Patent Publication Number: US-2022216808-A1

Title: Multilayered microhydraulic actuators

Description:
RELATED APPLICATIONS 
     This application claims priority to and benefit of U.S. Provisional Patent Application No. 63/134,284 (filed Jan. 6, 2021), which is incorporated here by reference in its entirety. 
    
    
     STATEMENT REGARDING FEDERAL FUNDING 
     This invention was made with Government support under Grant No. FA8702-15-D-0001 awarded by the U.S. Air Force. The Government has certain rights in the invention. 
    
    
     FIELD 
     This application relates to actuators and, more specifically, to multi-layered microhydraulic actuators. 
     BACKGROUND 
     Electrostatic motors have traditionally suffered from high voltage and low torque. The lack of a robust electrostatic motor technology is of particular concern in microsystems, because inductive motors do not scale well to small dimensions. Often microsystem designers must choose from a host of imperfect actuation solutions, leading to high voltage requirements or low efficiency and thus straining the power budget of a system. 
     Microelectromechanical (MEMS) motors can provide rotational actuation. At a micro-scale, higher driving frequency can increase power density, and smaller electrode gaps can reduce driving voltage. However, MEMS motors have relatively low torque and the inability to scale in three dimensions due to their inherently thin nature 
     To address these challenges a desirable electrostatic motor technology should offer relatively low-voltage, relatively high-torque, relatively high-efficiency, and the ability to scale. 
     SUMMARY 
     Microhydraulic actuators provide benefits such as relatively low-voltage, relatively high-torque, relatively high efficiency, and the ability to scale in thickness and in three dimensions. Microhydraulic technology operates by electrically distorting equilibrium surface tension state of attached liquid droplets with electrowetting. These droplets can be chemically pinned to a structure. Then, electrostatic forces can be used to attract the droplets and move the structure to create actuation. 
     Using this concept, a microhydraulic motor can include multiple microhydraulic layers arranged in a stack with electrical connections between the multiple microhydraulic layers. 
     A multilayer microhydraulic motor provided in accordance with the concepts as described herein may be capable of integrating forces from the multiple microhydraulic layers (e.g. two or more microhydraulic layers). By utilizing multiple microhydraulic layers, actuators have a depth and a significant volume to generate force and mechanical power. This results in a microhydraulic motor capable of generating forces larger than single layer microhydraulic motors. In embodiments, the achievable forces may be increased by up to three orders of magnitude or more compared with prior art, single layer, microhydraulic motors. Consequently, the multilayer microhydraulic motors described herein may be suitable for use in a wide variety of practical, real-world applications including, but are not limited to: robotic joints, optomechanical gimbals, unmanned arial vehicles (UAVs), medical devices, consumer electronics for foldable displays or haptic feedback, micro-assembly devices, and reconfigurable materials. 
     In an embodiment, an actuator that may provide some or all the benefits and features described in this disclosure comprises: a first layer structure; a second layer structure positioned adjacent to the first layer structure; and one or more liquid droplets positioned between the first layer structure and the second layer structure. The one or more liquid droplets are pinned to the first layer. The actuator also includes one or more electrodes positioned on the second layer and configured to move the first layer structure relative to the second layer structure by electrostatically attracting the one or more liquid droplets pinned to the first layer structure. 
     One or more of the following features may be includes. 
     The liquid droplets may be conductive. 
     The liquid droplets may comprise water. 
     The liquid droplets may be surrounded by a layer of oil. 
     The layer structures may be disc-shaped and the actuator may be a rotational motor. 
     The layer structures may comprise tracks and the actuator may be a linear motor. 
     The actuator may include a base layer structure configured to immobilize either the first layer structure or the second layer structure. 
     At least one of the liquid droplets may form electrical connections between the first layer structure and the second layer structure. 
     A control circuit may be coupled to the one or more electrodes and configured to selectively energize the one or more electrodes on one layer to electrostatically attract the liquid droplets on an adjacent layer. 
     The actuator may be a stepper motor and the control circuit may be configured to energize the one or more electrodes to step the first layer structure and the second layer structure relative to each other. 
     The control circuit may be electrically coupled to the electrodes through one or more of: the liquid droplets, a foldable flexible interconnect between the first layer structure and the second layer structure, a via through the first layer and/or the second layer, and a conductive pin coupled to the first layer and/or the second layer. 
     In another embodiment, an actuator comprises a plurality of stacked layer structures including: one or more first layer structures having liquid droplets pinned to at least one side of the one or more first layer structures; and one or more second layer structures having electrodes pinned to at least one side of the one or more second layer structures. The plurality of layer structures is stacked so that the sides of the layer structures having liquid droplets are facing the sides of the layer structures having electrodes. The actuator includes a control circuit electrically coupled to selectively energize at least one electrode of the one or more second layer structures, to cause the at least one electrode to electrostatically attract at least one liquid droplets of one or more first layer structures, to create relative motion between the first layer structures and the second layer structures. 
