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Mechanical and geometric advantages in compliant mechanism optimization

Michael Yu WANG

《机械工程前沿（英文）》 2009年第4卷第3期页码 229-241 doi: 10.1007/s11465-009-0066-1

摘要： This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism's structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.

关键词： compliant mechanisms topology optimization mechanical advantage pseudo rigid-body mechanisms

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Preload characteristics identification of the piezoelectric-actuated 1-DOF compliant nanopositioning

Ruizhou WANG, Xianmin ZHANG

《机械工程前沿（英文）》 2015年第10卷第1期页码 20-36 doi: 10.1007/s11465-015-0328-z

摘要：

Packaged piezoelectric ceramic actuators (PPCAs) and compliant mechanisms are attractive for nanopositioning and nanomanipulation due to their ultra-high precision. The way to create and keep a proper and steady connection between both ends of the PPCA and the compliant mechanism is an essential step to achieve such a high accuracy. The connection status affects the initial position of the terminal moving plate, the positioning accuracy and the dynamic performance of the nanopositioning platform, especially during a long-time or high-frequency positioning procedure. This paper presents a novel external preload mechanism and tests it in a 1-degree of freedom (1-DOF) compliant nanopositioning platform. The 1-DOF platform utilizes a parallelogram guiding mechanism and a parallelogram load mechanism to provide a more accurate actual input displacement and output displacement. The simulation results verify the proposed stiffness model and dynamic model of the platform. The values of the preload displacement, actual input displacement and output displacement can be measured by three capacitive sensors during the whole positioning procedure. The test results show the preload characteristics vary with different types or control modes of the PPCA. Some fitting formulas are derived to describe the preload displacement, actual input displacement and output displacement using the nominal elongation signal of the PPCA. With the identification of the preload characteristics, the actual and comprehensive output characteristics of the PPCA can be obtained by the strain gauge sensor (SGS) embedded in the PPCA.

关键词： nanopositioning preload characteristic packaged piezoelectric ceramic actuator compliant mechanism

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Modeling of large-deflection links for compliant mechanisms

Zhonglei FENG, Yueqing YU, Wenjing WANG,

《机械工程前沿（英文）》 2010年第5卷第3期页码 294-301 doi: 10.1007/s11465-010-0019-8

摘要： The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.

关键词： compliant mechanism pseudo-rigid-body model (PRBM) large-deflection link angular deflection approximation

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Untethered quadrupedal hopping and bounding on a trampoline

Boxing WANG, Chunlin ZHOU, Ziheng DUAN, Qichao ZHU, Jun WU, Rong XIONG

《机械工程前沿（英文）》 2020年第15卷第2期页码 181-192 doi: 10.1007/s11465-019-0559-5

摘要： For quadruped robots with springy legs, a successful jump usually requires both suitable elastic parts and well-designed control algorithms. However, these two problems are mutually restricted and hard to solve at the same time. In this study, we attempt to solve the problem of controller design with the help of a robot without any elastic mounted parts, in which the untethered robot is made to jump on a trampoline. The differences between jumping on hard surfaces with springy legs and jumping on springy surfaces with rigid legs are briefly discussed. An intuitive control law is proposed to balance foot contact forces; in this manner, excessive pitch oscillation during hopping or bounding can be avoided. Hopping height is controlled by tuning the time delay of the leg stretch. Together with other motion generators based on kinematic law, the robot can perform translational and rotational movements while hopping or bounding on the trampoline. Experiments are conducted to validate the effectiveness of the proposed control framework.

关键词： hopping and bounding gait compliant mechanism compliant contact balance control strategy legged locomotion control quadruped robot

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Analysis of frequency characteristics of compliant mechanisms

WANG Wenjing, YU Yueqing

《机械工程前沿（英文）》 2007年第2卷第3期页码 267-271 doi: 10.1007/s11465-007-0046-2

摘要： Much work is needed for a further study on the dynamic analysis of compliant mechanisms to improve their performance and operational accuracy. This paper uses the finite element method to develop a dynamic equation of the compliant mechanism. Natural frequencies and modes are derived. Using the differentials of a stiffness matrix to design parameters, a method for calculating the sensitivity of natural frequency is presented. The numerical simulation results indicate that the design parameters have an impact on the frequency characteristics of the compliant mechanisms and the proposed method is more accurate and convenient for analyzing frequency characteristics.

关键词： compliant mechanisms convenient sensitivity work analysis

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Understanding coupled factors that affect the modelling accuracy of typical planar compliant mechanisms

Guangbo HAO,Haiyang LI,Suzen KEMALCAN,Guimin CHEN,Jingjun YU

《机械工程前沿（英文）》 2016年第11卷第2期页码 129-134 doi: 10.1007/s11465-016-0392-z

摘要：

In order to accurately model compliant mechanism utilizing plate flexures, qualitative planar stress (Young’s modulus) and planar strain (plate modulus) assumptions are not feasible. This paper investigates a quantitative equivalent modulus using nonlinear finite element analysis (FEA) to reflect coupled factors in affecting the modelling accuracy of two typical distributed-compliance mechanisms. It has been shown that all parameters have influences on the equivalent modulus with different degrees; that the presence of large load-stiffening effect makes the equivalent modulus significantly deviate from the planar assumptions in two ideal scenarios; and that a plate modulus assumption is more reasonable for a very large out-of-plane thickness if the beam length is large.

