Design of a stiffness-adjustable compliant linear-motion mechanism

A stiffness-adjustable compliant linear-motion mechanism (CLMM) is desired in practical applications. In this paper loads are applied at the secondary stage of a paired double parallelogram (DP-DP) to adjust stiffness, based on the analysis of a combination of parallelograms. Pre-loaded parallelograms and loading springs are utilized to solve the loading problem in practical applications, and the redundant degree of freedom (DOF) is restricted to a certain extent. Meanwhile, the parasitic motion of the primary stage is diminished by arranging the configuration symmetrically. Furthermore, a model, capable of predicting stiffness characteristics, is developed through an energy approach based on the relation between applied forces and internal forces, and a Lagrange multiplier is exploited to deal with the constraints. Finally, the analytical model is verified by finite element analysis (FEA) and experiments, and the errors caused by parasitic motion are corrected for this analytical model.     

Nonlinear modeling of compliant mechanisms incorporating circular flexure hinges with finite beam elements

Modeling of compliant mechanisms incorporating flexure hinges is mainly focused on linear methods. However, geometrically nonlinear effects cannot be ignored generally. This work shows that nonlinear behavior plays an important role in the deformation and stress analysis, which consequently impacts the design of compliant mechanisms. In this study a nonlinear higher order finite beam element based modeling approach is presented strongly reducing the computation time of nonlinear models. Planar deformation and mechanical stress of a single circular flexure hinge under a wide range of loads is modeled and computed with the proposed approach. A comparison with a 3D-nonlinear finite element model shows very good agreement and validates the beam model. It is shown that the linear and nonlinear deformation behavior of a single flexure hinge deviate marginally so that linear modeling approaches are sufficient. Furthermore a planar displacement amplification mechanism incorporating circular flexure hinges is studied by means of the same method highlighting the distinct deviation of the behavior of the geometrically nonlinear model from its linear prediction. In conclusion the nonlinear behavior at the system level can not longer be neglected. Finally, a study shows that different designs of the displacement amplification mechanism are achieved when linear or nonlinear modeling approaches are applied.     

Design and development of compliant mechanisms for electromagnetic force balance sensor

Compared with the lever-type amplifier, the rhombus-type amplifier has attracted more attention by virtue of large displacement amplification ratio, compact structure, and linear output displacement. In this paper, a novel electromagnetic force balance sensor (EFBS) based on the rhombus-type amplifier is presented to measure the mass with high precision. First, the structure and operating principle of the EFBS are described, and the requirements for the design and manufacture of the amplifier are put forward. Then, the analytical models of the two-stage rhombus-type amplifier are given out, and two guiding mechanisms are analyzed and modeled. Furthermore, the validity of the established model is verified by finite element analysis (FEA). Thanks to the theoretical guidance, an electromagnetic force balance sensor based on the two-stage rhombus-type amplifier and double parallelogram flexure mechanism is designed and tested. The experimental results demonstrate that the developed EFBS can measure the mass of the objects with high precision, and also verifies the correctness of the analytical model. This provides a new concept for the structural design of the EFBS.     

A large range compliant XY nano-manipulator with active parasitic rotation rejection

There is an increasing demand to achieve manipulating operations in nanometric precision and a macro-range (over a millimeter) simultaneously. In principle, it is possible to satisfy both requirements in a compact size taking advantages of flexure-based mechanisms, whereas limitations such as the parasitic rotation, cross-axis coupling, saturation may adversely affect the motion quality in nanometric level practically. Here, we propose a novel design methodology to actively prevent parasitic rotation of XY compliant mechanisms. Further, by means of design synthesis and real-time motion control, the prototype of manipulator is fabricated, which enables large motion range (±3 mm) along each actuation axis. Experimental results demonstrate a travel range of 2 mm × 2 mm with high linearity, small cross-axis coupling (< 0.4%), and low parasitic rotation (< 6.9 μ rad over 0.5 mm × 0.5 mm motion range). Moreover, the high natural frequency (~ 60 Hz) of the manipulator facilitates it to achieve high-precision motion with tracking error < 80 nm (20 Hz sinusoids). The experimental results of the proposed nano-manipulator outperform most of the existing ones.     

