Actuators, Volume 12, Issue 1 (January 2023) – 45 articles

Trailing-edge noise (TE noise) is an aeroacoustic sound radiated from an isolated airfoil in the specific ranges of low-speed flow. We used a pulsed laser as an actuator to reduce the TE noise without modifying the airfoil’s surface. The wind tunnel test was conducted to verify the capability of an Nd:YAG laser as the actuator. The laser beam was focused into the air just outside the velocity boundary layer on the lower side of an NACA0012 airfoil. The experimental result shows that the TE noise is suppressed for a certain period after beam irradiations. We then analyzed the physical mechanism of the noise reduction with the laser actuation by the implicit large eddy simulation (ILES), a high-fidelity numerical method for computational fluid dynamics (CFD). The numerical investigations indicate that the pulsed energy deposition changes the unstable velocity amplification mode of the boundary layer, the source of an acoustic feedback loop radiating the TE noise, to another mode that does not generate the TE noise. The sound wave attenuation is observed once the induced velocity fluctuations and consequently generated vortices sweep out the flow structure of the unstable mode. We also examined the effect of the laser irradiation zone’s shape by numerical simulations. The results show that the larger irradiation zone, which introduces the disturbances over a wider range in the span direction, is more effective in reducing the TE noise than the shorter focusing length with the same energies. Full article

In order to decrease the transmission of vibration and achieve the attenuation of the vibration magnitude of an isolated object, a new type of permanent and electromagnet composite vibration isolation system is designed based on negative stiffness theory. Firstly, according to the characteristic analysis, the design of a permanent and electromagnet hybrid actuator is accomplished; secondly, the vibration isolation system model is established, and the active control strategy based on the fuzzy PID algorithm is designed. Finally, a test platform is built to verify the vibration isolation effect. The results indicate that the developed permanent and electromagnet composite vibration isolation system renders the sharp attenuation of external vibration in multiple frequency bands. When the external vibration frequency is within the frequency range of 20 Hz to 100 Hz, the vibration attenuation is greater than 80%; when the external vibration frequency is within the frequency range of 100 Hz to 500 Hz, the vibration attenuation rate is greater than 90%. Full article

In this study, an experimental investigation of separation control using a dielectric barrier discharge plasma actuator was performed on an NACA0015 airfoil over a wide range of Reynolds numbers, angles of attack, and nondimensional burst frequencies. The range of the Reynolds number was based on a chord length ranging from 2.52 × 10${}^5$ to 1.008 × 10${}^6$. A plasma actuator was installed at the leading edge and driven by AC voltage. Burst mode (duty-cycle) actuation was applied, with the nondimensional burst frequency ranging between 0.1–30. The control authority was evaluated using the time-averaged distribution of the pressure coefficient $Cp$ and the calculated value of the lift coefficient $C_l$. The baseline flow fields were classified into three types: (1) leading-edge separation; (2) trailing-edge separation; and (3) the hysteresis between (1) and (2). The results of the actuated cases show that the control trends clearly depend on the differences in the separation conditions. In leading-edge separation, actuation with a burst frequency of approximately $F^{+}=$ 0.5 creates a wide negative pressure region on the suction-side surface, leading to an increase in the lift coefficient. In trailing-edge separation, several actuations alter the position of turbulent separation. Full article

This paper presents an integrated controller for an autonomous articulated electric vehicle (AAEV) for path tracking and rollover prevention. The AAEV is vulnerable to rollover due to the characteristics of the articulated frame steering (AFS) mechanism, which shows improved maneuverability and agility but not front wheel steering. In addition, the ratio between height and track width is high, so the AAEV is prone to rolling over. Therefore, the proposed controller was designed to achieve the two goals, following the reference path and managing the velocity to improve the safety of the AAEV. Vehicle behavior was modeled by a kinematic model with actuation delay. A local linearization was used to improve the accuracy of the vehicle model and reduce the computational load. Reference states of the position and heading were determined to follow the reference path and prevent the rollover. A model predictive control (MPC)-based reference state tracker was designed to optimize the articulation angle rate and longitudinal acceleration commands. The simulation study was conducted to evaluate the proposed algorithm with a comparison of the base algorithms. The reference path for the simulation was an S-shaped path with discontinuous curvature. Simulation results showed that the proposed algorithm reduces the path tracking error and load-transfer ratio. Full article