关键词： coupling factors modelling accuracy compliant mechanisms equivalent modulus

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A brief review on nonlinear modeling methods and applications of compliant mechanisms

Guangbo HAO,Jingjun YU,Haiyang LI

《机械工程前沿（英文）》 2016年第11卷第2期页码 119-128 doi: 10.1007/s11465-016-0387-9

摘要：

Compliant mechanisms (CMs) have become one of the most popular research themes in mechanisms and robotics because of their merits. This paper aims to provide a brief systematic review on the advances of nonlinear static modeling approaches and the applications of CMs to promote interdisciplinary/multidisciplinary development for associated theories and other new applications. It also predicts likely future directions of applications and theory development.

关键词： compliant mechanisms modelling nonlinearity applications review

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一种新型激光打印压缩诱导扭转柔顺机构的成型过程和力学变形行为 Article

高捷, 顾冬冬, 马成龙, 戴冬华, 席丽霞, 林开杰, 高彤, 朱继宏, 杜月欣

《工程（英文）》 2022年第15卷第8期页码 133-142 doi: 10.1016/j.eng.2021.03.032

摘要：

本文采用激光粉末床熔融（LPBF）技术成型了一种基于自由约束拓扑（FACT）方法设计的新型压缩诱导扭转（CIT）柔顺机构。研究了LPBF 打印参数对激光打印CIT 柔顺机构成型性和压缩性能的影响。在375~450 W的优化激光功率范围内，样品的致密化水平均保持在98%以上，所获得的LPBF制造的CIT柔顺机构的相对密度随施加激光功率的变化不明显。增加激光功率有利于消除CIT 柔顺机构斜杆内的残余冶金孔隙。在450 W的激光功率下实现了0.2%的最高尺寸精度和20 μm的最低表面粗糙度。LPBF成型CIT柔顺机构的变形行为表现为四个典型阶段：弹性阶段、非均匀塑性变形阶段、强度破坏阶段和变形破坏阶段（或不稳定变形阶段）。采用450 W激光功率最优成形的CIT 柔顺机构在破坏前的累积压缩应变可达20%，展现了较大的变形能力。通过有限元模拟和实验验证相结合的方法，研究了CIT 柔顺机构的扭转行为和力学性能。在LPBF成型CIT柔顺机构的应变达到15%之前实现了轴向压缩应变与旋转角度之间的近似线性关系。

关键词：激光3D打印激光粉末床熔融压缩诱导扭转柔顺机构压缩-扭转性能力学性能

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Conceptual design of compliant translational joints for high-precision applications

Guangbo HAO,Haiyang LI,Xiuyun HE,Xianwen KONG

《机械工程前沿（英文）》 2014年第9卷第4期页码 331-343 doi: 10.1007/s11465-014-0321-y

摘要：

Compliant translational joints (CTJs) have been extensively used in precision engineering and microelectromechanical systems (MEMS). There is an increasing need for designing higher-performance CTJs. This paper deals with the conceptual design of CTJs via three approaches: parallelogram based method, straight-line motion mechanism based method and combination based method. Typical emerging CTJ designs are reviewed by explaining their design principles and qualitatively analyzing their characteristics. New CTJs are proposed using three approaches, including an asymmetric double parallelogram mechanism with slaving mechanism, several compact and symmetric double parallelogram mechanisms with slaving mechanisms and a general CTJ using the center drift compensation and a CTJ using Roberts linkage and several combination designs. This paper provides an overview of the current advances/progresses of CTJ designs and lays the foundation for further optimization, quantitative analysis and characteristic comparisons.

关键词： compliant mechanisms translational joints conceptual design parallelogram straight-line motion combination method

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Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on

Junjie ZHAN, Yangjun LUO

《机械工程前沿（英文）》 2019年第14卷第2期页码 201-212 doi: 10.1007/s11465-019-0529-y

摘要： This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties, which are described using a non-probabilistic bounded field model. Bounded field uncertainties are efficiently represented by a reduced set of uncertain-but-bounded coefficients on the basis of the series expansion method. Robust topology optimization of compliant mechanisms is then defined to minimize the variation in output displacement under constraints of the mean displacement and predefined material volume. The nest optimization problem is solved using a gradient-based optimization algorithm. Numerical examples are presented to illustrate the effectiveness of the proposed method for circumventing hinges in topology optimization of compliant mechanisms.

关键词： compliant mechanisms robust topology optimization hinges uncertainty bounded field

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Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

《机械工程前沿（英文）》 2006年第1卷第2期页码 131-145 doi: 10.1007/s11465-006-0018-y

摘要： We propose a level set method-based framework for the conceptual design of compliant mechanisms. In this method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity field in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady-state solution of the partial differential equation. Besides the above-mentioned methodological issues, some numerical examples together with prototypes are presented to validate the performance of the method.

