Bridge-type Amplification Mechanism Research Articles

Achieving low-frequency and high-speed motion based on bionic seal principle for piezoelectric actuator

In this paper, a novel stepping piezoelectric actuator with a compact structure is proposed, which is based on bionic seal principle. It consists of a bridge-type amplification mechanism (BAM) and a diamond-shaped amplification mechanism (DAM). The control signal adopts the square wave, so that the BAM and the DAM move in coordination, and the mechanism drives the mover without backward motion. Through theoretical analysis and finite element analysis (FEA), the displacement magnification ratio of the structure is calculated, and the size of the structure is preliminarily optimized. Finally, a test prototype is made for experimental verification. According to the experiment, urged by the input signal with the frequency of 2 Hz and the amplitude of 150 V to the BAM and DAM, the maximum speed of forward and reverse are 229.2 μm/s and 212.25 μm/s, respectively. It can reach a resolution of 42.1 nm in forward motion and 204.7 nm in reverse. When the load in the vertical direction reaches 50 N, it can still output a stable displacement motion curve. According to the displacement-time curves and the calculation of the moving speed under different voltages, frequencies, and loads, it is proved that this actuator has good low-frequency and high-speed driving performance.

Modeling and Analysis of a Conical Bridge-Type Displacement Amplification Mechanism Using the Non-Uniform Rational B-Spline Curve.

This paper presents a new analytical model of a conical bridge-type displacement amplification mechanism (DAM) considering the effect of external loads and a piezostack actuator (PSA). With the merits of simple implementation and better fitting, the non-uniform rational B-spline (NURBS) is employed to parameterize conical connecting beams of the DAM, and an analytical model of the displacement amplification ratio and input stiffness is established based on Castigliano's second theorem. After that, considering the interactions with elastic loads and PSA, the actual displacement amplification ratio of the conical DAM is obtained, and the effect of the shape of connecting beams in the performance of the DAM is further analyzed. The proposed analytical model is verified by finite element analysis (FEA), and the results show a maximum error of 6.31% between the calculated value and FEA results, demonstrating the accuracy of the proposed model. A prototype of the conical DAM with optimized shape is fabricated and experimentally tested, which further validates the effectiveness and accuracy of the proposed analytical model. The proposed model offers a new method for analysis and shape optimization of the bridge-type DAM under specific elastic loads.

Design and Development of a Hair-like Sensor with Bridge-Type Flexible Amplification Mechanisms.

Compared with lever-type amplification mechanisms, bridge-type flexible amplification mechanisms have advantages in terms of amplification ratio and structural compactness. Therefore, they can effectively replace the lever-type amplification mechanism in the existing hair-like sensors and realize the development of miniature hair-like sensors with high sensitivity. With that in mind, a highly sensitive hair-like sensor based on a bridge-type amplification mechanism with distributed flexibility is presented to measure the airflow rate. First, the structural composition and operating principle of the hair-like sensor are described. Then, detailed design and analysis of the hair-like sensor are carried out, focusing on the design of the hair post structure, amplification mechanism, and resonator. Furthermore, the designed hair-like sensor is processed and prepared, and some experimental studies are conducted. The experimental results demonstrate that the developed hair-like sensor can measure the airflow rate with high sensitivity up to 8.56 Hz/(m/s)2. This provides a new concept for the structural design of hair-like sensors and expands the application of bridge-type flexible amplification mechanisms in the field of micro/nano sensors.

An Improved Dynamic Model and Matrix Displacement Model for Distributed-Compliance Bridge-Type Amplification Mechanism