In this study, a type of direct-drive gearshift system integrated into a motor-transmission coupled drive system is introduced. It used two electromagnetic linear actuators (ELAs) to perform gearshift events. The adoption of ELAs simplifies the architecture of the gearshift system and has the potential to further optimize gearshift performance. However, a number of nonlinearities in the gearshift system should be investigated in order to enhance the performance of the direct-drive gearshift system. An active disturbance rejection control (ADRC) method was selected as the principal shifting control method due to the simple methodology and strong reliability. The nonlinear characteristics of the electromagnetic force produced by the ELA were subsequently reduced using the inverse system method (ISM) technique. The ADRC approach also incorporated an acceleration feedforward module to enhance the precision of displacement control. The extended state observer (ESO) module used a nonlinear function in place of the original function to improve the ability to reject disturbances. Comparative simulations and experiments were carried out between the ADRC method and improved ADRC (IADRC) method. The outcomes demonstrate the effectiveness of the designed control method. The shift force fluctuates less, and the shift jerk decreases noticeably during the synchronization procedure. In conclusion, combined with the optimized IADRC method, the direct-drive gearshift system equipped with ELAs shows remarkable gearshift performance, and it has the potential to be widely used in motor−transmission coupled drive systems for EVs. Full article

Learning from demonstration (LfD) is a practical method for transferring skill knowledge from a human demonstrator to a robot. Several studies have shown the effectiveness of LfD in robotic grasping tasks to improve the success rate of grasping and to accelerate the development of new robotic grasping tasks. A well-designed demonstration device can effectively represent human grasping motion to transfer grasping skills to robots. In this paper, an improved gripper-like exoskeleton with a data collection system is proposed. First, we present the mechatronic details of the exoskeleton and its motion-tracking system, considering the manipulation flexibility and data acquisition requirements. We then present the capabilities of the device and its data collection system, which collects the position, pose and displacement of the gripper on the exoskeleton. The collected data is further processed by the data acquisition and processing software. Next, we describe the principles of Gaussian mixture model (GMM) and Gaussian mixture regression (GMR) in robot skill learning, which are used to transfer the raw data from demonstrations to robot motions. In the experiment, an optimized trajectory was learned from multiple demonstrations and reproduced on a robot. The results show that the GMR complemented with GMM is able to learn a smooth trajectory from demonstration trajectories with noise. Full article

This paper studies the target tracking control strategy of a snake robot and proposes an adaptive sliding mode control method. The strategy ensures the robot follows the target path by controlling the joint angle through feedback, pushing the robot to reach the target position through gait function. In order to achieve target tracking, a kinematic model of a snake robot was first established in this paper. Then, we used double-sine serpentine gait to solve the problem of low steering efficiency caused by regular serpentine gait, and we explored the relationship between control parameters and robot steering. On the basis of gait, in order to further improve the efficiency of target tracking for the snake robot, an adaptive sliding mode control method, based on a new sliding mode reaching law, was proposed. Finally, the effectiveness and practicability of the proposed strategy was demonstrated by comparative analysis and simulation experiments. Full article

The robotic grinding system for a thin-walled workpiece is a multi-dimensional coupling system composed of a robot, a grinding spindle and the thin-walled workpiece. In the grinding process, a dynamic coupling effect is generated, while the thin-walled workpiece stimulates elastic vibration; the grinding spindle, as an electromechanical coupling actuator, is sensitive to the elastic vibration in the form of load fluctuations. It is necessary to investigate the electromechanical coupling dynamic characteristics under the vibration coupling of the thin-walled workpiece as well as the vibration control of the robotic grinding system. Firstly, considering the dynamic coupling effect between the grinding spindle and thin-walled workpiece, a dynamic model of the grinding spindle and thin-walled workpiece coupling system is established. Secondly, based on this established coupling dynamic model, the vibration characteristics of the thin-walled workpiece and the electromechanical coupling dynamic characteristics of the grinding spindle are investigated. Finally, a speed adaptive control system for the grinding spindle is designed based on a fuzzy PI controller, which can achieve a stable speed for the grinding spindle under vibration coupling and has a certain suppression effect on the elastic vibration of the thin-walled workpiece at the same time. Full article