关键词： splitting minimum dimensional optimization Hamilton-Jacobi topological

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Manufacturing error analysis of compliant 3-DOF microrobot

CHAO Dai-hong, LIU Rong, WU Yue-min, SHI Long, ZONG Guang-hua

《机械工程前沿（英文）》 2006年第1卷第3期页码 299-304 doi: 10.1007/s11465-006-0030-2

摘要： In the fields of micro/nanopositioning application, error analysis is an effective way to enhance the precision of micromanipulators. Manufacturing imperfections, which are inevitable, are the most important factors influencing the accuracy. Therefore, various manufacturing imperfections were studied by taking a planar 3 degrees of freedom (3-DOF) flexure hinge based microrobot as a case. By formulating static stiffness of the robot, mapping between manufacturing imperfections and end-effector positioning accuracy was obtained. Using the theoretical calculation and finite element method (FEM), effects of various machining imperfection types on end-effector positioning accuracy were evaluated. The results showed that errors of the radium of the hinges and angular differences of the centerline of the hinges were dominant factors resulting in output errors. Conclusions drawn from the experiments can be used to instruct the design of compliant parallel mechanisms by distributing various manufacturing differences of configurable parameters to guarantee precision in the positioning of the end-effector within the required range; they may also be helpful while calibrating this kind of manipulator.

关键词： centerline stiffness effective manipulator precision

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Mechatronic design of a novel linear compliant positioning stage with large travel range and high out-of-plane

Hua LIU, Xin XIE, Ruoyu TAN, Lianchao ZHANG, Dapeng FAN

《机械工程前沿（英文）》 2017年第12卷第2期页码 265-278 doi: 10.1007/s11465-017-0453-y

摘要：

Most of the XY positioning stages proposed in previous studies are mainly designed by considering only a single performance indicator of the stage. As a result, the other performance indicators are relatively weak. In this study, a 2-degree-of-freedom linear compliant positioning stage (LCPS) is developed by mechatronic design to balance the interacting performance indicators and realize the desired positioning stage. The key parameters and the coupling of the structure and actuators are completely considered in the design. The LCPS consists of four voice coil motors (VCMs), which are conformally designed for compactness, and six spatial leaf spring parallelograms. These parallelograms are serially connected for a large travel range and a high out-of-plane payload capacity. The mechatronic model is established by matrix structural analysis for structural modeling and by Kirchhoff’s law for the VCMs. The sensitivities of the key parameters are analyzed, and the design parameters are subsequently determined. The analytical model of the stage is confirmed by experiments. The stage has a travel range of 4.4 mm× 7.0 mm and a 0.16% area ratio of workspace to the outer dimension of the stage. The values of these performance indicators are greater than those of any existing stage reported in the literature. The closed-loop bandwidth is 9.5 Hz in both working directions. The stage can track a circular trajectory with a radius of 1.5 mm, with 40 mm error and a resolution of lower than 3 mm. The results of payload tests indicate that the stage has at least 20 kg out-of-plane payload capacity.

关键词： mechatronic design linear compliant positioning stage large travel range high out-of-plane payload capacity spatial parallelogram voice coil motor sensitivity analysis

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New nonlinear stiffness actuator with predefined torque‒deflection profile

《机械工程前沿（英文）》 2023年第18卷第1期 doi: 10.1007/s11465-022-0721-3

摘要： A nonlinear stiffness actuator (NSA) could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range, both of which are beneficial for physical interaction between a robot and the environment. Currently, most of NSAs are complex and hardly used for engineering. In this paper, oriented to engineering applications, a new simple NSA was proposed, mainly including leaf springs and especially designed cams, which could perform a predefined relationship between torque and deflection. The new NSA has a compact structure, and it is lightweight, both of which are also beneficial for its practical application. An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed. The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring. Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism, the sliding displacement between the cam and the leaf spring is very small, and consumption of sliding friction force is very low. Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles. Three kinds of prototype experiments, including verification experiment of the predefined torque‒deflection profile, torque tracking experiment, and position tracking experiment under different loads, were conducted. The results prove the accuracy of performing the predefined torque‒deflection profile, the tracking performance, and the interactive performance of the new NSA.

关键词： compliant actuator nonlinear stiffness actuator nonlinear spring predefined torque−deflection profile

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Theory and method of mechanism system design

Huijun ZOU, Qinghua LIANG, Qing ZHANG

《机械工程前沿（英文）》 2010年第5卷第4期页码 399-411 doi: 10.1007/s11465-010-0116-8

摘要： Conceptual design is the most critical and creative phase of design. Recently, increasing attention has been directed to supporting conceptual-level computer aided creative design and its theories and methodologies. Specifically, for conceptual design of mechanical products, this paper presents a novel function solving model for mechanical product design and highlights the importance of systematic synthesis to achieve creative design. Then it builds a framework as a function-effect-process-action- mechanisms (FEPAM) mapping process, which enables creative design on the basis of conceiving different action schemes. After that, several key points are elaborated including 1) representing and decomposition methods of functions and motion behaviors; 2) action scheme representing method based on network plan techniques; and 3) variation and creation methods based on action scheme transformations.

关键词： mechanism system creative design process model function solving model process action procedure mechanisms knowledge base principle of mechanism system composition