     One or more of the following features may be included. 
     The liquid droplets may comprise water. 
     The liquid droplets may be surrounded by a layer of oil. 
     The layer structures may be disc-shaped and the actuator may be a rotational motor. 
     The layer structures may comprise tracks and the actuator may be a linear motor. 
     The actuator may include a base layer structure configured to immobilize at least one layer structure of the plurality of layer structures. 
     The liquid droplets may form electrical connections between at least two-layer structures of the plurality of layer structures. 
     The actuator may be a stepper motor and the control circuit may be configured to energize the one or more electrodes to step the layer structures. 
     The control circuit may be electrically coupled to the electrodes through one or more of: the liquid droplets, a foldable flexible interconnect, a via through at least one of the layers of the plurality of layers, and a conductive pin coupled to at least two layers of the plurality of layers. 
     The control circuit may be configured to cause at least some of the layers to move in a same direction to increase a speed output of the actuator. 
     The control circuit may be configured to cause at least some of the layers to move in opposite directions relative to each other to increase a torque output of the actuator. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing features may be more fully understood from the following description of the drawings. The drawings aid in explaining and understanding the disclosed technology. Since it is often impractical or impossible to illustrate and describe every possible embodiment, the provided figures depict one or more exemplary embodiments. Accordingly, the figures are not intended to limit the scope of the invention. Like numbers in the figures denote like elements. 
         FIG. 1  is a transparent isometric view of a rotational actuator. 
         FIG. 2  is an exploded view of the rotational actuator of  FIG. 1 . 
         FIG. 3  is a cross-sectional view of stacked layers of an actuator. 
         FIG. 3A  is a magnified view of a portion of the actuator of  FIG. 3 . 
         FIG. 4  is a cross-sectional view of stacked layers of an actuator. 
         FIGS. 5A, 5B, and 5C  are diagrams of a layer showing a droplet side and an electrode side. 
         FIG. 5D  is a transparent, isometric view of a stack of layers showing electrical connections between the layers. 
         FIG. 6A  is an isometric view of a plurality of linear microhydraulic actuators configured to control motion of a ball camera. 
         FIG. 6B  is an isometric view of a portion of a linear hydraulic actuator. 
         FIG. 7  is a diagram of a stack of layers illustrating relative motion between layers. 
         FIG. 8  is a diagram of another embodiment of a stack of layers illustrating relative motion between the layers. 
         FIG. 9  is a graph showing comparing characteristics of a microhydraulic actuator of this disclosure with an inductive motor and biological muscles. 
         FIG. 10  is an isometric diagram of an embodiment of a microhydraulic actuator with foldable interconnects and a pin. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is an isometric diagram of a rotational actuator  100  comprising one or more disc-shaped layer structures  102 . In the example of embodiment of  FIG. 1  a plurality of layers structures  102   a - 102   g  are disposed in a stack  104 . The actuator  100  further includes a housing  105  having a top portion (or cap)  106  and a bottom portion (or base)  108  to hold the stack of layer structures (or “layers”)  104  in place. The actuator  100  also includes an axle  110  (or motor shaft) which the actuator can rotate or otherwise move. The axle may optionally include attachment structures (e.g. post  111 ) that can provide methods of attaching the actuator to other mechanical elements. Control circuit  112  is electrically coupled to one or more of the layers  102  to provide power and/or control the actuator&#39;s motion. For example, actuator  100  may be a motor such as a stepper motor and the control circuit  112  can control the rotation, direction of rotation, angular position (e.g. a rotational angle at which the axle  110  is stopped), and rotational speed of the axle  110 . 
     The control circuit  112  may be a single circuit or may comprise multiple circuits to control the actuator  100 . For example, the control circuit  112  may include analog and digital circuits such as 
     logic circuits that control the signals provided to electrodes of the actuator, power circuits that provide power to the actuator, safety circuits, filters, and signal shaping circuits, etc. In some embodiments, the control circuit  112  may be (or may include) a programmable circuit such as a processor that can execute software instructions stored in a memory, or programmable hardware such as a field-programmable gate array circuit. 
