Displacement Amplification Ratio Research Articles

A hybrid summation and multiplication displacement amplification mechanism for piezoelectric actuators

Abstract This paper reports a novel amplified piezoelectric actuator featuring compliant displacement amplification mechanism of hybrid summation and multiplication. The hybrid amplification mechanism uses the concept of nesting a pair of Scott-Russell linkages into a toggle linkage to realize the hybrid amplification functions of summation and multiplication. Also, compliant amplification mechanisms with double output ports are designed, enhancing the flexibility of designs and applications. The hybrid displacement amplification principle is mathematically explained in detail. It is demonstrated based on finite element simulations that the displacement amplification ratio, output stiffness and resonance frequency of the proposed hybrid amplification mechanism of summation and multiplication outperform those of the classic rhombus-type and bridge-type compliant mechanisms. The experimental testing results of a prototype show that the amplified piezoelectric actuator is capable of providing 315 μm strokes with the displacement amplification ratio of 16.2. The fundamental resonance frequency with piezoelectric stacks mounted is 1218 Hz. Comparison to typical designs in literature shows well comprehensive performances of statics and dynamics, verifying the advantages of such a hybrid amplification mechanism of summation and multiplication.

Development and Testing of a Dual-Driven Piezoelectric Microgripper with High Amplification Ratio for Cell Micromanipulation

Cell micromanipulation is an important technique in the field of biomedical engineering. Microgrippers play a crucial role in connecting macroscopic and microscopic objects in micromanipulation systems. However, since the operated biological cells are deformable, vulnerable, and typically distributed in sizes ranging from micrometers to millimeters, it poses a huge challenge to microgripper performance. To solve this problem, this paper develops a dual-driven piezoelectric microgripper with a high displacement amplification ratio, large stroke, and parallel gripping. By adopting modular configuration, three kinds of flexure-based mechanisms, including the lever mechanism, Scott–Russell mechanism, and parallelogram mechanism are connected in series to realize three-stage amplification, which effectively makes up for the shortage of small output displacement of the piezoelectric actuator. At the same time, the use of the parallelogram mechanism also isolates the parasitic rotation movement, and realizes the parallel movement of the gripping jaws. In addition, the kinematics, statics, and dynamics models of the microgripper are established by using the pseudo-rigid body and Lagrange methods, and the key geometric parameters are also optimized. Finite element simulation and experimental tests verify the effectiveness of the developed microgripper. The results show that the developed microgripper allows an amplification ratio of 46.4, a clamping stroke of 2180 μm, and a natural frequency of 203.1 Hz. Based on the developed microgripper, the nondestructive micromanipulation of zebrafish embryos is successfully realized.

Compliance analysis of transversely asymmetric flexure hinges for use in a piezoelectric Scott-Russell microgripper

Notch flexure hinges with longitudinal/transverse asymmetries can be widely found in compliant mechanisms to balance the performance trade-offs. However, the transverse asymmetry often leads to difficult analyses of kinetostatics and dynamics. In this paper, a miniaturized piezoelectric gripper featuring reversed Scott-Russell compliant amplifier with transversely asymmetric single-notched flexure hinges is designed for use in confined spaces. The compliance and vibration characteristics of the transversely asymmetric single-notched flexure hinges are quantitatively analyzed by a new transfer matrix method. The proposed theoretical methodology involves discretizing the transversely asymmetric flexure hinge into a series of constant beam segments with non-coaxial nodes, which enables a straightforward modeling process and hence simplifies the kinetostatic and dynamic analyses of compliant mechanisms comprised of complex flexure hinges. Comparative validations with respect to the finite element simulation and experiments confirm the advantages of easy operation and small-scale equation sets of the proposed modeling method. As to the designed piezoelectric microgripper with single-notched flexure hinges, the jaw displacement amplification ratio of 20 and resonance frequency of 1250 Hz has been experimentally tested with a small size of 38 mm × 15 mm × 7 mm.

