) will be much smaller if the bubble 104 is over that electrode, and much larger if the rotor 101 is contacting that electrode (or the dielectric insulating the electrode). Other sensors (e.g., optical sensors, resistive sensors, inductive sensors, capacitive sensors, etc.) may also be used.

[0036] As shown in FIG. 5, the drive voltage for each electrode (e.g., 501) may be bipolar (although unipolar drive voltage can work). The bipolar scheme shown is one in which each electrode of the stator electrodes 103, when it is not held at ground potential, is alternately at either a positive or a negative voltage with respect to ground. Preferably, the time-averaged voltage for each electrode is zero, which will help to avoid charge injection or charge accumulation. Another way is to excite drive electrodes (e.g., the stator electrodes 103) with a bipolar square wave signal instead of a fixed voltage. Yet another way is to switch the polarity of both the drive electrodes (e.g., the stator electrodes 103) and the rotor 101. This approach has the added advantage of doubling the size of the potential difference between the rotor 101 and stator electrode without requiring voltage rails that are twice as great.

[0037] One difficulty with the drive methods described so far is that the voltage of the rotor 101 must be controlled. The rotor voltage must either be held at ground potential or it must be connected to the drive voltage. This may be challenging since the rotor 101 rotates relative to the motor housing. Generally, some form of rotary electricalcoupling, such as a slip ring, may be necessary. An alternative is to ensure that an even number of stator electrodes 103 are “on” at all times, and that half of these are at one polarity while the other half are at the opposite polarity. For instance, in FIG. 3, at the instant in time pictured, electrodes 305 and 306 may be at a positive voltage relative to ground, while electrodes 307 and 308 are at an equal and opposite negative voltage relative to ground. Because these stator electrodes all have strong capacitive coupling to the rotor 301, the rotor 301 will adopt a potential halfway between the two polarities, which will be at or close to ground potential. This is called a “virtual ground” and requires no rotary electrical coupling. In the dual stator configuration of FIG. 4, this approach may be implemented by applying opposite polarities on each of the two stators 402. In some cases, these polarities are periodically switched to minimize charge injection or accumulation.

[0038] The switching schemes described so far may be energetically inefficient because we have envisioned connecting voltage supplies directly to the capacitive load of the motor via switches. It is well known that, when charging or discharging a capacitor in this way, 50% of the energy drawn from the supply will be lost to resistance no matter how high or low the resistance may be. Energy efficiency may be improved via any of a number of techniques (e.g., see Campolo et al.). In most such techniques, one or more inductor is introduced to create a resonant circuit along with the capacitive load. Diodes and / or switches enable such circuits to operate efficiently over a broad range of frequencies, not just the resonant frequency. It is also possible to incorporate DC to DC conversion in a drive circuit so that the system may be powered by a low voltage supply (e.g. see Karpelson, et al.).

[0039] Another means of controlling this class of motors is to excite all electrodes sinusoidally, which can be very efficient if the frequency of excitation is the resonant frequency of a capacitor-inductor circuit. The stator electrodes 103 would all be excited at the same frequency, but different phases:Vi(t) = Vosin(cOst)V2(t) = Vosin(c0st - 2n / nE)V3(t) = V0sin(cost - 2*2n / nE) (2)Vi(t) = V0sin(cost - (M)*2n / nE)

[0040] The rotor electrodes would be excited at the frequency cor= cos+ / - cob where cob is the rotational frequency of the bubble and cob is less than cos. FIG. 6 shows an illustrative configuration in which there are six stator electrodes and cos= 2Ocob. The difference in rotor and stator frequencies leads to voltages that beat at the frequency of bubble rotation. Importantly, the effective input torque of Equation (1) varies as the square of the voltage. As a result, the input torque is quite similar to that generated by switching between voltage rails (the scheme illustrated in FIG. 5), but the use of resonant excitation offers the potential of much greater energy efficiency.

[0041] An advantage of the electrostatic motor described herein, in addition to voltage excitation schemes intended to drive the motor, is that there is essentially no energetic cost to holding the rotor 101 or stator electrodes 103 at fixed potential, be it ground or drive potential. This enables the motor to exhibit mechanical behaviors that aren’t feasible with conventional electromagnetic motors. In particular, all stator electrodes 103 and the rotor 101 may be placed at ground potential which will enable the rotor to be freely backdriven. This is especially useful in highly dynamic applications such as walking, that often occur in robotics. Additionally, some or all of the stator electrodes 103 may be held at a fixed drive voltage while the rotor 101 is at ground. This will have the effect of securing the rotor 101 at a fixed angle in much the same way that activating a brake would achieve. This is especially useful in applications such as robotic grasping when a static force must be exerted in order to hold on to an object without dropping it. In this condition, an ordinary electromagnetic motor would continually expend energy and heat up.