       FIG. 2  is an exploded view of the rotational actuator  100  of  FIG. 1 . In this example, the layers  102   a  and  102   c  include. Holes  204  in the mounting structures allow the layers  102   a  and  102   c  to be coupled (e.g., mounting structures  202  on their outer edge fastened or otherwise coupled to a base layer  102   e  and/or bottom portion  108 . In this configuration, layers  102   a  and  102   c  may be held stationary relative to the bottom portion (or “base”)  108  while layers  102   f ,  102   b , and  102   d  rotate. In other configurations, all the layers  102  may rotate relative to the bottom portion  108 . In general, depending on the gearing desired in the actuator  100 , any number of the layers  102  may be configured to rotate or remain stationary relative to the base portion  108 . These gearing configurations will be discussed in greater detail below. In general, including a greater number of layers may provide more flexible options for gearing to adjust speed and torque output of the actuator. 
     The layers  102  may be formed from a rigid or semi-rigid material, such as a thin plastic, a ceramic, a glass, a metal, a semiconductor, etc. For example, the layers  102  may be provided from polyimide having a thickness less than about 1 mm, or less than about 0.01 mm thick. This may result in an actuator having a total thickness T that is 1 cm or smaller, or 1 mm or smaller, or 0.5 mm or smaller. 
     In embodiments, the layers will include grooves (see  FIG. 3 ) into which are disposed liquid droplets and/or electrical traces that form electrodes. Droplets of liquid on one or both surfaces of the layers separate the layers and allow them to rotate with relatively low friction. 
       FIG. 3  is a cross-sectional view of a stack  302  of layers  304 . The stack  302  and layers  304  may be the same as or similar to the stack  104  of layers  102  shown in  FIGS. 1 and 2 . The stack  302  may include a base layer  318  that may remain stationary with respect to the other layers  304 , and which defines one end of the stack. In embodiments, the base layer is mechanically secured to a housing or other structure so that it remains stationary. The stack  302  may also include a top (or cap) layer  320  that defines the opposite end of the stack. 
     In this example, the stack  302  includes five rotational layers (i.e. layers which may rotate or move around a central longitudinal axis  330 ): layers  304   a - d  and top layer  320 . In other embodiments, the stack  302  may include less than five or more than five rotational layers. In embodiments, the stack may comprise one or more rotational layers. 
     Each layer has first and second opposing surfaces. One or more of the layers  304  may have a first surfaces (e.g. surface  306 ) having liquid droplets (e.g. droplet  310 ) disposed or otherwise positioned thereon (and thus is sometimes referred to as a droplet surface). In embodiments, the liquid droplets may be semi-spherical or semi-cylindrical. In the example embodiment of  FIG. 3 , surface  306  is provided having one or more wells  315  in which droplets  316  are disposed. In this example embodiment, wells  315  are formed via a combination of wall structures  317  and recesses or indentations  319  ( FIG. 3A ). In embodiments, wells  315  may be provided from wall structures alone or recesses alone (i.e. it is not necessary to use a combination of recesses and wall structures). The liquid droplets may be disposed or positioned between layers and may be physically and/or chemically pinned to one of the layers. For example, liquid droplet  310  is positioned between layer  304   a  and layer  306   a . It is physically and/or chemically pinned within indentation  308  and wall structure  309  of layer  304   a . The combination of indentation and wall structure may provide the liquid droplet with a height H which is greater that a height which may be achieved using either the indentation or wall structure alone and may provide stability so that the liquid droplet  310  does not move relative to layer  304   a . However, the liquid droplet  310  is not physically or chemically pinned to layer  304   b  to allow layer  304   b  can move (e.g. rotate) relative to droplet  310  and layer  304   a . In general, the layers are formed from solid material, which may be flexible or rigid. The solid materials provide structure and are subject to internal forces of the actuator. The liquid droplets provide lubrication and motion, and act to provide electrostatic forces, as described herein. 
     In embodiments, the droplet side  206  of the layer  304   a  may comprise hydrophilic and hydrophobic solid surfaces, the hydrophilic areas wetted by the liquid droplets. The liquid droplets may comprise water containing 8 M LiCl, forming semi-cylindrical structured droplets. Uniform Laplace pressure may provide the shapes of the droplets. 
     In an embodiment, the rotational actuator may include two types of droplets: radial and circumferential, which may serve different functions. As will be described below in conjunction with  FIGS. 5A-5C . The radial (or “drive”) droplets (e.g. droplet  310 ) may be semi-cylindrical elongate droplets extending in a radial direction along the layers  304 . The circumferential “rail” droplets may extend circumferentially around areas of the layers  304  to form inner and outer rails, which may be used as conductors to carry electrical signals to and from the electrodes. At the edges of all droplets there may be a structure (e.g. a wall of polyimide) to increase droplet height and reduce viscous effects during actuation 
     One or more layers of oil  321  may be positioned around the liquid droplets to retain the liquid droplets in place and/or to prevent the liquid droplets from evaporating. The oil and the liquid droplets may also act as very low friction lubricant and/or bearings between the layers. As a result, friction between moving layers  304  in the stack  302  may be very low compared to friction between moving parts in traditional actuators. 
