Modelling and parameter design of a 3-DOF compliant platform driven by magnetostrictive actuators

Precision platforms composed of smart-material-based actuators and compliant mechanisms show advantages of high accuracy and fast response. This research focuses on a 3-degree-of-freedom compliant platform driven by magnetostrictive actuators. A parameterized physical model is established for the platform with consideration of three kinds of coupling effects. The magneto-mechanical coupling of the magnetostrictive actuator is described by a modified Jiles-Atherton model. The structural coupling of the platform is characterized in the process of stiffness matrix modelling and coordinate system transformation of the compliant components. The coupling between the magnetostrictive actuator and the compliant structure is considered in the overall actuation model. Parameter design is performed based on the numerical simulation of the proposed model. Due to the coupling effect, the dimensions of the compliant amplifier affect both the amplification ratio and the actuation stroke of the actuator. Thus, a combined optimization is essential to obtain the optimal design. The influences of the key dimensions on platform stiffness and actuation performances are demonstrated. With optimized key dimensions, the parasitic displacements can be effectively reduced at very little cost of the moving strokes. Open-loop experiments are taken to verify the accuracy of the proposed physical model, and closed-loop experiments are performed to demonstrate the platform performance on precision positioning. The main errors are caused by the friction in a sliding pair and the inertia of the loads.     

多输入多输出柔顺机构几何非线性拓扑优化

多自由度柔顺机构在微动精密定位和精密操作等领域有广泛的应用,柔顺机构拓扑实际上是一个几何非线性问题,因而研究多自由度柔顺机构几何非线性拓扑优化就显得十分必要.基于此,给出一种多输入多输出柔顺机构几何非线性拓扑优化设计的新方法.首先,建立增量形式平衡方程,采用Total-Lagrange描述方法和Newton-Raphson载荷增量求解技术获得几何非线性的结构响应.其次,推导描述多输入多输出柔顺机构柔性的几何增益公式和描述机构刚性的应变能公式,研究抑制耦合输出策略,给出描述输出耦合效应的计算公式,在此基础上建立考虑抑制输出耦合效应时多输入多输出柔顺机构的多目标几何非线性拓扑优化数学模型.目标函数敏度分析采用伴随求解技术,拓扑优化采用固体各向同性材料插值方法,并用移动近似算法进行迭代求解.最后,通过算例说明以上方法的正确性和有效性.研究结果表明,拓扑优化后柔顺机构可以按照预定要求运动,输出耦合现象得到了有效抑制,同时也说明了对柔顺机构进行几何非线性拓扑优化的必要性.     

Characterization of thermally stable compliant structures with internal fluidic channels

This paper represents a novel method to suppress the thermal effects of flexure mechanism-based nanopositioning system by fluid (air or water) flow under certain pressure conditions through the internal fluidic channels of the compliant structure. The nanopositioning system made of stainless steel was additively manufactured, and the rectangular fluidic channels were formed on each side of the double compound type flexure mechanism-based compliant structure. The motion behavior was characterized by measuring the stiffness and frequency responses of the compliant structure with the hammering test while filling compressed air or the water through the fluidic channels. The thermal behavior was characterized by measuring the temperature distribution over the compliant structure and thermal displacement under the various compressed air pressure and water flow-rate conditions. Dynamic behaviors of the nanopositioning system under various fluid-fed conditions were also characterized by the Finite Element Method and were validated with experimental results. As a result, the compressed air- or water-fed mechanisms have the following characteristics: (1) the damping may increase when the fluid exists in the channels, (2) the compressed air-fed mechanism can move the stage with nanometer precision with fast response time, and (3) the media filled in the fluidic channels significantly lower the temperature increase and reduce thermal displacement error. Interestingly, two-fluid flows of the compressed air and water showed a similar tendency in suppressing the temperature increase. The proposed method is expected to meet the increasing needs for nanometer motion accuracies and the efforts achieving high precision in the thermally stable environments requiring from semiconductor industries and precision machine tool industries.     

