Displacement Of Actuator Research Articles

Characterizing the transduction behavior of ionic polymer-metal composite actuators and sensors via dimensional analysis

Ionic polymer-metal composites (IPMCs) are functional smart materials that exhibit both electromechanical and mechanoelectrical transduction properties, and the physical phenomenon underlying the transduction mechanisms have been studied across the literature extensively. Here we use a new modeling framework to conduct the most comprehensive dimensional analysis of IPMC transduction phenomena, characterizing the IPMC actuator displacement, actuator blocking force, short-circuit sensing current, and open-circuit sensing voltage under static and dynamic loading. The information obtained in this analysis is used to construct nonlinear regression models for the transduction response as univariant and multivariant functions. Automatic differentiation techniques are leveraged to linearize the nonlinear regression models in the vicinity of a typical IPMC description and derive the sensitivity of the transduction response with respect to the driving independent variables. Further, the multiphysics model is validated using experimental data collected for the dynamic IPMC actuator and voltage sensor. With data collected from physical samples of IPMC materials in-lab, the regression models developed under the new computational framework are verified.

Large electrostrictive effect and dielectric properties of (K0.5Na0.5)NbO3-BaZrO3 ceramics

Electrostrictive materials are sought after in high-precision displacement actuators due to their ultra-low hysteresis electrostrain. Here we report a very promising electrostrictive material by doping barium zirconate into a sodium potassium niobate matrix. Also, the dielectric behaviors and electrostrictive properties of (1-x)K0.5Na0.5NbO3-xBaZrO3 (x = 0.10, 0.12, 0.14 and 0.16) ceramics are investigated in details. The doping of barium zirconate allows the diffuse phase transition to occur near room temperature. Diffuse dielectric anomalies at high temperatures are observed in poled ceramics, which are closely related to the activation of defects. High electrostrain (∼0.1 %) with ultra-low strain hysteresis (< 12 %) are obtained at x = 0.14. Moreover, electrostrain exhibits excellent stability over a wide temperature range from 30 ℃ to 120 ℃.Further, the electrostrictive coefficient of ∼0.066 m4/C2 for the component was determined at high temperatures and high electric fields, demonstrating the excellent potential of the K0.5Na0.5NbO3-BaZrO3 solid solutions as electrostrictive materials.

Hydrodynamics Modeling of a Piezoelectric Micro-Robotic Fish With Double Caudal Fins

Abstract An analytical hydrodynamics model for a piezoelectric micro-robotic fish with double caudal fins is presented in this paper. The relation between displacement of the piezoelectric actuator and oscillating angle of the caudal fin is established based on the analysis of the flexible four-bar linkage transmission. The hydrodynamics of caudal fins are described by airfoil and blade element theories. Furthermore, the dynamics and kinetics of the whole micro-robotic fish are analyzed and validated by experiments.

Texture technique to simultaneously achieve large electric field induced strain response and ultralow hysteresis in BMT-PMN-PT relaxor ferroelectric ceramics

Piezoelectric ceramics with large strain response and low hysteresis are highly desired for high precision displacement actuator applications. In this work, we report the simultaneous achievements of large strain response and ultralow hysteresis in [001]c oriented Bi(Mg1/2Ti1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 textured ferroelectric ceramics. X-ray diffraction and field-emission scanning electron microscopy were used to reveal the microstructure evolution process of textured ceramics during texture development. A large electric-field induced strain of 0.39% at 7 kV/mm and a ultralow hysteresis of 1.94% were achieved in textured ceramics with texture degree 90%. The as-prepared textured ceramics have a relatively good temperature stability, and the strain value varies from 0.36% to 0.29% at 6 kV/mm in the temperature range of 20-100 °C. This novel textured ceramics with a large strain and ultralow hysteresis will further provide a promising candidate for the application of large-displacement piezoelectric actuator with high precision displacement.

Hybrid screw fixation for femoral neck fractures: Does it prevent mechanical failure?

