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Compliant amplification mechanisms based on the triangular principle have attracted considerable applications in precision and other engineering fields due to their compactness and efficient amplification capacity. However, a fast engineering design for geometric nonlinearity of large strokes is still much challenging. We report herein a series of analytical equations of nonlinear amplification ratio, input and output stiffness for three commonly-used triangular-amplified compliant mechanisms, namely the rhombus, diamond and bridge types. The pronounced geometric nonlinearities of axially-loaded stiffening and kinematics-arching effects are explicitly formulated. The proposed nonlinear formulas can be directly degenerated as the linear models by vanishing the nonlinear terms, which enables a comprehensive analysis of linear and nonlinear kinetostatics, and hence offers a straightforward way for the fast performance evaluation and size synthesis/optimization. This relieves an engineer's experience and knowledge for an ab initio modeling process. The prediction error is discussed and some insights into the linear and nonlinear characteristics of the three commonly-used triangular-amplified compliant mechanisms are outlined that confirms the advantage of analytical equations bringing to a fast engineering analysis and design. • Analytical kinetostatic model for rhombus, diamond and bridge-type compliant mechanisms. • Linear and nonlinear displacement amplifying ratio, input and output stiffness are modeled. • Some insights into the linear and nonlinear characteristics are discussed and outlined. [ABSTRACT FROM AUTHOR]

Mechanically amplified piezoelectric actuators (APAs) can be found in many scenarios of precision engineering and instrumental devices. However, the electro-mechanical design of curvilinear APAs is difficult due to the existence of curved flexure beams and multi-domain electro-elasto dynamics. In this paper, the electro-mechanical behavior of elliptical APAs is studied by exploiting a novel electro-mechanical transfer matrix method. The motivation is to facilitate both the static and dynamic analyses of such a complex APA with curvilinear flexure beams by considering the multi-domain dynamics of piezoelectric stacks and compliant mechanisms from an electro-mechanical viewpoint. To this end, an analytical electro-elasto transfer matrix of piezoelectric stacks operating at the d 33 mode is derived in the form of Taylor's series based on Timoshenko beam theory. The dynamic response spectrum of displacement and impedance for elliptical APAs are insightfully captured by such an electro-mechanical model. Different topologies of elliptical APAs are also compared and the optimal configuration is suggested. At last, a proof-of-concept prototype is fabricated and tested with a special focus on experimental evaluation of the electro-mechanical coupling model. [Display omitted] • A new electro-elasto transfer matrix of piezoelectric stacks is derived. • Electro-mechanical analysis of elliptic-amplified piezoelectric actuators is realized. • Kinetostatics and dynamics of amplified piezoelectric actuators are involved. • Different topologies of elliptic-amplified piezoelectric actuators are compared. [ABSTRACT FROM AUTHOR]

Compliance and precision are two key aspects in designing flexure hinges for use in compliant mechanisms. A generalized method with the finite-discrete idea and beam transfer matrix is developed for quickly predicting the kinetostatic behaviors of single and multiple-axis notch flexure hinges. The transfer matrix of Timoshenko beams explicitly including the shear deformation effect is derived in a concise form of Taylor series expansion. The compliance and rotational precision matrices of general notch flexure hinges are then derived targeting for arbitrary cutout profiles with a step-by-step modeling procedure. It is easy to operate for comparing and synthesizing different flexure hinges within a unified modeling framework. All a designer has to do is to prepare the concerned profile function without being caught into the laborious and even unsolvable derivation of mechanics. Several groups of single and multiple-axis notch flexure hinges are adopted to verify the feasibility of the presented approach by comparing with the numerical and experimental results available in literature. The comparative results indicate the high prediction accuracy and easy operation of the proposed approach for a wide applicability of complex notch flexure hinges. [Display omitted] • Compliance and precision modeling of general notch flexure hinges are studied. • The analytical transfer matrix of spatial Timoshenko beams is derived. • A step-by-step modeling procedure without laborious formulas is provided. • Single-axis and hybrid multi-axis notch flexure hinges are used as a verification. [ABSTRACT FROM AUTHOR]