This article presents the formulation and application of a reduced-order thermomechanical finite strain shape memory alloy (SMA)-based microactuator model for switching devices under thermal loading by Joule heating. The formulation is cast in the generalized standard material framework with an extension for thermomechanics. The proper orthogonal decomposition (POD) is utilized for capturing a reduced basis from a precomputed finite element method (FEM) full-scale model. The modal coefficients are computed by optimization of the underlying incremental thermomechanical potential, and the weak form for the mechanical and thermal problem is formulated in reduced-order format. The reduced-order model (ROM) is compared with the FEM model, and the exemplary mean absolute percentage errors for the displacement and temperature are $0.973\%$ and $0.089\%$, respectively, with a speedup factor of $9.56$ for a single SMA-based actuator. The ROM presented is tested for single and cooperative beam-like actuators. Furthermore, cross-coupling effects and the bistability phenomenon of the microactuators are investigated. Full article

Soft actuators have a high potential for the creative design of flexible robots and safe human–robot interaction. So far, significant progress has been made in soft actuators’ flexibility, deformation amplitude, and variable stiffness. However, there are still deficiencies in output force and force retention. This paper presents a new negative pressure-driven folding flexible actuator inspired by origami. First, we establish a theoretical model to predict such an actuator’s output force and displacement under given pressures. Next, five actuators are fabricated using three different materials and evaluated on a test platform. The test results reveal that one actuator generates a maximum pull force of 1125.9 N and the maximum push force of 818.2 N, and another outputs a full force reaching 600 times its weight. Finally, demonstrative experiments are conducted extensively, including stretching, contracting, clamping, single-arm power assistance, and underwater movement. They show our actuators’ performance and feature coupling hardness with softness, e.g., large force output, strong force retention, two-way working, and even muscle-like explosive strength gaining. The existing soft actuators desire these valuable properties. Full article

Dielectric barrier discharge (DBD) has been one of the most promising techniques for flow control, but the practical application needs a large plasma surface. A three-electrode sliding discharge plasma actuator (SDPA) can generate plasma filling the inter-electrode distance. In this study, the performance of an SDPA for practical flight at low pressures is reported. When the pressure decreases, plasma discharge becomes more intensive. Current peaks and power consumption of electrode 1 become higher at low pressure. Sliding discharge is fully developed at 54 kPa, and the plasma morphology resembles plumes. PIV results show vortex structures and an induced wall jet above the actuator surface. A ‘potential-arc-discharge’ is observed at 38 kPa, leading to an inhomogeneous surface temperature distribution and a velocity decrease of the jet. Full article

Aiming at the decrease of tracking accuracy caused by nonlinear friction and strong coupling of the flexible upper-limb exoskeleton, an improved super-twisting sliding mode controller (ISTSMC) is proposed. Compared with the conventional super twisted sliding mode controller (STSMC), this method can replace the switching function under the integral term with a nonsmooth term, resulting in a faster response, less vibration when performing trajectory tracking, and reduced steady-state error. The introduction of the nonsmooth term causes the controller to have a stronger anti-interference ability. At the same time, the parameters of the ISTSMC can be adjusted in order to achieve the expected control performance. The effectiveness and feasibility of the proposed control algorithm are verified through experiments. Full article

Owing to the competitive advantages of fast response speed, large pushing force, high reliability, and high precision, the permanent magnet linear synchronous motor (PMLSM) has played an increasingly vital role in various high-speed and high-precision control systems. However, PMLSM exhibits nonlinear behavior in actual operation, and position tracking precision is negatively affected by friction, load changes, and other external disturbances. To meet the growing demand and solve the position tracking control problem for the PMLSM, the control system is critical. Sliding-mode control (SMC) has been used extensively in nonlinear control systems due to its superior performance characterized by simplicity, good dynamic response and insensitivity to parameter perturbation and external disturbances, and has been implemented in PMLSMs to track practical position. The objective of this article is to classify, scrutinize and review the major sliding-mode control approaches for position control of PMLSM. The three different conventional SMC methods, namely the boundary layer approach, the reaching law approach and the disturbance observer-based SMC, are discussed in detail. The four advanced forms of SMC, namely terminal SMC, super-twisting SMC, adaptive SMC and intelligent SMC, are also presented. A comparison of these approaches is given, in which the advantages and disadvantages of each approach are presented; additionally, they are presented in table form in order to facilitate reading. It is anticipated that this work will serve as a reference and provide important insight into position control of PMLSM systems. Full article

Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore, the complexity of the problem will increase when uncertainty also simultaneously affects the system under consideration. To address this issue, this paper investigated a feasible control strategy for nonlinear singular systems with time-varying delay that are subject to uncertainty and actuator saturation. The IT-2 fuzzy model was adopted to describe the dynamic of the non-linear delayed systems using lower and upper membership functions to deal with the uncertainty. Moreover, the polyhedron model was applied to characterize the saturation function. The goal of the control approach was to design a relevant IT2 fuzzy state feedback controller with mismatched membership functions so that the closed-loop system is admissible. On the basis of an appropriate Lyapunov–Krasovskii functional, sufficient delay-dependent conditions were established and an optimization problem was formulated in terms of linear matrix inequality constraints to optimize the attraction domain. Simulation examples are provided to verify the effectiveness of the proposed method. Full article

Recently, there have been significant developments in the field of vibration energy harvesters to feed sensors for structural health monitoring in aeronautics and other high technology fields. Within the framework of the EU InComEss project, new eco-friendly piezoelectric materials are under development. A foreseen application is vibration energy harvesting from the wing slats of aircraft. Semi-analytical models of the vibrating slat make it possible to estimate the maximum voltage that can be generated by a piezoelectric patch bonded to a slat surface. A more detailed analysis must consider details of the three-dimensional geometry of both the harvester and the bonding layer. This can only be carried out with multiphysics finite element software. A finite element model of a whole slat would require a large computational effort as millions of elements are typically needed to model very thin piezoelectric layers. To simplify this analysis, an integrated analytical–numerical method is proposed in this paper. A large-scale analytical model of the whole slat was used to calculate loads on the portion of the slat where a piezoelectric patch was attached. Then, a small-scale finite element model of the portion of the slat with the piezoelectric patch was used to calculate the open circuit voltage generated by the patch. The response of the harvester to random excitation, typical of aeronautic applications, was calculated. The effects of the details of the harvester design on the generated voltage were analyzed and discussed. Full article

This paper investigates the problem of finite-time distributed consensus control for non-triangular stochastic nonlinear multi-agent systems (SNMASs) with input constraints. Fuzzy logical systems are used to identify the unknown nonlinear dynamics of non-triangular SNMASs. A finite-time command filter is utilized to eliminate the issue of “explosion of complexity” in the conventional backstepping-based distributed control algorithm, and a fractional power error compensation mechanism is constructed to improve the distributed control performance of SNMASs. It is proved that the proposed distributed controller enables all of the closed-loop system’s signals to be semi-globally finite-time bounded in probability, and the consensus tracking errors will converge to a sufficiently small neighborhood of the origin in a finite time. Finally, the effectiveness of the presented finite-time distributed control scheme is illustrated with a simulated example. Full article

According to different working environments and functional requirements, radial magnetic bearings (RMBs) have various design methods. Some methods’ lack of effectiveness or accuracy is likely to cause significant differences in the structural performance of magnetic bearings, which will cause serious problems such as limited bearing capacity and complex control. This paper analyzes the structure topology of a magnetic bearing according to the application scenario of RMBs, then proposes a general design example of an 8-pole magnetic bearing based on magnetic circuit analysis and reveals the linearity between electromagnetic force and current as well as air gap through finite element analysis and the influence of magnetic saturation on the load capacity of the magnetic bearing structure. After completing the preliminary design, we further optimize the structure, take the genetic algorithm as an example to iterate the influence coefficient, and summarize and prospect. The design scheme and optimization method proposed in this paper only provide a valuable reference for researchers and factories when devising RMB devices. Full article

This paper presents a new non-contact alternating current impedance instrument (NCACII) with multiple frequencies to measure the electrical impedance during the hydration of cement-based materials. It implements two measurement techniques: the first technique is a frequency conversion measurement with a frequency variation range of 1–100 kHz. The second is to measure the variation in impedance with time. It provides a new way to analyze the pore structure of cement-based materials. In this instrument, we design a current sensor made from nanocrystalline T37. The experimental results demonstrate the detection accuracy of NCACII has been improved and indicates the superiority of nanocrystalline T37. Full article