柔性平行导向机构的静刚度分析

柔性机构是一种新型机构。作为一类最简单的柔性机构 ,柔性平行导向机构被广泛应用在精密定位场合。由于在精密操作中要求机构具有很高的定位精度 ,而机构的静刚度在很大程度上决定着这一指标。针对静刚度分析的重要作用以及目前对机构静刚度分析中存在的不足 ,采用结构分析中的柔度矩阵法建立了一种新的用来分析机构静刚度的理论模型。其结果相对原有模型更接近有限元仿真的结果     

Stiffness research on a high-precision, large-workspace parallel mechanism with compliant joints

Parallel-structure mechanisms, especially the non-backlash compliant parallel mechanisms, excel serial-structure ones in many indexes. This paper explores a novel six-strut compliant parallel mechanism based on the development of wide-range flexure hinges, and in this system the repeatability and resolution of sub-micron scale can be achieved over cubic centimeter motion range. The system stiffness, as a very important performance for compliant parallel mechanisms, directly influences the workspace, load-carrying capacity and driving-load capacity, etc. The system stiffness depends on the parallel mechanism's geometric dimensions and spatial layout, which is discussed in detail in this paper. The stiffness equation of individual flexure hinge is established firstly, and then the stiffness of the whole mechanism is modeled via assembling stiffness matrices and formulating constraint equations. Finally, the system stiffness influence plots are presented and discussed. The stiffness research on the six-strut compliant parallel mechanism provides further theoretical principles for designing and developing this kind of precision parallel devices.     

基于动力学性能的全柔性机构优化设计

全柔性机构是一种新型机构,多应用在精密定位场合。为保证该机构具有很高的定位精度和较强的抗环境干扰能力,仅以静力学性能作为指标进行机构的优化设计是不足以满足要求的,还需要对机构的动力学性能进行优化。研究以一具体的全柔性机构为例,给出一种基于机构动力学性能的结构优化设计方法。为此首先建立了该机构的动力学理论模型,为保证结果的准确性,还进行了有限元模拟;在设计过程中,同时考虑到了机构的静态特性与动态特性。该方法可有效地完成机构的尺度综合。     

Modeling and analysis of an over-constrained flexure-based compliant mechanism

Bridge-type micro-displacement amplifier with flexure hinges is a classic displacement amplification mechanism. Existing theoretic models cannot predict its amplification ratio and input stiffness accurately and make it very difficult to confirm the amplifier’s performance and error compensation by means of these models, which is very significant in ultra-precision positioning. This paper focuses on the development of design equations that can accurately calculate the ideal displacement amplification ratio and input stiffness of the amplifier based on the thought of statically indeterminate structure. Force Method, Maxwell–Mohr Method, principle of superposition and deformation compatibility are used together to establish uncanonical linear homogeneous equations. The analytical results are verified by FEA simulations. The influence of the geometric parameters on the amplifier performance is investigated. It is noted that amplifier performance is more sensitive to the longitudinal distance of flexure hinges. Besides, two same-sized amplifiers with the opposite output directions can be clearly differentiated by these equations.     

Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis

This paper presents the dimensionless empirical equations and graph expressions of three flexure hinges for compliant mechanism designs. The in-plane and out-of-plane stiffnesses of the flexure hinges are developed. The rotational precision, denoted by the midpoint stiffness, is derived for the purpose of optimized geometric design. Based on the developed methodologies, the influences of the geometric parameters on the performance of the flexure hinges are investigated, and the performance comparisons among the flexure hinges are conducted to further understand the characteristics of these kinds of compliant mechanisms.     

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.     

基于伪刚体模型法的全柔性机构位置分析

柔性机构是一种依靠构件元素的弹性变形传输所希望运动的机构。具有集中柔度的全柔性机构是其中的一种类型，其特征是机构中传统形式的铰链全部被柔性铰链所代替。对它的研究，近年来也已成为一个热点。为探索这类全柔性机构的运动学问题，首先建立起柔性铰链变形刚度模型。在此基础上，提出了一种扩展的伪刚体模型法，很好地解决了机构的位置正、反解问题。     

Accurate low DOF modeling of a planar compliant mechanism with flexure hinges: the equivalent beam methodology

A methodology for accurate and efficient finite elements method (FEM) simulations of planar compliant mechanisms with flexure hinges is presented. First, using symmetry/antisymmetry boundary conditions and 3D elements, one-eighth of a single hinge is simulated to determine its true stress/stiffness characteristics. A set of fictitious beams is derived, which have the identical characteristics. This set is used in conjunction with other beams that model relatively stiff links to generate an equivalent model of an entire mechanism consisting of the beam elements only. The model has a low number of degrees-of-freedom (DOF) and appears to be more accurate than any 2D FEM models, even those with very large number of DOF. The methodology has been developed specifically for the right circular flexure hinge; however, it can be applied to all types of revolute flexure hinges.     