Recent years have witnessed an ever-increasing research interest in experience-driven and topology-optimization design of flexure hinges for use in compliant mechanisms. In this paper, we report the bionic design of a new notch flexure hinge with adjustable curvatures inspired by the biconcave disk morphology of red blood cells. The biconcave shape maintains red blood cells excellent deformability and surface properties that motivates the bio-inspired design by learning from nature. By imitating the biconcave shape of red blood cells using the quartic Bézier curve, the contour of a cluster of bio-inspired flexure hinges in the presence of positive and negative curvatures can be parametrically adjusted. The closed-form equations of compliance, precision and the maximum stress of the bio-inspired flexure hinge are derived based on Castigliano's second theorem and Timoshenko beam theory. Comparative studies verify the well precision and low stress of such a new flexure hinge. At last, an amplified piezoelectric actuator is designed with the bio-inspired flexure hinge as an application case. Also interestingly, adjustable curvatures of the presented bio-inspired flexure hinge make the simultaneous shape and parameter optimization effective. [Display omitted] • The bionic design of a new notch flexure hinge inspired by red blood cells is reported. • The shape is adjustable in the presence of positive and negative curvatures. • The quartic Bézier curve is introduced to imitate the cutout profiles. • An amplified piezoelectric actuator is designed with the RBC-inspired flexure hinge. [ABSTRACT FROM AUTHOR]

• Two beam-discrete strategies discretizing the curved beam into a sequence of constant beams. • Unified transfer matrix of constant uniform beam for any curved beams. • Streamlining modeling procedure for asymmetrically nonuniform and curved beams. Nonuniform and curved beams can be found in extensive engineering scenarios, ranging from big-scale structures of buildings, bridges to small mechanical systems of aerofoils, blades, micromachines, robotics and sensors. However, variable curvature and transverse asymmetry often lead to a complicated dynamic modeling. In this paper, two beam-discrete strategies are comparatively presented for the free vibration analysis of transversely asymmetric and curved beams and even their combinations. The proposed methodology involves discretizing a general nonuniform and curved beams into a sequence of constant beam segments with non-coaxial nodes or inclination angles, which enables a modular transfer matrix modeling process and hence offers a new way to divide the complex modeling into easier steps. A unified transfer matrix is derived for constant beam elements with non-coaxial nodes and inclination angles accounting for the shear deformation, rotary inertia and axial load in any combinations. The proposed beam-discrete strategies with a unified transfer matrix provide a new perspective in contrast to previous investigations. The advantages of easy programming and small degrees of freedom in the traditional transfer matrix method is extended to transversely asymmetric nonuniform and curved beams. Comparative validation with several engineering beams confirms these advantages. [Display omitted] [ABSTRACT FROM AUTHOR]

Mechanically amplifying micro-stroke of actuators such as piezoelectric stacks through compliant mechanisms is an effective solution for use in micro/nano manipulation, precision positioning, gripping and manufacturing with large enough workspaces. This paper proposes a novel type of hybrid three-stage compliant displacement amplifier with a compact structure by synthesizing bridge-type and lever-type compliant mechanisms. A new index is introduced to measure its displacement amplification efficiency by considering the whole size and input stiffness. To facilitate design, the dynamic stiffness model is also derived to capture its kinetostatics and dynamics on both time and frequency domain. Then, the key structural parameters are efficiently optimized with the Pareto multi-objective optimization strategy. The capacity curve in terms of the resonance frequency, displacement amplification ratio and load capacity (output stiffness) is provided as well in a form of the Pareto optimal solution set. Experimental tests of two prototypes indicate a high displacement amplification efficiency of the current design, of which one prototype exhibits the output displacement of 0.7 mm and the resonance frequency of 874 Hz with a compact size of only 57 mm × 50 mm × 10 mm. [Display omitted] • A new displacement amplification mechanism with compactness is designed. • A new index is proposed to measure the displacement amplification efficiency. • Bridge-type and lever-type compliant mechanisms are synthesized. • A dynamic stiffness model is derived to capture its kinetostatics and dynamics. • The output stroke of 0.7 mm and resonance frequency of 874 Hz is realized. [ABSTRACT FROM AUTHOR]