IntroductionTraditionally, femoral neck fracture fixation has been performed using three partially threaded cancellous screws. However, fracture collapse with femoral neck shortening, and varus deformation frequently occurs due to posterior medial comminution and lack of calcar support. We hypothesize replacing the inferior neck/calcar screw with a fully threaded, length stable, screw will provide improved biomechanical stability, decrease femoral neck shortening and varus collapse. MethodsTen matched cadaveric pairs (20 femurs) were randomly assigned to two screw fixation groups. Group 1 (Hybrid) utilized one fully threaded calcar screw & two partially threaded superior screws. Group 2 (PT) utilized all partially threaded screws. Specimens underwent standardized femoral neck osteotomies, 45° from the horizontal, with 5 mm posteromedial wedge removed to simulate posteromedial comminution. Screws were placed using fluoroscopic guidance. Specimens were biomechanically tested using two loading sequences: 1) Axial load applied up to 700 N, followed by cyclic loading at 2 Hz with loads of 700 to 1,400 N for 10,000 cycles. 2) All surviving constructs were cyclically loaded to failure in stepwise incremental manner with max load of 4,000 N. Paired t-tests used to compare stiffness, cycles to failure, and max load to failure (defined as 15 mm load actuator displacement). ResultsConstruct stiffness was 2848 ± 344 N/mm in PT vs. 2767 ± 665 for Hybrid (P = 0.628). Load to failure demonstrated, hybrid superiority with max cycles to failure (3797 ± 400 cycles) vs. (2981 ± 856 cycles in PT) (p = 0.010), and max load prior to failure (3290 ± 196 N) vs. (2891 ± 421 N in PT) (p = 0.010). No significant difference in bone mineral density was noted in any of the specimens. ConclusionsOur study is the first to assess the biomechanical effects of hybrid fixation for femoral neck fractures. Hybrid screw configuration resulted in significantly stronger constructs, with higher axial load and increased cycles prior to failure. The advantageous mechanical properties demonstrated using a fully threaded inferior calcar screw provides a length stable construct which may prevent the common complication of excessive femoral neck shortening, varus collapse and poor functional outcome.

Differential resistance based self-sensing recurrent neural network model for position estimation and control of antagonistic Shape Memory Alloy actuator

The paper presents the development and experimental investigation of recurrent neural network (RNN) based self-sensing position estimation (SSPE) model for shape memory alloy actuator (SMA). RNN is used as an estimator in the position feedback control loop to replace the external additional position sensor. The model was inspired by the physics-based analogy of the Mass-Spring-Damper (MSD) system for the antagonistic SMA wire actuator. Actuator displacement presents the hysteresis and non-linear dynamic relationship with observed differential resistance (sensing signal) during phase transformation. The resistance variation causes due to dissimilar resistivity between primary phases of SMA material. The RNN based estimation model was considered because it consists of memory elements for storing the processed information and feedback connections for dynamic modeling of the system. RNN was trained with input sensing signal and target displacement datasets. The estimation accuracy of the model was real-time evaluated during trajectory tracking of reference signals in the feedback control loop. A quantitative performance analysis is assessed in terms of correlation (ℛ), mean absolute error (MEA), and root mean square error (RSME) of the learned model along with the developed actuator system. The tracking results confirm the close agreement between estimated and measured displacement at a reasonable accuracy.

Modeling and Compensation of Dynamic Hysteresis with Force-Voltage Coupling for Piezoelectric Actuators.

Piezoelectric actuators are widely used in the field of micro- and nanopositioning due to their high frequency response, high stiffness, and high resolution. However, piezoelectric actuators have hysteresis nonlinearity, which severely affects their positioning accuracy. As the driving frequency increases, the performance of piezoelectric actuators further degrades. In addition, the impact of force on piezoelectric actuators cannot be ignored in practical applications. Dynamic hysteresis with force-voltage coupling makes the hysteresis phenomenon more complicated when force and driving voltage are both applied to the piezoelectric actuator. Existing hysteresis models are complicated, or inaccurate in describing dynamic hysteresis with force-voltage coupling. To solve this problem, a force-voltage-coupled Prandtl–Ishlinskii (FVPI) model is proposed in this paper. First, the influence of driving frequency and dynamic force on the output displacement of the piezoelectric actuators are analyzed. Then, the accuracy of the FVPI model is verified through experiments. Finally, a force integrated direct inverse (F-DI) compensator based on the FVPI model is designed. The experimental results from this study show that the F-DI compensator can effectively suppress dynamic hysteresis with force-voltage coupling of piezoelectric actuators. This model can improve the positioning accuracy of piezoelectric actuators, thereby improving the working accuracy of the micro- or nano-operating system.