Structural Synthesis of Compliant Metamorphic Mechanisms Based on Adjacency Matrix Operations

A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s+1 links from an s-link mechanism (the final configuration). The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.     

多输入多输出柔顺机构拓扑优化及输出耦合的抑制

多自由度柔顺机构在微动精密定位和精密操作等领域有广泛的应用,因而研究多自由度柔顺机构的拓扑优化方法就显得十分必要。给出了一种多输入多输出柔顺机构拓扑优化设计的新方法。首先,推导了描述多输入多输出柔顺机构柔性的互应变能公式和描述机构刚性的应变能公式,研究了抑制耦合输出的策略,进一步给出了描述输出耦合效应的计算公式,在此基础上建立了考虑抑制输入输出耦合效应时柔顺机构的多目标拓扑优化设计模型。其次,基于改进的优化准则法给出了优化模型的有效求解算法。最后,通过算例说明了该方法的正确性和有效性,研究结果表明,拓扑优化后柔顺机构可以按照预定的要求运动,其输出耦合现象得到了有效抑制。     

区间参数柔性机构设计的混合元胞自动机方法

进行柔性机构设计时,应考虑不确定性参数对机构性能的影响。基于此,将柔性机构物理参数及其外载荷视为区间变量,基于柔性机构的刚性测度和柔性测度,建立在连续域中利用结构拓扑优化设计柔性机构的数学模型。采用固体各向同性惩罚方法进行设计域材料的参数化,将材料相对密度作为设计变量,结构受载时的应变能和交互势能线性加权的极大化作为目标函数,结构体积作为约束。优化设计求解策略采用混合元胞自动机方法,用区间有限元法进行结构总体分析以获取优化过程中的每次迭代信息,设计变量中的局部改变由基于比例—积分—微分控制律的局部设计规则来确定。数值算例证明了所建模型及其解法的有效性。按照数值算例结果之一进行等比例尺寸放大后的实物制造,并进行简单试验验证。     

Analysis of frequency characteristics and sensitivity of compliant mechanisms

Based on a modified pseudo-rigid-body model, the frequency characteristics and sensitivity of the large-deformation compliant mechanism are studied. Firstly, the pseudo-rigid-body model under the static and kinetic conditions is modified to enable the modified pseudo-rigid-body model to be more suitable for the dynamic analysis of the compliant mechanism. Subsequently, based on the modified pseudo-rigid-body model, the dynamic equations of the ordinary compliant four-bar mechanism are established using the analytical mechanics. Finally, in combination with the finite element analysis software ANSYS, the frequency characteristics and sensitivity of the compliant mechanism are analyzed by taking the compliant parallel-guiding mechanism and the compliant bistable mechanism as examples. From the simulation results, the dynamic characteristics of compliant mechanism are relatively sensitive to the structure size, section parameter, and characteristic parameter of material on mechanisms. The results could provide great theoretical significance and application values for the structural optimization of compliant mechanisms, the improvement of their dynamic properties and the expansion of their application range.     

柔顺机构的频率特性分析

以伪刚体模型为基础对平面柔顺机构的频率特性进行了详细的分析,并分别就机构截面参数、结构尺寸、材料参数对频率的影响进行了讨论;针对柔顺机构材料特点提出了新的频率特性比较指标,给出了数值算例,验证了评价指标的可靠性。     

Transmission angle in compliant slider-crank mechanism

The transmission angle is an important parameter for the quality of motion transmission in a mechanism. However, in the literature there is no study available on compliant mechanisms regarding their transmission characteristics. In this paper, the transmission angle of a compliant slider-crank mechanism is introduced. Similarity conditions for the transmission angle of the compliant slider-crank and its rigid body counterpart are devised via two theorems. A real model is manufactured and one of these theorems is verified experimentally. Finally, the effect of eccentric slider on motion transmission quality is discussed. It is believed that newly proposed theorems will find use in the design of compliant slider-crank mechanisms.     