• Unifying six beam theories into a single equation. • Unified dynamic stiffness matrix and transfer matrix. • Frequency-dependent mass and stiffness matrices. • Thorough comparison and scope of different beam theories for curved beams. High-precision, efficient and streamlined methods for the dynamic modeling and analyzing of engineering structures have consistently captured attention of designers and researchers. This paper addressed this increasing demand by presenting a generalized modeling and analyzing method. Specially, a unified model was proposed to integrate six beam theories into a single formula. Upon this model, a unified dynamic stiffness matrix was derived, serving as an elemental building block for formulating the transfer matrix, frequency-dependent mass and stiffness matrices as well as further integrating finite element method, dynamic stiffness matrix method and transfer matrix method. Through this transition, challenges associated with transcendental eigenvalue in dynamic stiffness matrix method and transfer matrix method was effectively resolved and the advantages of transfer matrix method in handling complex structure were maximized. Given the widespread utilization of curved beams in buildings, bridges, robotics and sensors, the proposed method was validated through comparative analysis with other methods, focusing on both curved and straight beams. Furthermore, this study delineated applicability scopes of different beam theories and provided the strategic approach for curved and straight beams. The feasibility of this strategy was demonstrated through an investigation involving a corrugated structure comprising both straight and curved beams. [ABSTRACT FROM AUTHOR]

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. [Display omitted] • A monolithically rhombus-nested compliant amplification mechanism is designed. • Geometrically nonlinear analytical model of amplification ratio is derived. • The dual functions of a precision actuator and force sensor are demonstrated. [ABSTRACT FROM AUTHOR]

• A DBCM is proposed for geometrically nonlinear analysis of compliant mechanisms. • The nonlinearities of load-stiffening and kinematics-arching effects are considered. • The nonlinear kinetostatics and large-amplitude vibration analyses are achieved. • The nonlinear amplitude-dependent resonance frequency is revealed. Compliant mechanisms with intermediate-deformation ranges are increasingly applied in large-stroke precision manipulators and other actuators. The nonlinearities of axially-loaded stiffening and kinematics-arching effects (P-Δ effects) have a pronounced influence on the kinetostatic and dynamic behaviors of such a class of compliant mechanisms. A dynamic beam constraint model (DBCM) with the pseudo-static characteristic is reported for the nonlinear kinetostatics and large-amplitude vibration analyses of intermediate-deformation compliant mechanisms. Firstly, the DBCM of flexure beams is derived in a closed-form equation on the frequency domain, including the P-Δ effects. A matrix-based modeling methodology with a step-by-step iteration procedure is then introduced to calculate the nonlinear performance of general planar compliant mechanisms with serial-parallel configurations avoiding inner force analysis and kinematics calculation. Except for the static constraint behaviors in the BCM, the amplitude-dependent resonance frequency is captured with the DBCM. Theoretical, numerical and experimental comparisons for a double parallel guiding flexure pivot and Scott-Russell compliant amplifying mechanism verify the feasibility of the DBCM. In summary, the DBCM enables both the nonlinear kinetostatics and large-amplitude vibration analyses of moderately large-stroke compliant mechanisms in a straightforward way. [ABSTRACT FROM AUTHOR]

Serial-parallel configurations are widely designed in compliant mechanisms. In this paper, the transfer matrix method is combined with D'Alembert's principle to develop a two-port dynamic stiffness model for analyzing the kinetostatics and dynamics of complex compliant mechanisms with serial-parallel configurations. In detail, two kinds of improved transfer matrices for parallel sub-chains are derived in a unified form by summarizing the common serial-parallel substructures in compliant mechanisms. Then, a two-port dynamic stiffness model describing the frequency-dependent input and output force-displacement relationship of compliant mechanisms is established. Based on the two-port dynamic stiffness model, procedures for solving the static and dynamic performances of compliant mechanisms are presented. The proposed approach is demonstrated by calculating the displacement amplification ratio, input/output stiffness, natural frequencies and forced dynamic response of two typical precision flexure manipulators. The advantage of the proposed approach lies in its capability to describe the simultaneous kinetostatics and dynamics for a large class of serial-parallel configurations with very few degrees of freedom (DOFs), differing from the previous Lagrange-based dynamic modeling methods in the context of compliant mechanisms and should be of interest to designers. • A concept of two-port dynamic stiffness model is proposed. • Two improved transfer matrices are developed for serial-parallel subchains. • The kinetostatics and dynamics of compliant mechanisms are solved. • Two examples verify the high accuracy and conciseness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses a piezoelectric-actuated compliant mechanism with two output ports to provide tensile and compressive forces along with high dynamic motions for static tension and high-cycle dynamic fatigue testing of small-scale specimens or other precision flexible manipulation applications. A rhombus-type planar multistage displacement amplifier with a pair of guiding flexible beams is designed to realize a millimeter stroke while retaining high fundamental frequency. Improved effect of the guiding flexible beams on the vibration modes and attenuating impact on the output displacement are analyzed respectively by finite element analysis and theoretical kinematics modeling. A prototype is manufactured and the experimental performance evaluation shows a maximum stroke range of 1.44 mm (±720 µm) with the fundamental frequency of 628 Hz. [ABSTRACT FROM AUTHOR]