     One or more of the layers  304  may also include a second surface (e.g. surface  312 ) having electrodes  314 . The electrodes  314  may be formed in or on layer  304   a  by printing, etching, or any other additive or subtractive technique suitable for providing traces in or on a substrate. The electrodes may be electrically coupled to and controlled by the control circuit  112  shown in  FIGS. 1 and 2 . In general, the electrodes of one layer (e.g. electrodes  314  of layer  304   a ) may be disposed or otherwise positioned so they are disposed over the liquid droplets of an adjacent layer. In the example embodiment of  FIG. 3 , electrodes  314  are adjacent (or “facing”) droplets  316  disposed on layer  320 . 
     In embodiments, the layers  304  can self-align. After self-alignment the translational misalignment may be less than  1 μm, and rotational misalignment less than  0 . 03 ° . Self-alignment can be obtained through patterned hydrophilic structures on opposite layers that mate, or in another technique through alignment pins. 
       FIG. 4  is a cross-sectional view of a stack  402  of layers  404 . The stack  402  and layers  404  may be the same as or similar to the stack  104  of layers  102  shown in  FIGS. 1 and 2 . The stack  402  may include base layers and top layers, as described in conjunction with  FIGS. 1-3 , but which are not shown in  FIG. 4 . In this example, the stack  402  includes five layers  404   a - e.  However, in other embodiments, the stack may include fewer or more than five layers. 
     Stack  402  may include a first type of layer having electrodes on both surfaces thereof. For example, layer  404   c  has one or more electrodes  406  on a first (or top) surface  408 , and also one or more has electrodes  410  on a second, opposite (or bottom) surface  412 . Stack  402  may also include a second type of layer that has liquid droplets on both surfaces thereof. For example, layer  404   d  has liquid droplets  414  on a first (or top) surface  416  and liquid droplets  418  on a second, opposite (or bottom) surface  420 . Regions (or spaces)  421  between the liquid droplets and the layers may be filled with oil  422  that surrounds the liquid droplets and, in conjunction with the liquid droplets, creates a low-friction interface between adjacent layers. 
     In this arrangement, the first type of layer with electrodes on both sides (e.g. layers  404   a ,  404   c , and  404   e ) and the second type of layers with liquid droplets on both sides (e.g. layers  404   b  and  404   d ) are stacked in an alternating fashion so that the liquid droplets are positioned or otherwise disposed between each pair of adjacent layers. 
       FIGS. 5A, 5B, and 5C  show a detailed top and bottom view of layer  502 . Layer  502  is a layer with a first side having liquid droplets and a second, opposite side having electrodes. Thus, layer  502  may be the same as or similar to the layers  304   a - d  shown in  FIG. 3 .  FIG. 5B  is an enlarged image of the droplet side of area  504  and  FIG. 5C  is an enlarged image of the electrode side of area  504  of the layer  502 . 
     Referring to  FIG. 5A , the first, droplet side of layer  502  may include an array of radial grooves  506  that each hold a liquid droplet. The radial grooves (and the droplets) may extend radially over a portion  508  of the radius, or along the entire length of the radius, of the layer  502  to create a ring  510 . 
     The layer  502  may also have one or more circumferential rails that include grooves  512 - 516  positioned around the radial grooves  506 . The circumferential grooves  512 - 516  may retain conductive liquid droplets that act as fluidic, electrical rails to carry signals to the electrodes. The rails may include one or more fluid vias  518  that allow motor brushes  520  to make electrical connections with the fluid within the rail as the brushes  520  pass over the vias  518 . 
     The rails in  FIG. 5B  are positioned outside the outer circumference of ring  510 . However, in embodiments, similar rails may be positioned on layer  502  inside the inner circumference of ring  510 . 
       FIG. 5C  shows the second, opposite side of layer  502 , which includes one or more electrodes  522 . The electrodes  522  may be electrically coupled to motor brushes  520  so that, as the brushes receive power from the control circuit, the electrodes become electrically charged. In embodiments, the electrodes  522  may become electrically charged when the brushes  520  pass over fluid vias  518  and meet the circumferential, conductive water droplets  512 - 516 , forming an electrical connection between the conductive water droplets and the brushes. 
       FIG. 5D  is a diagram showing the electrical power distribution network for a linear multilayer microhydraulic actuator (e.g. a linear motor). As mentioned above, electrical power may be distributed to some or all the layers in a stack. In embodiments, a liquid interconnect is used. Current (e.g. alternating current) flows from the base up through the fluidic rails  550  and vias  552 , to the brushes  554 , then to the drive electrodes  556 . It then couples to the drive droplets in the layer above or below and returns through the fluidic rails and vias back to the base. 