This paper establishes a matrix displacement model and an improved dynamic model for the static and dynamic performances analysis for a kind of bridge-type displacement amplification mechanism with distributed-compliance, which has better performances than traditional lumped-compliance bridge-type mechanisms. In the matrix displacement model, the stiffness matrix for two rigid bodies connected by flexures is first obtained by regarding the displacements and the forces on two mass centers of the rigid bodies as the node displacements and node forces. By extending and superimposing each elemental stiffness matrix, the global stiffness matrix for the flexure mechanism can be obtained to calculate the displacement amplification ratio and input stiffness of the bridge-type mechanism. In the improved dynamic model, in order to establish the Lagrangian dynamic model more accurately, the deflectional, axial, and rotational velocities of any point on the beam flexure are calculated by solving the derivatives of the deformation curves of beam flexures versus time to obtain the expression of the kinetic energy in the vibrating beams. On this basis, the three-degree-of-freedom vibration differential equation for the bridge-type mechanism is established by using the Lagrange method, and the natural frequency in the working direction is obtained accurately. The presented models are compared with the finite element analysis, and experiments for two case studies of the bridge-type distributed-compliance mechanism are presented. The comparisons results demonstrate the high prediction accuracy of the improved dynamic model.

A Structure Load Performance Integrated Model Method for the Bridge-Type Displacement Amplification Mechanism

The modeling of compliant bridge-type displacement amplification mechanisms has challenges due to the intrinsic coupling of kinematic and mechanical behaviors. A structure load performance integrated model method for the bridge-type displacement amplification mechanism is presented. The established modeling based on Castigliano’s second theorem considers the deformations of all members, the effect of external load and the nonlinear shear effect. Compared to the finite element model (FEM) and existing models, the established modeling precisely predicts significant nonlinearity of the displacement amplification ratio (DAR) with the driving force, strong sensitivity of DAR to the external load and corresponding relationships of structural parameters with DAR, which is the closest to the FEM result over existing models. The variance-based sensitivities of structural parameters to DAR are thoroughly analyzed, indicating that sensitive structure parameters need to be focused on. Modeling applications further prove the reliability and expandability of the proposed model method. The proposed model method can provide support for the design, optimization and control of compliant systems with bridge-type displacement amplification mechanisms.

Development and assessment of a novel two-degree-of-freedom vibration generator for generating and hiding optical information

Nanostructure-induced optical information is useful in everyday life, such as information communication and display. However, the machining methods of nanostructures still face several challenges, such as low machining efficiency and low surface quality. Therefore, this paper proposes a two-degree-of-freedom vibration generator to solve these issues. Firstly, the mechanical structure of this device is designed based on the compound bridge-type amplification mechanism. Then, the output stiffness, input stiffness, and dynamic features of this device are theoretically modeled. To mathematically establish the relationship between the nanostructure dimension and the optical information, the generation and hiding principles of optical information are next illustrated. Finally, experiments verify the effectiveness of this device. A quick response code that stores the website information is successfully machined on the workpiece. Besides, an optical number “2021” can be hidden by controlling the facet spacings of nanostructures. This developed vibration generator promotes the functional application of nanostructures, which can be used in information storage and protection.

Design and modeling of a piezo-driven three-dimensional bridge-type amplification mechanism with input/output guiding constraint.

Owing to the limited stroke of piezo stacks, compliant amplification mechanisms are widely employed to magnify the displacement of piezoelectric actuators for emerging applications in precision engineering. In this study, a three-dimensional (3D) bridge-type amplification mechanism composed of two serially connected bridge-type amplifiers with a novel constraint form has been developed. The parallel guiding beams mounted at the input and output ends significantly increase the lateral stiffness and minimize parasitic displacements for higher accuracy. Furthermore, a new theoretical model is established to predict the magnification behavior of the 3D amplifier that takes into account the displacement loss caused by the coupling of the two bridge-type amplifiers. The accuracy of this model and the mechanical performance of the developed amplifier are verified by conducting finite element simulations and experimental studies on the manufactured prototypes.