Geometrically nonlinear design of a rhombus-nested compliant amplification mechanism for use in precision actuators and sensors

A rhombus-nested compliant amplification mechanism is proposed for versatile usages of precision actuators and force sensors with an easy tuning of stiffness. Such a monolithically planar rhombus-nested compliant mechanism has the dual functions of two-stage displacement or force amplification by changing the input and output ports. It features a large ratio of inter-stage stiffness, thus resulting in an enhanced amplification ratio, load capacity and dynamic bandwidth. The geometrically nonlinear analytical equations of displacement amplification ratio and input stiffness are derived in the presence of pronounced axially-loaded stiffening and kinematic-arching effects based on the beam constraint model. It allows an insightful evaluation of geometrically nonlinear deformation behaviors sensitive to structural dimensions in a parametric way. Insights into geometrically nonlinear behaviors in the case of large-stroke and axially-loaded motions are discussed as well. A proof-of-concept prototype with embedded piezoelectric stacks is fabricated with the dimensions of 74mm × 60mm × 10 mm. The dual functions of precision actuator with amplified motion strokes and force sensor with enhanced sensitivity are experimentally demonstrated.

Design, computational analysis and experimental study of a high amplification piezoelectric actuated microgripper

Increasing applications of compliant microgripper demands flexibility in working with a wide range of micro-objects which requires a large workspace, high precision motion, low parasitic motion, and satisfactory bandwidth control. To meet the requirement of pick and place manipulation tasks, a high amplification piezoelectric actuated microgripper is proposed and investigated in this paper. The high amplification of the microgripper is achieved using a compound amplifier. The compound amplifier is assisted to magnify the embedded piezoelectric actuator’s displacement. Two cascaded lever-type mechanisms are symmetrically connected with a bridge-type mechanism and form a three-stage amplification mechanism-based compound amplifier. Further, the four-bar parallelogram mechanisms are integrated with the third-stage displacement amplification mechanisms to linearize the output motion of the microgripper jaws. The characteristics of the microgripper were evaluated by computational analysis and validated using experimental investigations. Further, the design parameters are identified from the geometrical model of the individual displacement transmission mechanisms to perform a response surface optimization on the configured mechanism by the computational method. The design optimization of the microgripper resulted in a high displacement amplification ratio with a large workspace. The experimental investigations show that the designed microgripper is capable of achieving a high displacement amplification ratio of 34.5 and a total output displacement of 529.4 μm. Further, the characteristics of the microgripper such as motion resolution, and parasitic motion indicate that it will be able to perform high-precision micro-object grasping/releasing tasks.

Development of Modified Rhombus Amplifier of Positioning Stage Compliant Mechanisms

Abstract This paper presents a modified design of rhombus-type amplifier used in positioning stage compliant mechanism. The new rhombus design is introduced to enhance the performance of rhombus and the results are promising. The new approach of rhombus amplifier is based on mixing the concept of rhombus type with the idea of hinges (reduced section portions) existed in bridge type. The performance of the proposed design is investigated by the pseudo rigid body model and validated by the finite element analysis. The new rhombus design improves displacement amplification ratio by (22.3%) with slightly change in master mode natural frequency (1.3%). The pseudo rigid body model for new rhombus design is consistent with the ANSYS results, and hence can be used in modelling and analysis of the new rhombus design.

Analysis and Optimization of a Novel Compact Compliant 2-DOF Positioner for Positioning to Assess Bio-Specimen Characteristics

A novel compact 2-DOF compliant positioner is developed for the purpose of achieving good characteristics such as high natural frequency, high displacement amplification ratio, good linear motion, and compact structure based on its symmetrical structure. To be specific, the developed stage is proposed according to an advanced six-lever displacement amplifier arranged at an inclination angle of the rigid bar utilizing right circular hinges and a parallel guiding mechanism with integrated flexure leaf hinges to attain the above-mentioned characteristics and reduce the decoupling mobility error. First, to quickly assess the initial quality response, an integration method of kinetostatic analysis, the Lagrange method, and finite element analysis was applied to evaluate and verify the quality characteristic of the stage. The experimental result showed that the error between the analytical method and the FEA method was 1.3%, which was relatively small and reliable for quickly assessing the primary quality response of the proposed positioner. Next, to boost the important output characteristics of the developed positioner, the integration approach of the response surface method and NSGA-II algorithm was utilized to find the optimal design variables. Finally, a prototype was manufactured based on the CNC milling method to validate the experimental and FEA analysis results. The attained results show that the optimal results of safety factor and output displacement were 2.4025 and 248.9 µm. Moreover, the FEA verification results were 2.4989 and 242.16 µm, with errors for safety factor and output displacement between the optimal result and the FEA result of 3.86% and 2.78%, respectively. In addition, the simulation and experimental results of the first natural frequency were 371.83 Hz and 329.59 Hz, respectively, and the error between the FEA result and experimental result for the first natural frequency was 11.36%. Furthermore, the achieved results show that the relationship between input displacement and output displacement of the experimental result and the FEA result of the developed structure achieved a good linear connection. These results suggest that the proposed positioner will be a potential structure employed in precise positioning systems and nanoindentation testing positioning systems for checking bio-specimens’ behaviors.