     Path  558  illustrates the electrical power delivery path  558  through the actuator. Signals enter from a connector at the base, connect with a metal via to the brush electrodes, capacitively couple to the water 8M LiCl rails through an electrical double layer, ionically conduct through the fluidic rails and vias to Pt brush electrodes in each layer, transfer through a metal via to the Al drive electrodes, couple capacitively to the drive droplets to form the electrowetting capacitor, then return though the 8 M LiCl reference rail into the brush electrodes in the base, and return to the connector. 
     In embodiments, a flexible, foldable interconnect may also provide electrical connectivity between the layers. The interconnect may be formed from a flexible material, such as a thin plastic film, and may include one or more conductive elements. Conductive pins coupled between layers may also be used to provide electrical conductivity between the layers. 
     In the embodiment shown in  FIGS. 5A-C , the electrodes may have an elongate shape and may extend in a radial direction, like the liquid droplets  506 . This arrangement may be beneficial for a rotational actuator. However, in other embodiments, the liquid droplets and/or electrodes may have other shapes and be arranged in other positions depending on the type of actuator and motion desired. 
     For example,  FIGS. 6A and 6B  show a microhydraulic actuator configured to rotate a ball camera (e.g. artificial eye)  602 .  FIG. 6A  is an exploded view of a stack  603  of semi-circular layers  604 , and another stack  606  of semi-circular layers  608 . When the stacks  603  and  606  are assembled, they create a track-shaped actuator that can rotate the ball camera  605 . Additional stacks  610  and  612  may be added to rotate the ball camera in six degrees of freedom. 
     In this example, the stacks create a rail or track that can be used to move or rotate an object along the track. In general, the stacks can be manufactured in any desired shape to create rotary actuators, linear actuators, or actuators of any other shape and motion in addition to the rotary and track actuators described above. 
     Operation 
     The actuators described above operate by creating electrostatic (i.e. Coulomb) forces between the electrodes and the liquid droplets. When the electrode is energized, it creates an electrical field. The electrical field generates an electrostatic attractive force between the electrode and the liquid droplet. That force pulls the electrode and the droplet toward each other and moves the respective layers, creating the actuator&#39;s motion. 
       FIG. 7  is a cross-sectional diagram of three layers of an actuator, illustrating the operation of the electrostatic forces. In this example, assume that base layer  702  remains stationary and that layers  704  and  708  move relative to base layer  702 . 
     As illustrated, base layer  702  includes a droplet side  710  and at least two droplets  712 ,  714 . Layer  704  includes an electrode side shown with eight electrodes  716 ,  718 ,  720 ,  722 ,  724 ,  726 ,  728 , and  730 ; and a droplet side having droplets  732  and  734 . Similarly layer  708  has an electrode side shown with eight electrodes  736 ,  738 ,  740 ,  742 ,  744 ,  746 ,  748 ,  750 ; and a droplet side having droplets  752  and  754 . 
     To create the motive force, electrodes  716  and  724  are activated with a positive charge. The positive charge of the electrodes induces a negative charge in the nearby areas of droplets  714  and  712 . These two opposing charges create attractive, electrostatic forces indicated by arrows  756  and  758 . The forces pull the layers together and, as a result, layer  704  moves in the direction of arrow  760 . 
     Similarly, an attractive force can be achieved by activating the electrodes with a negative charge. For example, in this example, electrodes  736  and  744  are activated with a negative charge, which induces a positive charge in nearby liquid droplets  734  and  732 , respectively. These opposing charges also create attractive, electrostatic forces indicated by arrows  762  and  764 . The forces pull layers  704  and  708  together and, as a result, layer  708  moves in the direction of arrow  766 . 
     In embodiments, multiple phases may be used to create continuous motion of the layers. Assume that electrodes  736 ,  738 ,  740 , and  742  are activated in four subsequent phases. Electrode  736  is activated first and pulls layer  708  left relative to layer  704 . Then electrode  736  is turned off and electrode  738  is activated and pulls layer  708  further left relative to layer  704 . Next, electrode  738  is turned off and electrode  740  is activated and pulls layer  708  further left relative to layer  704 . In the fourth phase, electrode  740  is turned off and electrode  742  is activated and pulls layer  708  yet further left relative to layer  704 . Then the four phases can be repeated with a new set of four actuators (e.g. actuators  744 - 750 ) that come in proximity with droplet  734 . In this way, the electrodes can be activated so that the actuator acts like a stepper motor. One skilled in the art will recognize that, by actuating the electrodes in different patterns, the control circuit can precisely control speed, position, and direction of each layer. 