Kinetostatic analysis of compliant mechanisms are crucial at the early stage of design, and it can be difficult and laborsome for complex configurations with distributed compliance. In this paper, a kinetostatic modeling method for flexure-hinge-based compliant mechanisms with hybrid serial-parallel substructures is presented to provide accurate and concise solutions by combining the matrix displacement method with the transfer matrix method. The transition between the elemental stiffness matrix and the transfer matrix of flexure hinges/flexible beams is straightforward, enabling the condensation of a hybrid serial-parallel substructure into one equivalent two-node element simple. A general kinetostatic model of the whole compliant mechanisms is first established based on the equilibrium equation of the nodal force. Then, a condensed two-port mechanical network representing the input/output force-displacement relations of single-degree-of-freedom (DOF) compliant mechanisms and the Jacobian matrix for multi-DOF compliant mechanisms are respectively built. Comparison of the proposed method with the compliance matrix method in previous literature, finite element analysis and experiment for three exemplary mechanisms reveals good prediction accuracy, suggesting its feasibility for fast performance evaluation and parameter optimization at the initial stage of design. [ABSTRACT FROM AUTHOR]

A semi-analytical modeling method towards the static and dynamic analyses for a class of flexure hinge-based compliant mechanisms or their composed systems is presented to provide accurate and efficient solutions. It is realized by firstly transforming the theoretical compliance matrix of a flexure hinge into a unified elemental stiffness matrix of a variable cross-section beam. Then, the semi-analytical finite element model of complex compliant mechanisms is established based on Lagrange’s equation taking the flexure hinge, the flexible beam and the lumped mass as the minimum elements. Shearing effects of the flexure hinge and rotary inertia of the flexible beam are included to enhance the modeling accuracy. A comparison of the method with another existing theoretical method and the finite element software ANSYS for two exemplary compliant mechanisms reveals a maximum deviation of less than 8% regarding the static displacement and the fundamental frequency but with a much substantial reduction of degrees of freedom. The results suggest the presented method is applicable to time-critical scenarios such as dynamic topology optimization and real-time feedback control simulation for complex compliant mechanisms. [ABSTRACT FROM AUTHOR]

Compliant amplifying mechanisms and guiding mechanisms are prevalently adopted in most present piezo-actuated precision positioning stages. By considering the coupled relations among piezoelectric actuator, compliant amplifying mechanism and guiding mechanism, an analytical method towards the statics modeling of the kinematic performance for precision positioning stages is presented. In this method, these three parts are separately modeled and coupled together in series by defining input/output stiffness. Then two static displacement models with different stiffness definitions are established and mathematically proved to be equivalent, both of which may be versatile for practical applications. A comparison of the proposed method with the finite element analysis for a flexure-based XY positioning stage reveals less than 10% deviations and indicates that the workspace significantly decreases with consideration of the finite stiffness of piezoelectric actuator and the elastic effect of guiding mechanism. The proposed method offers a modular and assembled statics modeling tool for analysis and design of a wide class of flexure-based precision positioning stages. [ABSTRACT FROM AUTHOR]