Shape memory alloys (SMAs) are widely used in aerospace, automobile, and other fields because of their excellent properties, such as large driving force and large deformation. A training method with a bidirectional memory effect is proposed for SMA actuators. The trained SMA units can be heated and cooled to change their shape (shorten and extend). The trained SMA is used as an actuator to drive the deformation of a structure. Due to the obvious hysteresis characteristics of SMA, a temperature-displacement hysteresis model based on the Preisach model is proposed in order to reduce the influence of hysteresis in the process of structural deformation. The F function method (FFM) is used for Preisach numerical implementation, and a PID control method is used for the precise control of structural deformation. Compared with the PID control method without hysteresis model, this method is superior to the PID control method in response speed and control accuracy. The maximum relative error of three target points in the experiment is 5.45%, which is better than the PID control method without this model. The hysteresis model can be applied to the displacement control of a SMA-based actuator. Full article

This paper addresses the displacement path-following problem for a class of disturbed cart-pendulum systems under the fake data injection (FDI) actuator attacks. A filter operator is proposed to estimate the weight vector caused by unknown attacks and disturbances, so that the actuator attacks can be parameterized using neural networks. Then, combined with filter signals and based on adaptive neural network and integral sliding-mode techniques, robust path-following control schemes are proposed to withdraw the impacts of disturbances and FDI attacks. The uniformly ultimately bounded stability results of the closed-loop cart-pendulum system with neural network weight estimations and sliding functions are achieved based on Lyapunov stability theory. Finally, a simulation model of a material robot is used to verify the proposed control strategy. Full article

With technological advances and industrial upgrading, high-performance equipment has put higher demands on the performance of electro-mechanical actuators. With a view to making electro-mechanical actuators more reliable and integrated, firstly, an integrated electro-mechanical actuator module (IEMM) with multiple structural forms was proposed in this paper, and a comparative analysis was performed on the characteristics of different transmission schemes. Then, the feasibility of manufacturing the IEMM’s main bearing components using Carbon Fiber Reinforced Polymer (CFRP) with higher specific stiffness, specific modulus and specific strength was demonstrated by finite element simulation (FEA) software, in a bid to further reduce the weight of the IEMM. Next, a parameter estimation model, a heating power calculation model, and a thermal resistance calculation model were built, so that there is no need to rebuild the whole system model under different demand indexes. On this basis, a multi-objective optimization design model was built with light weight, low power loss, and high level of integration as optimization aims to achieve better comprehensive performance in the early design phase of the IEMM system. However, IEMM’s higher level of integration and its shell made of CFRP with a thermal conductivity of less than 5 W/m°C posed a challenge to the heat dissipation of the motor stator. Therefore, a thermal network model needs to be created in AMESim to evaluate the temperature of IEMM’s parts and components under different working conditions. Finally, the process of IEMM performance optimization design was described and improved, and performance optimization design was conducted by taking one of IEMM’s transmission schemes as an example. Full article

The composite material flywheel rotor of a flywheel energy storage system (FESS) has a low natural frequency. When the system suffers from noise interference, the magnetic bearing generates a force with the same frequency as the natural frequency and causes vibration to occur. Thus, it is necessary to suppress the natural vibration of the magnetic suspended (MS) FESS. The LMS adaptive notch filter is generally adopted for vibration suppression. The vibration suppression performance of the system is different when the insertion position of the notch filter is different. This paper analyzes the influence of the notch filter in different insertion positions of the control system. Through the transfer function from noise to magnetic bearing force, theoretical analysis of the influence of different positions of the notch filter is performed. Corresponding experiments are performed in a 500 kW MS FESS prototype. The theoretical analysis is verified experimentally. Full article

Although exosuits have several advantages compared to exoskeleton type of wearable robots, they have limitations, such as bulkiness and low control performance. This study addresses the design and evaluation of a compact, lightweight, and highly responsive actuator to be used for exosuits, based on the Quasi-Direct Drive (QDD) actuation. The design requirements of the actuator were set based on the actuation system used in the state-of-the-art exosuit from Harvard University (HE) so that it could be an improvement compared to HE. Several design concepts were comparatively evaluated to select the optimal design, and a design for the pulley embedded QDD (PEQDD) actuator was selected. The PEQDD was fabricated using mechanical components selected based on the design constraints or designed through mechanical analysis. Using a dynamometer, the efficiency map of the PEQDD was drawn. The control bandwidth comparison test with the motor originally used for HE showed improved bandwidth from 6.25 Hz to 20 Hz. Preliminary testing was done in walking and running conditions using an exosuit utilizing PEQDD. The test results showed that the actuator performance met all the design requirements. Full article