Design, analysis, and experimental investigations of an asymmetrical under-actuated micro-gripper

In this paper, we present a new asymmetrical under-actuated micro-gripper which can perform twisting and gripping operation to the target simultaneously actuated by a single piezoelectric actuator. Two improved hybrid amplification mechanisms were designed integrated with three different flexure hinges to enhance dynamic performances. Kinematics and dynamics models of the micro-gripper including input stiffness, displacement amplification ratio, and natural frequency based on pseudo-rigid-body method and Lagrange’s equations were derived. Proposed models were evaluated by finite element simulation studies. Experimental results shown that our designed micro-gripper possesses good performance in terms of clamping reliability and dynamic response.

Design and analysis of a microgripper for trans-scale clamping based on a compliant multistable mechanism.

Piezoelectric actuators commonly used in microgrippers have a small stroke, and their accuracy is reduced by the transmission amplification unit, which leads to a contradiction between the clamping range and the clamping accuracy in existing piezoelectric-actuated microgrippers. This paper proposes a design scheme to divide the total clamping range of the microgripper into segments based on the compliant multistable mechanism (CMM). First, by using the stable equilibrium positions of the CMM, the total clamping range of the microgripper is divided into multiple smaller clamping sub-intervals to accommodate objects of different scales. Then, the theoretical models of the displacement amplification ratio of the microgripper amplification mechanism and the stiffness of the microgripper in different clamping sub-intervals are established, and the force-displacement characteristics of the CMM are analyzed. Next, through finite element simulation, the correctness of the theoretical analyses is verified, and it is shown that objects between 0 µm and 1.650mm can be clamped using four clamping sub-intervals under a five times displacement amplification ratio. Finally, a microgripper of the CMM consisting of two three-segment fully compliant bistable mechanisms connected in series is designed and machined, and microgripper segmented clamping experiments are conducted. The experimental results demonstrate the feasibility of the design scheme proposed in this paper.

Design of a Piezoelectric-Driven Microgripper With Three Working Modes

This article presents the conceptual design of a novel reconfigurable piezoelectric-driven microgripper to obtain both excellent static and dynamic performance for complex micromanipulation. For the first time, a flexure-based compliant microgripper is designed to realize three working modes. The analytical model of the microgripper is established based on the beam deformation theory and pseudo-rigid-body modeling approach. The multiobjective optimization is performed based on the response surface methodology to determine the structural parameters of the microgripper. A finite-element model-based simulation study is implemented to evaluate the gripper's static and dynamic performance. Moreover, a prototype of the microgripper has been fabricated for experimental testing. The results reveal that the microgripper obtains a large displacement amplification ratio of 55.17 in mode I, a high natural frequency of 838.09 Hz in mode II, and a balanced performance in mode III. The micromanipulation capability of the microgripper has been demonstrated by executing gripping–holding–releasing operations of various tiny objects.

Rigid-Compliant Hybrid Cellular Expansion Mechanisms With Motion Amplification and Superposition

Abstract Motivated by heat dissipation, the rigid-compliant hybrid cellular expansion mechanisms with motion amplification and superposition are proposed in this paper. Compared with existing studies, the expansion mechanism is not only easy to realize the plane tessellation via cellular design due to its regular polygon structure but also has the ability of motion amplification and superposition due to its compliant displacement amplifier and rigid scissors. First, the scheme of expansion mechanisms, especially the working principle of motion amplification and superposition, is introduced. The configuration design of a family of expansion mechanisms is presented, including varying number of edges, concave/convex property, and inner/outer layout. Second, the constraint condition and analytical modeling of relations between output performances of expansion mechanisms and dimensional parameters are carried out. Third, the displacement amplification ratio of expansion mechanisms and output performances of several typical expansion mechanisms when they act as cells to tessellate a plane with a constrained area are analyzed. Finally, the output performances of expansion mechanisms are verified via the finite element analysis. The results show that proposed cellular expansion mechanisms are beneficial for realizing plane tessellation and offer motion amplification and superposition, which provide prospects in the field of mechanism design such as metamaterials.