With the merits of multiplying displacement amplification ratio and compact structure, flexure-based multistage compliant mechanisms have been widely proposed in recent ten years. Experimental output displacement, however, is attenuated more or less in various designs and is even reduced to less than 10% of the original ambitious design in some prototypes. In this paper, the issue on attenuated displacement amplification of multistage compliant mechanisms is theoretically investigated. A formula of displacement amplification ratio is established based on the elastic beam theory and by defining an impedance factor, which describes the hindering effect of the second layer on the preceding layer. The high accuracy of the model is verified by finite element analysis with no more than 5% deviations. It allows a designer to quickly get an intuitional sense of why the output displacement is attenuated and how each parameter affects the mechanisms’ performance. Thanks to the theoretical guidance, a new planar two-stage compliant mechanism with relatively high frequency response and large range as well as no assembly error is designed and tested. Experiments show a natural frequency of 3.3 kHz in the output direction and displacement of 198 μm, which agrees with the theoretical prediction. [ABSTRACT FROM AUTHOR]

• Mechanical modeling of spatial compliant mechanisms is studied. • Lumped and distributed compliance in serial-parallel configurations are involved. • Three-dimensional dynamic stiffness matrix of spatial flexure hinges is derived. • Spatial mechanisms with irregular-shaped rigid bodies can be concisely treated. • A piezoelectric Z-θ x -θ y precision tilting manipulator is optimally designed. There have been a number of studies on the analysis and design of planar compliant mechanisms. However, it is more difficult to obtain an exact and concise description of the kinetostatics and dynamics for spatial compliant mechanisms. A general approach is herein presented for analyzing and designing spatial compliant mechanisms by combining a three-dimensional (3-D) dynamic stiffness model with the Pareto multi-objective optimization strategy. The investigation is devoted to small deformation providing a programmable solution for serial-parallel configurations with out-of-plane degrees of freedom (DOFs). Particularly, the 3-D dynamic stiffness model is well applicable to describe the kinetostatic and dynamic behaviors of spatial compliant mechanisms with both distributed and lumped compliance involving irregular-shaped rigid bodies. The Pareto optimal solution set in terms of concerned performances is provided and the optimum structural parameters can be straightforwardly determined. With the presented method, a new piezoelectric Z-θ x -θ y precision tilting manipulator is optimally designed. Experimental results show the strokes of 0.27 mm, 4.3 mrad, 4.3 mrad and the fundamental resonance frequencies of 470 Hz, 520 Hz and 520 Hz in the three motion DOFs. [ABSTRACT FROM AUTHOR]

• Coupling dynamics in piezo-actuated compliant mechanisms under external loads is investigated. • A new modeling approach in Laplace domain is proposed to capture the coupling dynamic characteristics. • The coupled dynamic model in the form of control block diagram is analytically derived. • Kinetostatic and dynamic performances of a flexure-based precision manipulator are calculated. Piezoelectrically actuated compliant mechanisms are key techniques in designing micro/nano manipulators, precision positioning stages/grippers and many other mechanical instruments. By considering the coupling relationship among piezoelectric actuator, compliant mechanisms and their external loads, a new modeling methodology in Laplace domain is proposed to capture the coupling dynamic characteristics of such a complex system. The coupled dynamic model of piezo-actuated compliant mechanisms subjected to mass-spring-damper loads with an accessorial force is analytically derived in the form of transfer function based on the concept of two-port dynamic stiffness model and control theory. The coupled dynamic model is further transformed into a generalized control block diagram in a unified form. As an application case, the static and dynamic performances of a typical flexure-based precision manipulator actuated by amplified piezoelectric stacks are analyzed with the presented model. It is demonstrated, both numerically and experimentally, that the proposed approach is accurate and straightforward for solving the coupled dynamic modeling issue in piezo-actuated compliant mechanisms subjected to external loads, and would be general enough for a wide class of applications involving multi-domain dynamic problems. [ABSTRACT FROM AUTHOR]