[0042] As just explained, the electrostatic motor described herein can be made freely backdrivable; however, it is often desirable in robotics and other areas, such as haptic interface, to control the degree of backdrivability. For instance, it may be desirable to make the electrostatic motor emulate a torsional spring or torsional damper when backdriven. This may be achieved by measuring the torque applied to the output shaft (e.g., the output shaft 204) and using this as a feedback signal for controlling the motor’s velocity.

Claims

CLAIMSWhat is claimed is:

1. An electrostatic motor comprising: an axis of rotation; a stator comprising a plurality of stator electrodes and wherein the plurality of stator electrodes comprise adjacent stator electrodes distributed radially about the axis of rotation; and a rotor comprising at least one rotor electrode, wherein at least one of the stator and rotor is flexible and wherein the stator and the rotor are concentric with the axis of rotation; wherein, based on application of a voltage pattern to the adjacent stator electrodes and the at least one rotor electrode, forms, via electrostatic attraction, one or more contact regions between the stator and rotor and at least one bubble of non-contact between the stator and rotor; wherein sequencing of the voltage pattern to the adjacent stator electrodes causes the at least one bubble to rotate about the axis of rotation; and wherein rotation of the at least one bubble causes the rotor to rotate about the axis of rotation.

2. The electrostatic motor of claim 1, wherein at least a portion of the plurality of stator electrodes are insulated by a dielectric.

3. The electrostatic motor of claim 2, wherein a thickness of the dielectric, divided by its relative permittivity, is less than one micron.

4. The electrostatic motor of claim 1, wherein the rotor is saddle-shaped.

5. The electrostatic motor of claim 1, wherein the stator is conical.

6. The electrostatic motor of claim 1, wherein a thickness of the rotor and of the stator is less than 1mm.

7. The electrostatic motor of claim 1, wherein the rotor and stator are cylindrical.

8. The electrostatic motor of claim 1, wherein surfaces of one or both of the rotor and the stator are embossed, textured, or perforated.

9. The electrostatic motor of claim 1, further comprising one or more sensors that identify a location of the at least one bubble, wherein the sequencing of the voltage pattern is based on measurements from the one or more sensors.

10. The electrostatic motor of claim 9, wherein the sensors are capacitive sensors.

11. The electrostatic motor of claim 1, wherein voltages of the voltage pattern are bipolar with respect to ground potential.

12. The electrostatic motor of claim 1, wherein voltages of the voltage pattern are sinusoidal.

13. The electrostatic motor of claim 12, wherein a frequency of an applied rotor voltage differs from a frequency of an applied stator voltage.

14. The electrostatic motor of claim 13, wherein a difference between the frequency of the applied rotor voltage and the frequency of the applied stator voltage determines a rate of bubble rotation.

15. The electrostatic motor of claim 11, wherein application of the voltage pattern causes the rotor to be held at virtual ground.

16. The electrostatic motor of claim 1, wherein application of the voltage pattern causes the motor to act as a brake.

17. The electrostatic motor of claim 1, wherein application of the voltage pattern allows the motor to be freely backdrivable.

18. An electrostatic motor comprising an axis of rotation;a plurality of segments concentric with the axis of rotation, wherein each segment of the plurality of segments includes at least one stator and at least one rotor; wherein each segment of the plurality of segments comprises one of a flexible stator or a flexible rotor; wherein a plurality of stator electrodes are located on each of the at least one stator and at least one rotor electrode on each of the at least one rotor; wherein application of a voltage pattern to at least some of the stator electrodes causes contact due to electrostatic attraction between sections of the at least one stator and the at least one rotor and a plurality of bubbles of non-contact between the at least one stator and the at least one rotor; wherein a sequencing of the voltage pattern leads to rotation of the plurality of bubbles around the axis of rotation; and wherein rotation of the plurality of bubbles leads to rotation of the at least one rotor around the axis of rotation.

19. The electrostatic motor of claim 18, wherein the each of the at least one stator is mounted to a common housing and each of the at least one rotor is mounted to a common shaft.

20. The electrostatic motor of claim 18, further comprising two or more stators, wherein each of the at least one rotor contacts two stators.

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