Design and Performance Analysis of Precision Micro-drive Amplification Mechanism

At present, there are shortcomings in the research of micro-drive amplification mechanism, such as insufficient precision and additional force. In this paper, a kind of micro-drive amplification mechanism is designed and its positioning accuracy is simulated. Firstly, a kind of micro-drive amplification mechanism is designed, which can accurately transform the input displacement of piezoelectric ceramic actuator (PZT) into the output displacement of a certain number of amplification. the theoretical motion magnification ratio of the mechanism is 3:1. Secondly, the kinematics and simulation of the mechanism were studied, and the conversion performance of the mechanism was analyzed. The results showed that the micro-drive amplification mechanism has the advantage of high positioning accuracy (maximum positioning error is 4.67%). Finally, through strength analysis and modal analysis, the performance of micro-drive amplification mechanism is studied. This study has some reference value for the research and application of precision micro-drive amplification mechanism.

Investigation of the Dynamics of a 2-DoF Actuation Unit Cell for a Cooperative Electrostatic Actuation System

The mechanism of the inchworm motor, which overcomes the intrinsic displacement and force limitations of MEMS electrostatic actuators, has undergone constant development in the past few decades. In this work, the electrostatic actuation unit cell (AUC) that is designed to cooperate with many other counterparts in a novel concept of a modular-like cooperative actuator system is examined. First, the cooperative system is briefly discussed. A simplified analytical model of the AUC, which is a 2-Degree-of-Freedom (2-DoF) gap-closing actuator (GCA), is presented, taking into account the major source of dissipation in the system, the squeeze-film damping (SQFD). Then, the results of a series of coupled-field numerical simulation studies by the Finite Element Method (FEM) on parameterized models of the AUC are shown, whereby sensible comparisons with available analytical models from the literature are made. The numerical simulations that focused on the dynamic behavior of the AUC highlighted the substantial influence of the SQFD on the pull-in and pull-out times, and revealed how these performance characteristics are considerably determined by the structure’s height. It was found that the pull-out time is the critical parameter for the dynamic behavior of the AUC, and that a larger damping profile significantly shortens the actuator cycle time as a consequence.

Effect of different prestretching index and preloading on actuation behaviors of dielectric elastomer actuator

Herein, the prestretching indexes of dielectric elastomers (DE) were determined by measuring the tensile properties, and then the actuation displacement and output force of the conical dielectric elastomer actuator (CDEA) with different prestretching index and different preloading were discussed in detail, finally, the three indexes of thickness, generatrix and circumferential stretch are proposed to calculate the strain energy density of the CDEA. The experimental results show that the large prestretching ratio will cause the obvious instability of DE. Two materials showed obvious thin neck phenomenon and finally fracture. The stress–strain curve of DE shows hysteresis phenomenon under cyclic loading, and with the increase of cycle times, the unit stress and the unit hysteresis loss rate both decrease, and the change range is larger. When the prestretching of outer domain is the same, the displacement and force of CDEA increase with the increase of voltage, and the displacement curve appears parallel distribution under different voltage. The Gent model can better reflect the nonlinear deformation behavior of CDEA. This study provides valuable guidance for the design of high performance DEA and the application of dynamic DEA.

Design, Analysis and Experiment of a Bridge-Type Piezoelectric Actuator for Infrared Image Stabilization.

Piezoelectric actuators are widely used in the optical field due to their high precision, compact structure, flexible design, and fast response. This paper presents a novel piezoelectric actuator with a bridge-type mechanism, which can be used to stabilize the images of an infrared imaging system. The bridge amplification mechanism is used to amplify the actuation displacement, and its structural parameters are optimized by the response surface method. The control strategy of the image stabilization system is formulated, and the overall structure of the infrared image stabilization system is designed according to the principle of image stabilization and the control strategy. The prototype was fabricated and verified by a series of experiments. In the test, the laminated piezoelectric ceramics are used as the driving element, and its maximum output displacement was about 17 μm under a voltage of 100 V. Firstly, the performance of the piezoelectric amplification mechanism was tested, and the maximum displacement of the piezoelectric micro-motion mechanism was 115 μm. The displacement amplification ratio of the mechanism was 5.7. Then, the step distance and response time of the micro-displacement mechanism were measured by inputting the stepping signal. When the input voltage increased to 3 V, 5 V, and 7 V, the stepping displacements of the mechanism were 2.4 μm, 4.1 μm, and 5.8 μm. Finally, the image stabilization effect of the designed mechanism was verified by imaging timing control and feedback signal processing.