     In this example, both layers  704  and  708  are rotating to the left, i.e. in the direction of arrows  760  and  766 , while base layer  702  is stationary. Accordingly, the speed of each layer&#39;s rotation is based on the frequency of the phases, and on the speed of the adjacent layer. For example, layer  704  is rotating with an angular velocity of θ relative to base layer  702 . Assuming the phases of electrode activation on both layers are the same, top layer  708  is rotating with a speed of θ relative to middle layer  704 . Thus, top layer  708  is rotating with a speed  20  relative to bottom layer  702 . Additional layers added on top of layer  708  and rotating in the same direction may have increased speed. For example, a fourth layer added on top of layer  708  may rotate with an angular velocity of 3θ relative to bottom layer  702 , a fourth layer may rotate with an angular velocity of 4θ, etc. 
     Referring to  FIG. 8 , the frequency and direction of the phases of the electrodes can be changed to change the speed and/or torque output of the actuator. In this example, an additional layer is shown to illustrate the concept. 
     In layer  704 , the four-phase electrode activation may be reversed so that electrodes  730  and  722  are activated first, then electrodes  728  and  720 , then electrodes  726  and  718 , and then electrodes  724  and  716 . As a result, the motion of layer  704  with respect to base layer  702  is also reversed, resulting in layer  704  moving to the right (as indicated by arrow  768 ), with a velocity of θ in the direction of arrow  768 . Layer  708  is configured to more to the left, as indicated by arrow  766 . And layer  802  is configured to move to the right, as indicated by arrow  804 . 
     In this example, because the direction of some of the layers is reversed, the angular velocity of layer  704  is θ (in the direction of arrow  768 ) relative to the base layer  702 , the angular velocity of layer  708  is zero relative to the base layer  702 , and the velocity of layer  802  is θ (in the direction of arrow  804 ) relative to layer  702 . In other words, in this example, every other row has a velocity θ, and the alternate rows have a velocity of zero relative to the base layer. However, the torque produce by layer  802  is increased relative to the torque produced by layer  704 . If, for example the torque produced by layer  704  is τ, the torque produced by layer  802  may be 2τ. 
     The examples shown in  FIGS. 7 and 8  include three and four layers, respectively. Of course, the actuators presented in this disclosure can have any arbitrary number of layers; they are not limited to three or four layers as shown in these examples. Thus, depending on the configuration, the velocity of the layers and the torque of the actuator can be configured to any arbitrary velocity and torque within the mechanical confines of the particular actuator&#39;s configuration. 
     The figures in this disclosure, including  FIGS. 7 and 8 , may not be drawn to scale. For example, in  FIGS. 7 and 8 , there is a gap between sets of actuators (e.g. gap  806  between electrodes  722  and  724 ). This gap is shown for ease of illustrating multi-phase actuator activation and is not necessarily present in embodiments of the actuator. Of course, some actuator configures may include gaps between some or all electrodes depending on the actuator configuration. 
     The speed and torque configurations described above are a subset of possible layer arrangements. In general, a multilayer stack can comprise M regular, and N inverted electrode order layers, alternating up through the actuator. Alternatively, the forward and reverse layers need not alternate. An actuator may have multiple forward direction layers and multiple reverse-direction layers in any order. The ability to provide configurations with different gear ratios, i.e. different speed and/or torque configurations described above, may be beneficial for micro-actuator applications where the disclosed microhydraulic actuators may provide gearing solutions that are more efficient, smaller, and lighter than traditional actuator solutions. 
       FIG. 9  is a plot of maximum unloaded angular velocity and blocked torque density for various rotational actuators. Inductive motors tend to have a high speed at low torque density, while microhydraulic motors and biological joints tend to have a low velocity and a high torque density. Different M layer configuration can exchange speed for torque. The microhydraulic actuators that were measured for this chart had droplets with 40 μm pitch, while 15 μm droplet pitch devices are projected from scaling trends. 
       FIG. 10  is an isometric view of an embodiment of a microhydraulic actuator  1000  with foldable layers. Actuator  1000  may have a plurality of stator layers  1002 ,  1004 ,  1006 , etc. The stator layers may be connected by one or more interconnection elements  1008 , which connect to the stator layers via a hinge (e.g. hinges  1010 ,  1012 ). Each stator layer  1002 ,  1004 ,  1006  may be associated with a movable rotor layer (e.g. rotor layer  1014 ) which may be rotatably coupled to the stator layer. As described above, the rotor layer may include a plurality of liquid droplets that can be used to create actuator motion. The stator layers may include one or more electrodes that can generate electrostatic force between the electrodes and the liquid droplets, as describe above, to generate actuator motion. 