Design, Analysis and Experimental Test of the Bridge-type Displacement Amplification Mechanism Based on the Topology Optimization of Flexure Hinge

Design, Analysis and Experimental Test of the Bridge-type Displacement Amplification Mechanism Based on the Topology Optimization of Flexure Hinge

Fractional order zero phase error tracking control of a novel decoupled 2-DOF compliant micro-positioning stage

This study focuses on a piezo-actuated two-degrees-of-freedom (2-DOF) decoupled compliant micro-positioning stage driven by a novel compound bridge-type amplification mechanism embedded with Scott-Russell mechanism. According to the system identification, the transfer functions of two working directions are obtained. Both of the measured dynamic cross couplings between them are also lower than −40 dB, demonstrating that the single-input-single-output control strategy can be adopted reasonably. Based on the identified frequency response, a fractional order proportional-integral (FOPI) controller is designed for the 2-DOF compliant micro-positioning stage. Compared with the integer order proportional-integral (IOPI) controller using same parameters, the amplitude error of the FOPI controller is 2% lower than that of IOPI controller. Additionally, a fractional order zero phase error controller (FOZPETC) is designed by obtaining the inverse of the fractional order closed-loop system in a large frequency range. And the gain of the corrected control system is 1 in a wide frequency band to eliminate the phase error in the close-loop control system. Finally, using the compound control strategy of FOZPETC+FOPI, a series of trajectory tracking tests are carried out on the proposed novel 2-DOF compliant micro-positioning stage. All the experimental results prove that the designed controller can achieve good positioning and tracking performance of the micro-positioning stage, and confirm the effectiveness of the compound control strategy of FOZPETC+FOPI.

A novel amplification ratio model of a decoupled XY precision positioning stage combined with elastic beam theory and Castigliano's second theorem considering the exact loading force

Abstract A novel mathematical model which can precisely calculate the amplification ratio of a bridge-type amplification mechanism has been proposed. The elastic beam theory and the Castigliano’s second theorem were utilized to establish the mathematical model with consideration of the deformation of input beams, output beam, connecting beams and flexure hinges. The proposed model was compared with existing theoretical models and finite element model (FEM), and the results validated that the proposed model featured a better performances and was the most proximal model to the FEM analysis. With the interval of the adjacent flexible hinges changed, the error at the peak of amplification ratio with the FEM was limited to 6.76%, which was lower than most of the typical existing models. To further verify the effectiveness and expansibility of the proposed method, a decoupled XY precision positioning stage was investigated. Considering the influence of the loading force exerted on amplification mechanism, the displacement amplification ratio model of the positioning stage was established, and the results were further proved through the finite element simulation. The experimental results presented that the amplification ratios for X-direction and Y-direction motions are 5.83 and 5.71, the measured workspace of the stage is 174.9 μm × 171.3 μm, and the cross-coupling error was evaluated to less than 3%.

Design and control of a piezoactuated microfeed mechanism for cell injection

A novel microfeed mechanism for cell injection driven by a piezoelectric actuator (PEA) was developed in this study to fulfill the requirement of a precise cell membrane puncture. A bridge-type displacement amplification mechanism was designed based on a compliant mechanism principle and the micrometric displacement characteristic of the PEA to realize the zero-clearance precision motion of the microfeed mechanism using a flexure hinge as a supporting member. Static and modal analyses and structural optimization specific to the bridge-type amplification mechanism were performed to acquire a high inherent frequency and a large displacement amplification coefficient. A simulation verification of the mechanism’s mechanical performance was implemented. A sliding-mode control strategy was proposed, considering that the complicated nonlinear hysteresis effect of PEA might cause low system precision. Cell puncturing experiments were performed on zebrafish embryos to demonstrate the performance of the proposed methodology. In comparison with existing studies, the manipulation precision of the proposed technique was less than 1.1 μm with a strong robustness. Thus, this new approach could be beneficial for the progress of cell puncture technology.

Design and experiment of a slender nonresonant linear piezoelectric motor based on bridge-type amplification mechanism

A miniature non-resonance type linear piezoelectric motor based on a mechanical bridge-type amplification mechanism has been developed. The slender motor measures 29 mm × 5 mm × 3.5 mm. The stator consists of a parallel bridge amplifier and two multilayer piezoelectric actuators. The working principle of the motor is analyzed, and the physical performance of the bridge amplification mechanism is obtained by a finite element analysis. A prototype of the motor is manufactured, and the model is verified by experiment, and the mechanical properties of the motor characterized. The test results show that when the phase difference between the two driving signals is 90°, the output driving force of the motor reaches its maximum. The motor speed increases linearly from 2.2 mm/s to 7.6 mm/s when the driving frequency ranges from 100 Hz to 1100 Hz under the conditions of peak driving voltage 140 V, bias voltage 70 V and holding force 2.2 N. The motor speed decreases with the increase of load. When the driving frequency is 900 Hz and the holding force is 6 N, the maximum driving force can reach 1.41 N.