On the modeling of flexure hinge mechanisms with finite beam elements of variable cross section

In this paper, a modeling technique for flexure hinge mechanisms is studied. Beam elements of variable cross sections are deployed within a finite element procedure to model a circular flexure hinge. The resulting finite element model has very few degrees of freedom and is accurate in both static and dynamic analysis. Furthermore the modeling approach is applied to an amplifier mechanism. Comparing the results of the proposed model with a 3D finite element reference model, high accuracy for a broad spectrum of hinge parameters is reported while reducing the number of degrees of freedom immensely.     

Design of a low-cost nano-manipulator which utilizes a monolithic, spatial compliant mechanism

This paper presents the design of a novel, low-cost nano-manipulator which uses a six-axis compliant mechanism which is driven by electromagnetic actuators. The mechanism's monolithic, planar geometry is easily fabricated via planar manufacturing processes, enables compact packaging and incorporates a flexure mechanism for achieving small transmission ratios. The manipulator tolerates ±1 mm actuator misalignment with less than 0.1% full-scale position error. Measurements over a 100 nm × 100 nm × 100 nm work volume show resolution better than our measurement capability of 5 nm and open-loop parasitic errors less than 5 nm. Measurements over a 100 μm × 100 μm × 100 μm work volume show open loop errors less than 0.2% full-scale. The mechanism's equilateral symmetry and planar geometry make it possible to limit thermal drift in position and orientation to less than 23 nm and 4 μrad over a 30 min start up period. The nano-manipulator, built at US$ 2000 cost (excludes electronics), is used as an ultra-precision fiber optic aligner.     

Development of models for additively manufactured actuators using compliant Wren mechanism

Compliant Wren mechanisms (CWM) constitute specific compliant structures of particular interest. Derived from Wren mechanisms, they can exhibit a large variety of motions, from quasi translation to quasi rotation. In this paper, the development of models for the analysis and synthesis of CWM is considered. A kinematic model is introduced first to assess all possible motions when used as an actuator. Then the static model and stress expressions are derived to help their design. These derivations are achieved for two types of geometries, corresponding to the geometries of interest. CWM are filigree structures, whose manufacturing is difficult to consider without additive manufacturing. A specific work on their production using selective laser melting (SLM) is then achieved to ensure the reliability of their production. As a proof of concept, a pneumatically actuated component is then developed and tested. It is composed of two CWM of different geometries. It offers the possibility to obtain translation and rotation using a single pressure input. The developed models are investigated using finite element models and experiments using additively manufactured structures.     

Design and forward kinematics of the compliant micro-manipulator with lever mechanisms

This paper presents the forward kinematics of a five-bar compliant micro-manipulator. To overcome the limited displacement of such a flexure-based mechanism driven by piezoelectric actuators, lever mechanisms are utilized to enlarge the working range. The mechanical design of the micro-manipulator is firstly described. Mathematical formulations for the five-bar mechanism are described and the solutions are developed to decide the end-effector position in Cartesian space. The amplification factor of the lever mechanism is also derived based on the analytical solution of the four-bar linkages. The velocity of the end-effector is obtained by differentiating the forward position kinematic equation, and the local mobility index of the five-bar compliant mechanism is determined and analysed. Based on linearization of trigonometric functions and constant Jacobian matrix, numerical simulations are carried out to investigate the performance of the five-bar compliant manipulator and to determine the optimal geometric parameters for the configuration. The comparisons between the exact solution and simplified methodologies are conducted. Experiments are carried out to validate the established model and the performance of the developed micro-manipulator.     

Design,simulation and testing of an isotropic compliant mechanism

In this paper, the concept of isotropic compliance is extended to the field of compliant mechanisms. Starting from the design of a rigid-body mechanism, a planar compliant system is determined by applying the rigid-body replacement method. The static behaviour of the isotropic compliant mechanism is validated by finite element simulations and experimental tests. The extension of the proposed method to the Euclidean Space E(3) is discussed.