     In embodiments, the stator layers (e.g.  1002 ,  1004 ) and the interconnection elements (e.g.  1008 ) may include conductors (not shown) etched or embedded thereon that provide electrical interconnectivity between the layers. The conductors can carry power and/or control signals between the layers and to/from the control circuit. 
     Additionally or alternatively, the stator layers may include one or more holes or vias (such as via  1016 ) through which one or more conductive pins (such as pin  1018 ) can be inserted. The conductive pins  1018  may provide electrical connectivity and carry power and/or control signals between the layers and to/from the control circuit. 
     Various embodiments of the concepts, systems, devices, structures and techniques sought to be protected are described herein with reference to the related drawings. Alternative embodiments can be devised without departing from the scope of the concepts, systems, devices, structures and techniques described herein. It is noted that various connections and positional relationships (e.g., over, below, adjacent, etc.) are set forth between elements in the above description and in the drawings. These connections and/or positional relationships, unless specified otherwise, can be direct or indirect, and the described concepts, systems, devices, structures and techniques are not intended to be limiting in this respect. Accordingly, a coupling of entities can refer to either a direct or an indirect coupling, and a positional relationship between entities can be a direct or indirect positional relationship. 
     As an example of an indirect positional relationship, references in the present description to disposing or otherwise positioning element “A” over element “B” include situations in which one or more intermediate elements (e.g., element “C”) is between elements “A” and elements “B” as long as the relevant characteristics and functionalities of elements “A” and “B” are not substantially changed by the intermediate element(s). 
     Also, the following definitions and abbreviations are to be used for the interpretation of the claims and the specification. As used herein, the terms “comprise,” “comprises,” “comprising, “include,” “includes,” “including,” “has,” “having,” “contains” or “containing,” or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, an apparatus, a method, a composition, a mixture or an article, that comprises a list of elements is not necessarily limited to only those elements but can include other elements not expressly listed or inherent to such apparatus, method, composition, mixture, or article. 
     Additionally, the term “exemplary” is used herein to mean “serving as an example, instance, or illustration. Any embodiment or design described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments or designs. The terms “one or more” and “one or more” are understood to include any integer number greater than or equal to one, i.e. one, two, three, four, etc. The terms “a plurality” are understood to include any integer number greater than or equal to two, i.e. two, three, four, five, etc. The term “connection” can include an indirect “connection” and a direct “connection”. 
     References in the specification to “embodiments,” “one embodiment, “an embodiment,” “an example embodiment,” etc., indicate that the embodiment described can include a particular feature, structure, or characteristic, but every embodiment may or may not include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. 
     For purposes of the description hereinafter, relative or positional terms including but not limited to the terms “upper,” “lower,” “right,” “left,” “vertical,” “horizontal, “top,” “bottom,” and derivatives thereof shall relate to the described structures and methods, as oriented in the drawing figures. The terms “overlying,” “atop,” “on top, “positioned on” or “positioned atop” mean that a first element, such as a first structure, is present on a second element, such as a second structure, where intervening elements such as an interface structure can be present between the first element and the second element. The term “direct contact” means that a first element, such as a first structure, and a second element, such as a second structure, are connected without any intermediary elements. 
     Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. 
     The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. The term “substantially equal” may be used to refer to values that are within ±20% of one another in some embodiments, within ±10% of one another in some embodiments, within ±5% of one another in some embodiments, and yet within ±2% of one another in some embodiments. 
     The term “substantially” may be used to refer to values that are within ±20% of a comparative measure in some embodiments, within ±10% in some embodiments, within ±5% in some embodiments, and yet within ±2% in some embodiments. For example, a first direction that is “substantially” perpendicular to a second direction may refer to a first direction that is within ±20% of making a 90° angle with the second direction in some embodiments, within ±10% of making a 90° angle with the second direction in some embodiments, within ±5% of making a 90° angle with the second direction in some embodiments, and yet within ±2% of making a 90° angle with the second direction in some embodiments. 
     In this disclosure, the term actuator refers to a component or device that causes motion and control by creating motion of one or more parts of a machine. Actuators include, but are not limited to, motors. In this disclosure, the terms actuator and motor are sometimes used interchangeably. 
     It is to be understood that the disclosed subject matter is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings. The disclosed subject matter is capable of other embodiments and of being practiced and carried out in various ways. 
     Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting. As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based, may readily be utilized as a basis for the designing of other structures, methods, and systems for carrying out the several purposes of the disclosed subject matter. Therefore, the claims should be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the disclosed subject matter. 