Design, Modeling, and Testing of a Novel XY Piezo-Actuated Compliant Micro-Positioning Stage.

A novel decoupled XY compliant micro-positioning stage, based on a bridge-type amplification mechanism and parallelogram mechanisms, is designed in this paper. Analytical models of the bridge-type amplification mechanism and parallelogram mechanisms are developed by Castigliano’s second theorem and a Beam constrained model. The amplification ratio, input stiffness, and output stiffness of the stage are further derived, based on the proposed model. In order to verify the theoretical analysis, the finite element method (FEM) is used for simulation and modal analysis, and the simulation results indicate that the errors of the amplification ratio, input stiffness, and output stiffness of the stage between the proposed model and the FEM results are 2.34%, 3.87%, and 2.66%, respectively. Modal analysis results show that the fundamental natural frequency is 44 Hz, and the maximum error between the theoretical model and the FEM is less than 4%, which further validates the proposed modeling method. Finally, the prototype is fabricated to test the amplification ratio, cross-coupling error, and workspace. The experimental results demonstrate that the stage has a relatively large workspace, of 346.1 μm × 357.2 μm, with corresponding amplification ratios of 5.39 in the X-axis and 5.51 in the Y-axis, while the cross-coupling error is less than 1.5%.

Strain-based multimode integrating sensing for a bridge-type compliant amplifier

This paper presents a compact strain-based multimode sensing approach, in which sensing units are monolithically combined in a compound compliant bridge-type amplification mechanism. Under the same strain gauges configuration, this approach can realize different-mode precision sensing for output displacement, input displacement and input force measurement. Based on elastic beam theory and the modified geometric analysis method, an output/input displacement-sensing model only relating to the moment, and an input force-sensing model only relating to the axial force are analytically derived. These analytic sensing models indicate their good linear sensing performance, which is validated experimentally. The related experiments and analysis indicate that it has excellent heat-insulating performance, and their measurement accuracies can reach the tens of nanometer level for displacement sensing and the sub-Newton level for force sensing in void output loads, which fulfill the requirements of most of the nano-positioning stages.

柔顺桥式位移放大机构的非线性建模与优化

柔顺桥式位移放大机构的非线性建模与优化

Topological design of compliant orthogonal displacement amplification mechanism under the unidirectional input force

The orthogonal displacement amplification mechanism is used to output and amplify the displacement perpendicular to the direction of the input force, and its configuration often uses a typical bridge-type. However, the bridge-type amplifier to achieve orthogonal shift conversion must enter the bidirectional symmetric input forces, otherwise the output will produce parasitic displacement. In view of this problem, the topology optimization method is used to find the new configuration of the displacement amplification mechanism, so that it can still realize the orthogonal displacement transformation under the unidirectional input force condition. Based on the solid isotropic material with penalization (SIMP) topological description method, the ratio of output and input displacements is maximized as the objective function, the ratio of parasitic displacement and output displacement as one of constraint functions, and the topological optimization mathematical model of the compliant orthogonal displacement amplifier is established under the unidirectional input force. The sensitivity information of the objective and constraint functions is deduced by the adjoint matrix method, and the optimization problem is solved by the method of moving asymptotes (MMA). The topology optimization results of orthogonal displacement amplifier are given through numerical examples, and the effect of spring stiffness on the topology optimization result is also discussed. Finally, the parasitic motions of the displacement amplification mechanism obtained from topology optimization and the bridge-type amplification mechanism are compared through the finite element analysis and experiment. Finite element simulation and experiment confirm the correctness and validity of the proposed method.