Manufacturing of multi-material compliant mechanisms using multi-material molding

Multi-material compliant mechanisms enable many new design possibilities. Significant progress has been made in the area of design and analysis of multi-material compliant mechanisms. What is now needed is a method to mass-produce such mechanisms economically. A feasible and practical way of producing such mechanisms is through multi-material molding. Devices based on compliant mechanisms usually consist of compliant joints. Compliant joints in turn are created by carefully engineering interfaces between a compliant and a rigid material. This paper presents an overview of multi-material molding technology and describes feasible mold designs for creating different types of compliant joints found in multi-material compliant mechanisms. It also describes guidelines essential to successfully utilizing the multi-material molding process for creating compliant mechanisms. Finally, practical applications for the use of multi-material molding to create compliant mechanisms are demonstrated.     

全柔性机构与MEMS

柔性机构是一种新型机构。首先描述了柔性机构和全柔性机构的概念及特点,论述了它们与MEMS之间的关系。然后详细介绍了全柔性机构在MEMS领域内包括微装配、微操作等应用背景下的状况及前景。最后就对全柔性机构研究中的几个关键技术问题如机构的分析、设计及加工,柔性铰链的选择与设计,驱动器的选择及设计等进行了探讨。     

Spring-joint method for topology optimization of planar passive compliant mechanisms

There is seldom approach developed for the initial topology design of flexure-based compliant mechanisms. The most commonly-used approaches, which start with an existing rigid-body mechanism, do not consider the performances between different topologies. Moreover, they rely heavily on the rigid-body topology, therefore limit the diversity of compliant mechanisms topology. To obtain the optimal initial topology of such mechanisms directly from problem specifications without referencing to the existing mechanism topologies, a spring-joint method is presented for a restricted class of the serial passive flexure-based compliant mechanisms, which are the building blocks of parallel compliant mechanisms. The topology of the compliant mechanisms is represented by a serial spring-joint mechanism（SSJM） that is a traditional rigid-body mechanism with a torsional spring acting on each joint, and is described by position vectors of the spring-joints. A simplified compliance matrix, determined by the position vectors, is used to characterize the tip of the SSJM kinematically, and is optimized to ensure the desired freedoms of the compliant mechanisms during optimization. The topology optimization problem is formulated as finding out the optimal position of the spring-joints in a blank design domain with an objective function derived from the simplified compliance matrix. In design examples, syntheses of the compliant mechanisms with both single freedom and two decoupled freedoms are presented to illustrate the proposed method. The proposed method provides a new way for the initial design of flexure-based compliant mechanisms.     

Mechanical and geometric advantages in compliant mechanism optimization

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.     

压电双晶片驱动的仿生柔性扑翼机构研究

分析了昆虫的翅膀-胸部运动系统,并以此为基础,仿生设计出压电双晶片驱动,柔性双摇杆机构放大位移并带动仿生翅拍动的扑翼系统.分析了压电双晶片的工作原理,讨论了柔性四杆机构的自由度和运动学,并对整个系统的准静力学进行探讨,以确定能否产生足够的力克服空气阻尼.仿真和实验结果表明,通过柔性机构放大压电双晶片位移,能实现仿生翅所需运动,同时进一步的优化设计将有助于改进扑翼机构的运动性能.     

分布式柔性机构拓扑优化设计的理论和算法

将连续体结构的拓扑优化技术应用到分布式柔性机构的设计中,基于变密度法和优化准则法推导并建立柔性机构拓扑优化的一种显式的设计变量收敛格式。结合分布式柔性机构优化设计的人工弹簧模型和虚拟载荷法,提出一种新型的分布式柔性机构拓扑优化设计的多准则优化模型,同时综合考虑柔性机构设计的机械效率要求和结构的刚度要求,并利用伴随敏度分析法进行敏度分析。数值算例证明研究方法的有效性,并分析和讨论优化模型和收敛格式中有关优化设计参数对柔性机构优化设计结果的影响。用激光快速成形技术验证柔性机构概念设计的合理性。     

整体式空间3自由度精密定位平台的优化设计与试验

根据柔顺薄板的弹性变形原理,设计一种整体式空间三自由度柔顺并联微动平台.分析该平台的输入耦合特性,对三种输入耦合形式对定位精度的影响进行讨论.基于有限元法,给出平台的刚度模型,对平台的结构尺寸进行优化设计,并通过ANSYS仿真分析验证优化结果的正确性.在此基础上进一步建立平台的位置正解和位置逆解方程,对平台的定位精度进行试验研究,提出一种基于理论分析模型的试验修正方法,该方法能有效提高平台的定位精度,研究表明该平台具有亚微米级的定位精度.     