     Although the disclosed subject matter has been described and illustrated in the foregoing exemplary embodiments, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the disclosed subject matter may be made without departing from the spirit and scope of the disclosed subject matter. 
     Accordingly, it is submitted that that scope of the patent should not be limited to the described implementations but rather should be limited only by the spirit and scope of the following claims. 
     All publications and references cited herein are expressly incorporated herein by reference in their entirety 
     Various embodiments of the concepts, systems, devices, structures, and techniques sought to be protected are described above with reference to the related drawings. Alternative embodiments can be devised without departing from the scope of the concepts, systems, devices, structures, and techniques described. It is noted that various connections and positional relationships (e.g., over, below, adjacent, etc.) may be used to describe elements in the description and drawing. These connections and/or positional relationships, unless specified otherwise, can be direct or indirect, and the described concepts, systems, devices, structures, and techniques are not intended to be limiting in this respect. Accordingly, a coupling of entities can refer to either a direct or an indirect coupling, and a positional relationship between entities can be a direct or indirect positional relationship. 
     As an example of an indirect positional relationship, positioning element “A” over element “B” can include situations in which one or more intermediate elements (e.g., element “C”) is between elements “A” and elements “B” as long as the relevant characteristics and functionalities of elements “A” and “B” are not substantially changed by the intermediate element(s). 
     Also, the following definitions and abbreviations are to be used for the interpretation of the claims and the specification. The terms “comprise,” “comprises,” “comprising, “include,” “includes,” “including,” “has,” “having,” “contains” or “containing,” or any other variation are intended to cover a non-exclusive inclusion. For example, an apparatus, a method, a composition, a mixture or an article, that comprises a list of elements is not necessarily limited to only those elements but can include other elements not expressly listed or inherent to such apparatus, method, composition, mixture, or article. 
     Additionally, the term “exemplary” is means “serving as an example, instance, or illustration. Any embodiment or design described as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments or designs. The terms “one or more” and “at least one” indicate any integer number greater than or equal to one, i.e. one, two, three, four, etc. The term “plurality” indicates any integer number greater than one. The term “connection” can include an indirect “connection” and a direct “connection”. 
     References in the specification to “embodiments,” “one embodiment, “an embodiment,” “an example embodiment,” “an example,” “an instance,” “an aspect,” etc., indicate that the embodiment described can include a particular feature, structure, or characteristic, but every embodiment may or may not include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it may affect such feature, structure, or characteristic in other embodiments whether or not explicitly described. 
     Relative or positional terms including, but not limited to, the terms “upper,” “lower,” “right,” “left,” “vertical,” “horizontal, “top,” “bottom,” and derivatives of those terms relate to the described structures and methods as oriented in the drawing figures. The terms “overlying,” “atop,” “on top, “positioned on” or “positioned atop” mean that a first element, such as a first structure, is present on a second element, such as a second structure, where intervening elements such as an interface structure can be present between the first element and the second element. The term “direct contact” means that a first element, such as a first structure, and a second element, such as a second structure, are connected without any intermediary elements. 
     Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another, or a temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. 
     The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. The term “substantially equal” may be used to refer to values that are within ±20% of one another in some embodiments, within ±10% of one another in some embodiments, within ±5% of one another in some embodiments, and yet within ±2% of one another in some embodiments. 
     The term “substantially” may be used to refer to values that are within ±20% of a comparative measure in some embodiments, within ±10% in some embodiments, within ±5% in some embodiments, and yet within ±2% in some embodiments. For example, a first direction that is “substantially” perpendicular to a second direction may refer to a first direction that is within ±20% of making a 90° angle with the second direction in some embodiments, within ±10% of making a 90° angle with the second direction in some embodiments, within ±5% of making a 90° angle with the second direction in some embodiments, and yet within ±2% of making a 90° angle with the second direction in some embodiments. 
     The disclosed subject matter is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings. The disclosed subject matter is capable of other embodiments and of being practiced and carried out in various ways. 
     Also, the phraseology and terminology used in this patent are for the purpose of description and should not be regarded as limiting. As such, the conception upon which this disclosure is based may readily be utilized as a basis for the designing of other structures, methods, and systems for carrying out the several purposes of the disclosed subject matter. Therefore, the claims should be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the disclosed subject matter. 
     Although the disclosed subject matter has been described and illustrated in the foregoing exemplary embodiments, the present disclosure has been made only by way of example. Thus, numerous changes in the details of implementation of the disclosed subject matter may be made without departing from the spirit and scope of the disclosed subject matter. 
     Accordingly, the scope of this patent should not be limited to the described implementations but rather should be limited only by the spirit and scope of the following claims. 
     All publications and references cited in this disclosure are expressly incorporated by reference in their entirety.