Modelling and Analysis of Characteristics of a Piezoelectric-Actuated Micro-/Nano Compliant Platform Using Bond Graph Approach.

The piezoelectric-actuated flexure-based compliant platform is commonly adopted in many fields of micro and nanotechnology. In this paper, bond graph modeling, and kinematic and dynamic characteristics of a piezoelectric-actuated micro-/nano compliant platform system are investigated. During modeling, the bond graph model of the piezoelectric actuator (PZT) is derived by considering both the electrical domain and the mechanical domain. Considering the compliances of flexure hinges and elastic linkages, as well as the input ends, the bond graph model for the bridge-type displacement amplification mechanism in the compliant platform is established by combining pseudo-rigid-body (PRB) model theory and elastic beam theory. Based on the interactions between the PZT subsystem and compliant platform subsystem, the kinematic performance of the proposed compliant platform system is evaluated through both computer simulations and experimental tests. Furthermore, the frequency responses, dynamic responses and load capacity of the compliant platform system are studied. This paper explores a new modeling method for a piezoelectric-actuated compliant platform system, which can provide an effective solution when analyzing the micro-/nano system.

Kinetostatic Modeling of Bridge-Type Amplifiers Based on Timoshenko Beam Constraint Model

In this paper, we develop an accurate kinetostatic modeling method for bridge-type amplifiers by incorporating the impacts of nonlinear shear effect, center-shifting and load-stiffening. To account for the nonlinear stress-stiffening and shear effects, a Timoshenko Beam Constraint Model (TBCM) is first investigated to accurately predict the deformations of the short beam flexure hinges popularly employed in the bridge-type amplifiers. Accordingly, a flexible branched chain model is established for bridge-type amplifiers, where the input and output displacements, as well as the displacement amplification ratio and the input stiffness, are derived. The results indicate significant nonlinearities of the amplification ratio and the input stiffness with respect to the driving forces, which are further verified by the finite element analysis (FEA) results. The proposed modeling method can derive a more accurate model of the bridgetype amplification mechanism to capture its kinetostatic behaviors, which can better support the design and control of flexure mechanism based nano-manipulating systems.

Design, analysis and validation of the bridge-type displacement amplification mechanism with circular-axis leaf-type flexure hinges for micro-grasping system

For stable and flexible manipulation, realizing parallel grasping and large output stroke simultaneously has become a key issue in the researches on micro-grasping system. The typical solution is to use compliant orthogonal displacement amplification mechanism (such as bridge-type mechanism), in which the flexure hinges are generally axial load-dominated, whereas the deflection of traditional straight-axis flexure hinges is not related to the axial load under small deflection assumption. In this study, a bridge-type mechanism with circular-axis leaf-type (CALT) flexure hinges is designed, analyzed and validated. Through modeling the generalized displacements of CALT flexure hinge, the positive direction of its axis in the bridge-type mechanism is designed. The precise models of load relations for the CALT flexure hinges in the bridge-type DAM are established, and the multi-objective parametric optimization is further given. Small deflection-based static FEA results verify the generalized displacements’ models of CALT flexure hinge as well as the parametric optimization result. Compared with the corresponding bridge-type mechanism with the largest output displacement in the traditional researches, the output displacement of optimal result is improved effectively. For the design validation, the optimal design result is further applied to construct a piezoelectric-driven microgripper, which grasps parallelly and enlarges the output stroke simultaneously.

Amplification ratio analysis of a bridge-type mechanical amplification mechanism based on a fully compliant model

This study proposes a new mathematical model for the amplification ratio of a single-stair bridge-type amplification mechanism. To overcome the limitations of previous models, all members of the amplification mechanism are assumed to be compliant. The proposed model is compared to conventional models as well as analysis results using finite element models, after which the effects of the dimensions of each member are investigated. In addition, design optimization is carried out. Finally, the usefulness of this mathematical model is verified by an experiment using the optimally designed mechanism. As a result, the proposed mathematical model very aptly describes the displacement amplification ratio of the single-stair bridge-type amplification mechanism.