• A group of flexure hinges with elliptical transverse cross-sections is developed. • Analytical equations for the ETC flexure hinges are obtained and verified. • The ETC hinges bridge the knowledge gap between CTC and RTC hinges. • The ETC flexure hinges can effectively reduce the stress concentration. • ETC-based compliant mechanisms can achieve higher actuation efficiency. Flexure hinges are fundamental elements of compliant mechanisms. Therefore, the development of novel primitive flexure hinges is of great value. In this study, the basic structures of notch-type flexure hinges were extended by focusing on their transverse cross-sections, that is, the cross-sections perpendicular to the central axis. A group of primitive flexure hinges with variable elliptical transverse cross-sections (ETC) was developed and investigated. Analytical models for ETC flexure hinges were developed and verified through finite element analyses and experiments. The anisotropic two-axis compliances of the ETC flexure hinges were evaluated using computational analyses. The differences and relations in compliances, rotational precisions, and stresses between the ETC and existing primitive flexure hinges are discussed. An application case of the ETC flexure hinges is presented, which improves the ETC-based compliant mechanisms that can achieve much higher actuation efficiency owing to the simultaneous increase in compliances and decrease in stress concentration. The ETC flexure hinges enhance the design space of the primitive flexure hinges, addressing the knowledge gap between flexure hinges with rectangular and circular transverse cross-sections. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper proposes an effective methodology for the fluid-dynamic design optimization of the main spool of a piezoelectric servo valve. The aim is to improve global performances of the piezoelectric servo valve by reducing the flow force acting on the main spool and the mass of the main spool. The main disturbance forces acting the main spool were analyzed. The steady-state flow force acting on the main spool was derived and the relationship between the flow force and the design parameters of the main spool was established. The design problem of the main spool was formulated mathematically as a multi-objective optimization problem. The minimum steady-state flow force and the minimum mass of main spool were considered as optimization objectives. The elitist non-dominated sorting genetic algorithm (NSGA-II) was applied and a set of Pareto-optimal solutions was calculated. The optimized results were analyzed and the final design parameters of the main spool were selected for the simulation analysis and experimental research. The computational fluid dynamics (CFD) simulation was employed to calculate the forces acting on the main spool. Simulation results show the flow force acting on the optimized main spool is significantly reduced. The unoptimized and optimized main spools were machined and experimental study was performed. Results show that the piezoelectric servo valve equipped with the optimized main spool has better response performance and dynamic bandwidth. The dynamic bandwidth is measured to 172 Hz under the amplitude attenuation of −3 dB. Compared with the piezoelectric servo valve with unoptimized main spool, the dynamic bandwidth of the piezoelectric servo valve with optimized main spool is increased by 26%. • The design problem of the main spool of a piezoelectric servo valve is formulated as a multi-objective optimization problem. • The minimum steady-state flow force and the minimum mass of main spool are considered as optimization objectives. • The multi-objective optimization problem is solved by using multi-objective evolutionary algorithm NSGA-II. • Experimental results show that the optimized main spool has better response performance and dynamic bandwidth. • The dynamic bandwidth of the piezoelectric servo valve with optimized main spool achieves an increase of 26%. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the function projective synchronization is investigated in coupled partially linear chaotic systems. By Lyapunov stability theory, a control law is derived to make the state vectors asymptotically synchronized up to a desired scaling function. Furthermore, based on function projective synchronization, a scheme for secure communication is presented in theory. The corresponding numerical simulations are performed to verify and illustrate the analytical results. [Copyright &y& Elsevier]

• We proposed a new compliant amplification mechanism for piezoelectric actuators. • Kinetostatic models of the mechanism are derived and compared with FEA. • An optimization design is obtained based on the analytical models. • We designed an experimental hardware to test the fabricated prototype. This paper proposes a new compliant mechanism for the stroke amplification of piezoelectric actuators. Compared with the existing ones, this compliant stroke amplification mechanism (CSAM) has several advantages including lightweight, less stress concentration, large motion range, as well as ease of manufacture in macro- and micro-scales, mainly due to the completely distributed compliance and largely reduced moving mass. Kinetostatic models of the CSAM, with consideration of the payloads applied on the output stage, are derived for quick and insightful determinate analysis, which enables optimization of the associated parameters to achieve different objectives. The results obtained from the kinetostatic models are in reasonable agreement with the FEA simulation results, with less than 3.8% difference when the input displacement is less than 10 µm. An optimization method, based on the analytical models, is introduced and employed to increase the amplification ratio of the CSAM by up to 240%. The optimized CSAM is an excellent candidate for the stroke amplification of piezoelectric actuators, which is fabricated and experimentally tested. The optimization method is able to be extended to design other compliant mechanisms with optimized size, shape and topology configuration simultaneously. [ABSTRACT FROM AUTHOR]