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.

Emerging Technologies in Displacement Amplification of Lever and Bridge-Type Compliant Mechanism: A Review Article

This review article provides a survey of emerging technologies in displacement amplification of lever-type and bridge-type compliant mechanisms. The displacement amplification is possible with a compliant mechanism. The compliant mechanism is beneficial and efficient because of simplicity in the design and where there is accuracy, compactness, and precision is needed. We can use various categories of displacement amplification of the compliant mechanism depending upon the application. In recent years, displacement amplification of compliant mechanisms gain more attention to the researchers due to the superiority of the mechanical compliant mechanism is compared with a rigid-body mechanism. Displacement amplification compliant mechanism such as bridge types, lever type, a micro-Leverage Mechanism has briefly discussed. The performance parameters such as the principle of working, types of displacement compliant mechanism, fabrication process, operating frequency and displacement amplification ratio are found out

Accounting for hysteretic characteristics in P‐delta analysis of structures

AbstractStudies in the literature have shown that P‐delta () effects are highly influenced by the hysteretic characteristics of a structural system. However, international buildings and bridge codes prescribe ‐induced amplification factors, limits for negligible effects and limits for dynamic instability that neglect this influence. As a result, different margins of safety against actions are currently specified for different structural systems, with steel structures, for example, presenting reduced margins of safety with respect to concrete structures. Adopting a sub‐set of the PEER earthquake record database composed of 1964 earthquake records, this paper presents a statistical analysis of displacement amplification ratios for systems with different hysteretic models, fundamental periods and ductility levels. In terms of both elastic and inelastic stability coefficients, limit values of the stability coefficient for negligible effects and dynamic instability are proposed for the most common structural typologies, such as steel, well and poorly detailed reinforced concrete, and self‐centering structures. Analytical estimates of the median, 84th and 98th percentile values of the displacement amplification that take into account the combined effect of stability coefficient, ductility level and hysteretic properties are proposed.

Analysis and Optimization of Dynamic and Static Characteristics of the Compliant-Amplifying Mechanisms.

Compliant amplifying mechanisms are used widely in high-precision instruments driven by piezoelectric actuators, and the dynamic and static characteristics of these mechanisms are closely related to instrument performance. Although the majority of existing research has focused on analysis of their static characteristics, the dynamic characteristics of the mechanisms affect their response speeds directly. Therefore, this paper proposes a comprehensive theoretical model of compliant-amplifying mechanisms based on the multi-body system transfer matrix method to analyze the dynamic and static characteristics of these mechanisms. The effects of the main amplifying mechanism parameters on the displacement amplification ratio and the resonance frequency are analyzed comprehensively using the control variable method. An iterative optimization algorithm is also used to obtain specific parameters that meet the design requirements. Finally, simulation analyses and experimental verification tests are performed. The results indicate the feasibility of using the proposed theoretical compliant-amplifying mechanism model to describe the mechanism's dynamic and static characteristics, which represents a significant contribution to the design and optimization of compliant-amplifying mechanisms.

Design and test a pneumatically actuated microgripper based on structural stiffness.

In response to the problem that the actual amplification ratio of the compliant motion amplification mechanism cannot be further improved, this paper introduces a two-stage amplification microgripper based on structural stiffness that is driven by pneumatics. The mechanism not only has the advantages of good symmetry, compact structure, and large output displacement but can also reduce the relative error of the theoretical and experimental amplification ratios. The first-stage mechanism selects high-stiffness mechanisms and high-stiffness flexure hinges, and the second-stage mechanism uses low-stiffness mechanisms and low-stiffness flexure hinges. The arrangement order of the mechanism is determined by the working mode analysis. The specific dimensions of the mechanism and flexure hinges are determined through structural size optimization so that the amplification performance of the mechanism will be optimal. The experimental results show that the displacement amplification ratio of both the opening and closing of the microgripper is 41.8.