Designing control algorithm and experimental validation for piezo stepping actuator

Piezo-stepping actuator is one device that produces large displacement while some voltage is applied to it or vice-versa by micro-meter accuracy and nanometer resolution. The displacement in stepper actuators happens with steps. A linear stepping movement of the base of the actuator is proposed in this paper. A linear stepping motion of the piezo actuators is achieved with four sets of push–pull actuators and four sets of lock release actuators. The designed stepper actuator produces linear displacements. The design and control of the stepper actuators are explained in the paper. A trapezoidal signal is being generated from the triangular wave moreover this is implemented as the input for the smooth functioning of a stepping actuator. Control operation of push–pull and lock-release actuators was performed and for various input displacements the experimental displacements of actuators were achieved and the results were plotted. Control operation of Push-pull and lock release assembly was conducted for varying input displacement and corresponding experimental displacement is measured and also the results were plotted. The actuator assembly was proficient in driving the linear guideways.

Active vibration control of an elastic rotor by using its deformation as controlled variable

An elastic gyroscopic rotor system is modelled using the finite element method. The rotor is supported with two piezoelectric actuators which allow a dynamic manipulation of the rotational axis. The piezos are modelled as displacement actuators causing a base excitation. It is known from the literature that actively reducing the displacements of the rotor in the self-centring area leads to increasing bearing forces. We propose an approach which theoretically allows the use of the rotor displacements for active control without significantly increasing the bearing forces, even in the self-centring area. We use the relative displacements of the rotor for control which are proportional to the deformation of the rotor. The relative displacements are the difference between the absolute displacements, which describe the rotor centre, and a virtual active rotor axis which is a linear interpolation of the theoretically load-free actuator displacements of the piezos. A combination of integral force feedback and the least-mean-squares algorithm is chosen for control which takes full advantage of complex time signals. The analytic optimum of this control shows resonances which match with the resonances of the unsupported rotor if only the bearing forces are minimized. We refer to them as force-free resonances. While minimizing the absolute displacements in addition to the bearing forces only eliminates the first resonance, minimizing the relative displacements in addition eliminates all resonances. Using an additional weighting of the controller part prevents the force-free resonances and eliminates the difference between using the absolute and relative displacements. This is confirmed by experiments on the test-rig. However, there is no additional resonance when using the absolute displacement in addition to the bearing forces. Using the relative displacements allow for a higher reduction of the bearing forces caused by unbalance excitation in comparison to the absolute displacements when no weighting of the controller output is used. The test-rig results also show that it is not possible to eliminate the first conventional resonance peak which comprise forward and backward whirl vibrations by only controlling the bearing forces in the first bearing plane. The additional consideration of the absolute or relative displacements is able to eliminate these resonances with just a low increase of the bearing forces after the second resonance.

A detailed solution framework for the out‐of‐plane displacement of circular dielectric elastomer actuators

AbstractThe out‐of‐plane displacement (OPD) of a circular dielectric elastomer actuator (DEA) membrane has been explored in recent years for a variety of important applications. Circular DEAs consist of an elastomer membrane that is prestretched to a rigid frame and coated with compliant electrodes. Such a simple configuration has found many interesting applications such as in pumps, pulse tracking, hopping search and rescue robots, dielectric elastomer generators for renewable energy harvesting, linear actuators, and many others. Here, we present an easy‐to‐implement solution framework of the OPD for circular DEAs via a detailed numerical solution using the shooting method (SM) on a system of differential algebraic equations (DAE). The material model incorporated follows the robust Gent hyperelastic representation, and a comparison (of the OPD of a single‐cone DEA) against a neo‐Hookean based solution is included. The SM‐based numerical solution to the resulting boundary value DAE problem is applied to a practical range of values based on the reported literature. Analysis of the results and comparison against other studies are provided. The current work provides a go‐to framework for implementation in further research and development that can be useful to a broader audience including nonexperts in the field of soft robotics.

