Flexure-based compliant mechanisms are becoming increasingly promising in precision engineering, robotics, and other applications due to the excellent advantages of no friction, no backlash, no wear, and minimal requirement of assembly. Because compliant mechanisms have inherent coupling of kinematic-mechanical behaviors with large deflections and/or complex serial-parallel configurations, the kinetostatic and dynamic analyses are challenging in comparison to their rigid-body counterparts. To address these challenges, a variety of techniques have been reported in a growing stream of publications. This paper surveys and compares the conceptual ideas, key advances, and applicable scopes, and open problems of the state-of-the-art kinetostatic and dynamic modeling methods for compliant mechanisms in terms of small and large deflections. Future challenges are discussed and new opportunities for extended study are highlighted as well. The presented review provides a guide on how to select suitable modeling approaches for those engaged in the field of compliant mechanisms.

This paper develops a compact piezo-actuated XYZ flexure mechanism with an integrated polyvinylidene fluoride (PVDF) based displacement sensor. The sensing scheme is, by sticking a shaped PVDF film on the guiding flexible beams and using the kinematic relationship of the clamped-sliding flexible beam, widely available in compliant mechanisms. The optimal shape of PVDF is found by maximizing the sensitivity with an analytical sensing model. A pseudostatic model is also established to predict and optimize the kinetostatics and dynamics of the manipulator without calculating the elastic/kinetic energies or using Lagrange's equation. Thus, the dynamic modeling is simplified as a statics-similar problem. A comparison of the theoretical model with finite-element analysis reveals its high accuracy and substantially concise step. Finally, the manipulator is tested having the stroke range of 112 μm × 112 μm × 123 μm and the resonance frequency of 682 Hz × 687 Hz × 3.88 kHz with relatively large stroke range and high frequency in the Z-motion. Moreover, the experimental output of the proposed PVDF sensor matches well with the laser sensor, providing a new way with ignorable volume, high sensitivity, large bandwidth, and low cost to measure the displacement of compliant mechanisms, in which the space is usually confined and assembling a bulky transducer is difficult.

This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way based on D'alembert's principle. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo-static model. The superiority of the proposed method is that when it is used for the dynamic modeling of compliant mechanisms, the traditional dynamic modeling procedures, such as calculation of the elastic and kinetic energies as well as using Lagrange's equation, are avoided and the dynamic modeling is converted to a statics-similar problem. Comparison of the proposed method with an elastic-beam-based model in previous literature and finite element analysis for an exemplary XY precision positioning stage reveals its high accuracy and easy operation.

Piezoelectric actuators are particularly interesting in high-speed precision flow control valves due to their fast dynamic response and simple structure. However, concurrently improving the dynamic bandwidth and flow rate has been a challenging issue. In this article, a novel two-stage flow control valve driven by amplified piezoelectric actuator is proposed, fabricated, and tested with the step response time of 5 ms, flow rate of 70 L/min, and the dynamic bandwidth of 155 Hz at the supply pressure of 30 bar. An improved rhombus-type compliant mechanism with double output ports is proposed to amplify the microstroke of piezostacks with a relatively high resonance frequency. Two pilot sliding spools are differentially actuated moving the main spool back and forth, modulating the flow rate and direction. The coupling dynamics of the piezohydraulic valve is also formulated on the Laplace domain with the concept of two-port dynamic stiffness model and control theory. The influence of key structural parameters on the flow characteristics is analytically calculated, and the optimal static and dynamic performances are obtained. The theoretical prediction is in reasonable agreement with the experimental results in the closed-loop control, proving that the operational concept is viable.

Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces, low stress levels, and flexible design parameters, which have attracted considerable attention in precision engineering, metamaterials, robotics, and so forth. However, serial–parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design. Here, the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial–parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods. Consequently, serial–parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step‐by‐step procedure. Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach. In conclusion, the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial–parallel compliant mechanisms and beam structures, including curved flexure hinges and irregular‐shaped rigid bodies.

This paper introduces an extended dynamic stiffness modeling approach for concurrent kinetostatic and dynamic analyses of planar flexure-hinge mechanisms with lumped compliance. First, two novel dynamic stiffness matrices are derived for two types of flexure hinge connected to rigid bodies by shifting the end node to the mass center of rigid bodies considering the geometric effect of rigid motion. A straightforward modeling procedure is then proposed for the whole compliant mechanism based on d'Alembert's principle by selecting the displacements at both the mass center of rigid bodies and the rest end nodes of flexure hinges as the hybrid state variables. With the presented method, the statics and dynamics of flexure-hinge mechanisms with irregular-shaped rigid bodies in complex serial-parallel configurations can be analyzed in a concise form. The presented method is compared with other theoretical models, finite element simulation, and experiments for three case studies of a bridge-type compliant mechanism, a leveraged XY precision positioning stage, and a Scott–Russell-mechanism-based XYθ flexure manipulator. The results reveal the easy operation and well prediction accuracy of the presented method.