Reliability-Based Multi-Objective Optimization Design of a Compliant Feed Drive Mechanism for Micromachining

In precision engineering, the use of compliant mechanisms (CMs) in positioning devices has recently bloomed. However, during the course of their development, beginning from conceptual design through to the finished instrument based on a regular optimization process, many obstacles still need to be overcome, since the optimal solutions often lie on constrained boundaries or at the margin of safe/unsafe domains. Accordingly, if uncertainty occurs during the fabrication or operation of the mechanism, it might lose its functions, rendering the design infeasible. This paper proposes a universal design process for positioning CMs, consisting of two steps: optimal design of the pseudo-rigid-body model, and reliability-integrated multi-objective optimization design using NSGA-II algorithms. This optimization algorithm is applied in the design of a feed drive mechanism for micromachining. The optimal design is also fabricated and tested. The results calculated for the displacement amplification ratio, natural frequency, and input/output stiffness using different approaches, including analytical methods, simulations, and experiments, were compared to evaluate the efficiency of the proposed synthesis method, and show discrepancies of less than 5%. Thus, the results convincingly support the applicability of the proposed optimization algorithm for the design of other precision-positioning CMs prone to failure in vulnerable conditions.

Design of an over-constraint based nearly-constant amplification ratio compliant mechanism

A constant displacement amplification ratio is less investigated in compliant mechanisms. This study addresses this need by presenting an over-constraint based nearly-constant amplification ratio compliant mechanism (OCARCM) that alleviates the change in displacement amplification ratio. The free-body diagram (FBD) combined with the generic beam constraint model (BCM) method is employed to obtain the closed-form solutions that accurately and insightfully elaborate the nonlinear kinetostatic characteristics of the OCARCM. Comparative analysis is provided between the proposed OCARCM and the widely-used bridge-type compliant amplifier in terms of the ability to remain a constant amplification ratio, with and without external payloads. The closed-form models are verified by the nonlinear finite element results (FEA) with a maximum difference of 1%. In our case studies, it shows that the amplification ratio of the OCARCM changes by 1% over the range, while that of the bridge-type amplifier changes by approximately 14% under the same conditions. The results also reveal that a higher amplification ratio results in a greater variation in the ratio. An experiment based on the CNC machined aluminium alloy prototype with distributed-compliance is conducted, and experimental results show a maximum error of 3.4% for the amplification ratio compared with the analytical or FEA results.

Graphic Transfer Matrix Method for Kinetostatic and Dynamic Analyses of Compliant Mechanisms

Abstract Kinetostatic and dynamic analyses of compliant mechanisms with complex configurations continue to be an attractive issue for obtaining a process-concise and result-accurate solution. In this paper, the transfer matrix method (TMM) is improved for a unified linear kinetostatics and dynamic modeling of compliant mechanisms with complex serial-parallel configurations in an oriented graphic way. In detail, the transfer matrices of typical building blocks commonly used in compliant mechanisms are summarized and derived. Then, a graphic transfer matrix modeling procedure capturing both the kinetostatics and dynamics of general compliant mechanisms is introduced. The displacement amplification ratio, input/output stiffness, parasitic error, natural frequencies, and frequency response of a typical compliant microgripper and a planar parallel three-degrees-of-freedom (3DOF) nanopositioner are calculated with such a graphic transfer matrix method. The advantages of the proposed modeling method lie in its convenience and uniformity in formulating both the kinetostatic and dynamic behaviors of a class of compliant mechanisms with distributed and lumped compliances in a transfer matrix manner, which has minimal DOF and is easily programmed.

Design and feedforward control of a two-degree-of-freedom positioning stage with bidirectional piezoelectric drive

The positioning stage composed of piezoelectric stacks and flexible mechanisms is highly competitive in the field of micro/nanomanipulation. Driving stroke and positioning accuracy are the two most important factors to evaluate the positioning stage. However, the attenuation of the driving stroke caused by the stiffness load of the flexible mechanism is an important but neglected problem. On the other hand, the hysteresis of piezoelectric ceramics directly affects the positioning accuracy of the platform. In this study, a two-degrees-of-freedom positioning stage with low displacement attenuation and hysteresis is proposed. Static and dynamic models of the positioning stage were established to derive analytical models of the displacement amplification ratio, structural stiffness, and natural frequency. The displacement transfer coefficient was introduced to establish an equivalent physical model for structural stiffness and displacement attenuation. Genetic algorithms were used to optimize the structural parameters. Finite element analysis is performed to verify the accuracy of the analytical model. The hysteresis is suppressed by the combination of bidirectional piezoelectric driving and inverse Bouc-Wen model feedforward compensation. The measurement results indicated that the proposed positioning stage had a displacement transfer coefficient of 0.82, which was 95.89% lower than the hysteresis of the piezoelectric stack.