BIOMECHANICAL SIMULATION OF RADIAL HEAD SUBLUXATION IN CADAVERIC PEDIATRIC ELBOWS

Background:Radial head subluxation, known as pulled elbow or Nursemaid’s elbow, is a common pediatric condition that occurs when a longitudinal traction force is applied to an elbow that is pronated and extended. Although the stability of the proximal radioulnar joint has been previously examined in cadaveric models, there are no current studies quantifying the biomechanics of nursemaid’s elbow. The purpose of our study was to demonstrate and quantify the axial traction force required to produce a nursemaid’s elbow in a pediatric cadaver specimen.Methods:Two fresh-frozen cadaveric elbows from a single 3 year-old male donor were dissected by a fellowship-trained orthopedic surgeon. An Instron 5944 testing machine with a 2 kN load cell was used to perform uniaxial testing. The radius and humerus were mounted to the Instron machine, and loaded in the axial direction with the elbow in full extension. Loading occurred at a rate of 10 mm/sec for 4 seconds, during which the force and actuator displacement were continuously recorded. The local instantaneous load and extension displacement at the time of subluxation were recorded, and data was synced with high-frame-rate video footage used to confirm the annular ligament subluxation.Results:The load to failure required to produce the nursemaid’s elbow injury in the first elbow was 31N, with a failure displacement of 4.6mm. The second elbow demonstrated a load to failure of 26N, with a failure displacement of 4.6mm. After subluxation, we reduced the annular ligament from the first specimen. The elbow was then re-tested and demonstrated a load to failure of 20N, with a failure displacement of 2.6mm.Conclusion:Axial traction applied to a pediatric cadaver specimen results in subluxation of the annular ligament into the radiocapitellar joint. The mean load to failure is 28.5N, and a lower load to failure was required to produce a recurrent subluxation in a previously injured specimen. Lower load for a recurrent subluxation may be attributed to damage on the annular ligament due to the first subluxation.Figure 1.Red arrows mark the proximal edge of the radial head before (A) and after (B) subluxation due to applied axial force.

Electrostatically Tuned Optical Filters Based on Hybrid Plasmonic-Dielectric Thin Films for Hyperspectral Imaging.

Hyperspectral imaging has a wide range of uses, from medical diagnostics to crop monitoring; however, conventional hyperspectral imaging systems are relatively slow, bulky, and rather costly. In this paper, we present an inexpensive, compact tunable optical filter for hyperspectral applications. The filter is based on a Fabry-Pérot interferometer utilizing hybrid metallic-dielectric mirrors and actuated using a MEMS electrostatic actuator. The optical filter is designed using the transfer matrix method; then, the results were verified by an electromagnetic wave simulator. The actuator is based on a ring-shaped parallel plate capacitor and is designed using COMSOL Multiphysics. An actuation displacement of 170 nm was used, which is the required distance to tune the filter over the whole visible range (400–700 nm). There are two designs proposed for the optical filter: the first was optimized to provide maximum transmission and the other is optimized to have minimum full-width-half-maximum (FWHM) value. The first design has a maximum transmission percentage of 94.45% and a minimum transmission of 86.34%; while the minimum FWHM design had an average FWHM value of 7.267 nm. The results showed improvements over the current commercial filters both in transmission and in bandwidth.

A Technique for Mimicking Soft Tissue Manipulation from Experimental Data to a Wave Equation Model for a New Laparoscopic Virtual Reality Training System

Background: The difficulty of laparoscopic procedures and the specific psychomotor skills required support the need for a training system for intensive and repetitive practice to acquire the specific skills. The present VR training systems have some limitations with respect to the soft tissue models in the training system. This is associated with the need for a real-time simulation, which requires a balance between computational cost and accuracy. Objective: The primary objective of the study is to develop a two dimensional wave equation model that closely mimics the soft tissue manipulation in a laparoscopic procedure for a VR training system. Methods: A novel mathematical model based on the wave equation is prepared to represent the interaction between the laparoscopic tool and the soft tissue. The parameters within the model are determined through experimental analysis of a soft tissue phantom. The experimental setup involves a linear actuator applying force to the soft tissue phantom to generate deformation. Data acquisition is conducted through a camera and a robotic force acquisition system which measures force, displacement of the linear actuator and records a video. Through image processing, the displacements of the markers on the phantom’s x-y plane during its deformation are determined and these parameters are used to develop the model, which finally is validated through a comparative analysis. Results: The results from the developed model are observed and compared statistically as well as graphically with the finite element model based on deformation data. The results show that the deformation data between the developed model and the available model is significantly similar. Conclusion: This study demonstrates the adaptability of the wave equation to meet the needs of the specific surgical procedure through modification of the model based on the experimental data. Moreover, the comparative analysis further corroborates the relevance and validity of the model for the surgical training system.