Motion and stress analysis of direct-driven compliant mechanisms with general-purpose finite element software

Compliant mechanisms with embedded direct-driven actuators are gaining a wide interest in manufacturing systems as well as structural systems. In this paper, we present a procedure for motion analysis of a compliant mechanism which is driven by three embedded piezoelectric actuators with a general-purpose finite element system, in particular, ANSYS. This includes finite element modeling of the piezoelectric actuator and finite element modeling of the compliant mechanism. An experimental validation was conducted, which shows that the model is highly accurate. The contribution of this paper is a novel application of finite element methods with multidisciplinary elements to motion and stress analysis of compliant mechanisms with embedded piezoelectric actuators. In the current literature, for a complaint mechanism, either the piezoelectric actuator is modeled with absence of piezoelectric effects or a pseudo rigid body approach is applied with poor accuracy. Another contribution lies in the use of a general-purpose finite element software system, which will greatly increase the generalization of finite element modeling applications.     

柔顺机构几何非线性拓扑优化设计

对柔顺机构几何非线性拓扑优化设计理论进行了深入研究。首先,建立增量形式平衡方程,采用Total-Lagrange描述方法和Newton-Raphson载荷增量求解技术获得几何非线性的结构响应。其次,基于固体各向同性材料插值方法,建立体积约束下,输出位移最大为目标函数的柔顺机构几何非线性拓扑优化数学模型,目标函数敏度分析采用伴随求解技术,并用移动近似算法进行迭代求解。最后,通过算例说明以上方法的正确性和有效性。研究结果表明,应用上述方法对柔顺机构进行几何非线性拓扑优化设计能够得到合理拓扑图,并比线性分析所得机构的稳定性更高,同时也说明了对柔顺机构进行几何非线性拓扑优化的必要性。     

二维微执行器几何非线性拓扑优化设计与试验

多自由度柔顺机构在微动精密定位和精密操作等领域有广泛的应用,并且柔顺机构拓扑优化后所得机构都是锯齿状跳跃边界的几何图像,不能直接应用于工程实际,因而对多自由度柔顺机构拓扑优化、提取与试验研究就显得十分必要。基于此,以二维微执行器为例,进行多自由度柔顺机构几何非线性拓扑优化、拓扑图提取与试验研究。首先,给出了考虑耦合抑制输出的多输入多输出柔顺机构几何非线性拓扑优化数学模型及优化算法。其次,针对柔顺机构性能特点,给出了一种拓扑提取方法。提取过程包括灰度图像二值化、密度等值线方法边界近似和曲线重构三个部分。最后,以二维微执行器为基础,采用线切割加工工艺,研制了二维微执行器原型,并对其位移性能进行了试验测试,结果表明,该二维微执行器试验结果与理论分析结果基本吻合,达到了设计要求,同时也验证了所提方法的有效性。     

Topology design and analysis of compliant mechanisms with composite laminated plates

To improve the small deformation and high stress level in hinge zones of compliant mechanisms with isotropic material, a topology optimization method of compliant mechanisms with composite laminated plates was proposed. Based on the anisotropy and designability of composite laminated plates, a topology optimization model of compliant mechanisms with composite laminated plates was built to maximize the deformable capability. Numerical examples of designing compliant inverters and grippers were investigated to demonstrate the effectiveness of the proposed method. The influence mechanism of layer sequences on topologic shapes, deformation and loading capability were also discussed. The results showed that the deformable capability and stress levels of compliant mechanisms with composite laminated plates were further improved by a reasonable configuration of layer sequences.