There are uncertainties and disturbances in the DC-DC buck converters system; in terms of actual working conditions, they are often very complex, exhibiting a polynomial form of time series. Therefore, a single controller and an observer that can only estimate slowly varying disturbances will lose their effectiveness. The generalized proportional integral observer can generally be used to estimate the disturbances in the polynomial form of time series, but it is usually necessary to select a high gain to achieve the fast convergence of the observer, which makes it sensitive to measurement noise. Therefore, before designing the controller that needs to estimate information, it is necessary to design a new structure that combines an observer and a Kalman filter. The filter is used for noise filtering, and the observer is used for the online reconstruction of disturbances. This can solve the above problems. Then, the whole control strategy is designed based on backstepping control. Theoretical analysis and experimental verification can effectively illustrate the feasibility and superiority of this strategy. Full article

An electromagnetic variable valve (EMVV) system can significantly reduce pumping loss and discharge loss of the engine by enabling variable valve timing and variable valve lift. However, the valve seat easily produces a larger impact collision with the engine cylinder head because of fast valve seating velocity, greatly decreasing engine life. Therefore, in this paper, a valve seating buffer (VSB) is designed to solve the problem of large electromagnetic valve seating impact. Firstly, a scheme of an EMVV system with embedded buffer is proposed, the collision model is established to resolve the problem of the soft landing of the valve and the effectiveness of the model is verified by experiment. In addition, the structure, material and dimension parameters of the proposed buffer are designed, and some key parameters of the buffer are optimized by the Nelder–Mead (N–M) algorithm. Finally, a co-simulation model of the actuator and the buffer is built, and the valve seating performance is analyzed. The co-simulation results show that the valve seating velocity and rebound height of the EMVV system with the designed buffer are reduced by 94.8% and 97%, respectively, which verifies the advantages of the designed VSB. Full article

Tensegrity is a structure consisting of rigid bodies and internal tensile members, with no contact between the rigid bodies. The model of an arm with a tensegrity structure is not movable as it is, but we believe that it can be made movable and flexible by incorporating springs. We developed an arm that incorporates springs in the arm’s tensile members by extending the model of an arm with a tensegrity structure. Then, as an evaluation of the developed arm, we measured the ranges of motions and the forces required for that motion. We also developed a mechanism that allows the arm to bend and extend. We believe that this method of making the tensegrity arm controllable by incorporating springs will be useful in the development of flexible robotic arms for caregiving using robots and other applications. Full article

Employing cables with strong flexibility and unidirectional restraints to operate a camera platform leads to stability issues for a camera robot with long-span cables considering the cable mass. Cable tensions, which are the constraints for the camera platform, have a critical influence on the stability of the robot. Consequently, this paper focuses on two special problems of minimum cable tension distributions (MCTDs) within the workspace and the cable tension sensitivity analysis (CTSA) for a camera robot by taking the cable mass into account, which can be used to investigate the stability of the robot. Firstly, three minimum cable tension distribution indices (MCTDIs) were proposed for the camera robot. An important matter is that the three proposed MCTDIs, which represent the weakest constraints for the camera platform, can be employed for investigating the stability of the robot. In addition, a specified minimum cable tension workspace (SMCTW) is introduced, where the minimum cable tension when the camera platform is located at arbitrary position meets the given requirement. Secondly, the CTSA model and cable tension sensitivity analysis index (CTSAI) for the camera robot were proposed with grey relational analysis method, in which the influence mechanism and influence degree of the positions of the camera platform relative to cable tensions was investigated in detail. Lastly, the reasonableness of the presented MCTDIs and the method for the CTSA with applications in the stability analysis of the camera robot were supported by performing some simulation studies. Full article

This study proposes a force plate with a planar spring and an eddy current displacement sensor to measure the ground reaction force (GRF) of a small insect and reveal its motion characteristics. The proposed force plate comprises a circular aluminum plate, four aluminum springs symmetrically connected to the plate, and an eddy current displacement sensor under the plate. The diameter and thickness of the fabricated plate were 8 and 0.1 mm, respectively. The spring width was 0.4 mm. When a force is applied to the plate, the plate moves vertically downward. Then, an eddy current displacement sensor detects the plate displacement without contact. The applied force can be measured using Hooke’s law. The proposed force plate has the advantages of ease of fabrication and cost-effectiveness. The central displacement variation and resonant frequency of the designed springs were evaluated by simulation. Then, we calibrated the fabricated force plate to obtain the sensitivity variation and resonant frequency. The experimental results suggest that the proposed force plate can effectively measure the GRF of a small insect. Full article