Enhanced Electrostrictive Coefficient and Suppressive Hysteresis in Lead-Free Ba(1−x)SrxTiO3 Piezoelectric Ceramics with High Strain

Lead-free piezoelectric ceramics with both low hysteresis and superior electrostrictive coefficient features are crucial toward providing desired performance for intelligent electrical devices, especially in high-precision displacement actuators. In this work, we propose a novel scenario, which is to design the phase transition around ambient temperature to enhance electrostrictive effect and inhibit hysteresis. In other words, the dense ceramics with cubic phases (C) and tetragonal phases (T) coexisting at RT (room temperature) were designed. According to this scenario, the Ba(1−x)SrxTiO3 (abbreviated as BT-100xST) ceramics were fabricated by the conventional solid-state reaction method. The relaxor behavior, ferroelectric properties, crystal structure and microstructure of BT-100xST ceramics have been investigated in detail. As a result, the BT-100xST ceramics with x = 0.20–0.40 present relaxor behavior which was indicated by dielectric constant as a function of temperature and (polarization–electric field) P–E hysteresis loops. The BT-30ST ceramics exhibit enhanced electrostrictive coefficient Q33 (&gt;0.034 m4/C2), and the electrostrictive strain and low hysteresis achieves 0.11% and 2%, respectively. The BT-100xST ceramics are considered as a prospective option for application in displacement actuators with high sensitivity and high precision.

Properties of Silicone Rubber-Based Composites Reinforced with Few-Layer Graphene and Iron Oxide or Titanium Dioxide.

The increasing demand for polymer composites with novel or improved properties requires novel fillers. To meet the challenges posed, nanofillers such as graphene, carbon nanotubes, and titanium dioxide (TiO2) have been used. In the present work, few-layer graphene (FLG) and iron oxide (Fe3O4) or TiO2 were used as fillers in a room-temperature-vulcanized (RTV) silicone rubber (SR) matrix. Composites were prepared by mixing RTV-SR with nanofillers and then kept for vulcanization at room temperature for 24 h. The RTV-SR composites obtained were characterized with respect to their mechanical, actuation, and magnetic properties. Fourier-transform infrared spectroscopy (FTIR) analysis was performed to investigate the composite raw materials and finished composites, and X-ray photoelectron spectroscopy (XPS) analysis was used to study composite surface elemental compositions. Results showed that mechanical properties were improved by adding fillers, and actuation displacements were dependent on the type of nanofiller used and the applied voltage. Magnetic stress-relaxation also increased with filler amount and stress-relaxation rates decreased when a magnetic field was applied parallel to the deformation axes. Thus, this study showed that the inclusion of iron oxide (Fe3O4) or TiO2 fillers in RTV-SR improves mechanical, actuation, and magnetic properties.

Micromachined Subterahertz Waveguide-Integrated Phase Shifter Utilizing Supermode Propagation

In this work, we propose a new concept of phase shifting by tuning the coupling distance between two parallel silicon slabs that support the propagation of an in-phase supermode. A prototype device was implemented in the 220-330-GHz band by integrating the micro-electro-mechanical system (MEMS)-actuated phase-shifting mechanism, based on two moveable parallel-coupled high-resistivity silicon slabs, inside a metallized hollow rectangular waveguide in silicon-on-insulator (SOI) micromachining technology. The prototype device has been characterized to a maximum continuous phase tunability of 550° with a maximum insertion loss of 1.87 dB achieved at 330 GHz. A maximum figure-of-merit (FOM) of 375°/dB is achieved at around 320 GHz, which presently is the highest FOM value reported for any phase shifter in the subterahertz (sub-THz) frequency range. The bandwidth covers the whole waveguide band with an average and worst case insertion loss of 1.94 and 2.5 dB, respectively, a worst case insertion-loss variation of 0.7 dB and a phase error better than 4° for all phase states. A large displacement of MEMS electrostatic comb-drive actuators that are co-fabricated in the micromachined waveguide platform is achieved by a driving voltage of 50 V. The prototype footprint is 7.3 ×5.3 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .