Analysis of a planar 3 degree-of-freedom adjustable compliance mechanism

In this work, a planar three degree-of-freedom parallel mechanism as another type of assembly device which utilizes joint compliances is proposed. In order to generate the desired operational compliance characteristics at RCC point, these joint compliances can be adjusted either by properly replacing the joint compliances or by actively controlling stiffness at joints. The operational compliance matrix for this mechanism is obtained explicitly by symbolic manipulation, and its operational compliance characteristics are examined. It is found that the RCC point exists at the center of the workspace when the mechanism maintains symmetric configurations. Compliance characteristics and its sensitivity of this mechanism are analyzed with respect to the magnitude of the diagonal compliance components and two different matrix norms by measuring compliance sensitivity. It is expected that the analysis results provide the designer with a helpful information to determine a set of optimal parameters of this RCC mechanism.     

Tricept机械手静刚度解析建模方法

以Tricept机械手的3自由度球坐标型并联机构为例,提出含恰约束支链的球坐标型并联构型装备静刚度解析建模方法。该方法首先借助子结构综合思想将末端执行器位姿变形分解为无约束主动支链的拉压变形、恰约束支链的弯曲变形及其扭转变形3个部分,然后利用虚功原理和结构矩阵法建立各子结构系统的静柔度模型,最后借助线性叠加原理组集整机末端静柔度模型。在建模过程中,侧重研究恰约束支链弯曲刚度以及铰链刚度的建模方法。在此基础上,考察了Tricept机械手中3自由度并联机构静刚度在工作空间中的变化规律,并借助全局性能指标评价了主要构件柔度对整机柔度的贡献。     

Stiffness modeling of flexure parallel mechanism

Stiffness plays an important role in the precise performance of flexure-based ultra-precision manipulation systems. The finite element method (FEM) is currently used to determine the stiffness of the flexure parallel mechanism (FPM) with specified dimensions and free shape. This paper presents the stiffness model based on the way the flexure members are connected together in serial or parallel combinations. The modeling allows one to formulate the functional relationship between stiffness and dimensions as well as the free shape of the FPM in the design process. For illustration, stiffness matrices of a double linear spring and a three degree-of-freedom (DOF) translational flexure parallel mechanism are established. The proposed analytical model is validated by FEM model and experiments.     

3自由度柔性微机器人的静刚度分析

柔性微机器人要求具有很高的定位精度，而其静刚度在很大程度上决定着这一指标。针对目前对柔性微机器人静刚度分析中存在的不足，采用了结构分析中的柔度矩阵法：首先建立起机构中柔性单元的柔度模型，同时通过不同坐标系间的转换和单元节点处位移协调方程和力平衡方程的建立，递推出机器人末端相对参考坐标系下的静刚度矩阵。最后，以3自由度并联柔性微机器人为实例分析了该机器人的静刚度。分析表明：利用柔度矩阵法分析柔性微机器人运动学问题不仅便于计算，更接近柔性机构的本质。     

Modeling and design of planar parallel-connection flexible hinges for in- and out-of-plane mechanism applications

The paper studies the planar parallel-connection, small-deformation flexible hinge chains formed of serially-coupled individual segments with variable cross-sections. It introduces the concept of virtual flexible hinge that is quasi-statically equivalent to the actual parallel-hinge configuration. General compliance and stiffness matrices are formulated for the virtual hinge under in-plane and out-of-plane loads by combining the transformed compliances of the individual hinge segments. Two classes are specifically analyzed: one comprises geometrically parallel, straight-axis hinge designs and the other includes concentric, circular-axis hinge configurations. From each class, particular designs with identical and transversely symmetric hinges of right circularly corner-filleted geometry are further investigated. Specifically, the behavior of parallelogram mechanisms with straight-axis hinges and of stage devices with circular-axis hinges is analyzed. Their elastic responses are validated by finite element analysis and their stiffnesses are subsequently studied in terms of offset geometric parameters.     

一种新型3自由度大行程微定位平台设计与分析

为解决微定位平台大行程与高精度之间的矛盾,提出一种新型的3自由度柔性并联机构。该机构三条支链采用特殊方式与动平台相连,使整体机构结构紧凑且具有良好的力学传递性能。同时,机构采用行程大,分辨率高,便于控制的电磁驱动器作为驱动部件,保证机构在不需要引入放大机构的前提下便可获得较大的行程和较高的分辨率。使用大行程柔性铰链代替普通的球铰,降低了加工制造难度和机构刚度模型的求解难度。采用螺旋理论分析了3-P(4S)并联机构末端运动特征,结合单元刚度矩阵法和矩阵位移法推导了3-P(4S)柔性并联机构的静刚度模型,并采用ANSYS进行了分析验证。     

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.     

Mechanical design,modeling, and identification for a novel antagonistic variable stiffness dexterous finger

This study traces the development of dexterous hand research and proposes a novel antagonistic variable stiffness dexterous finger mechanism to improve the safety of dexterous hand in unpredictable environments, such as unstructured or man-made operational errors through comprehensive consideration of cost, accuracy, manufacturing, and application. Based on the concept of mechanical passive compliance, which is widely implemented in robots for interactions, a finger is dedicated to improving mechanical robustness. The finger mechanism not only achieves passive compliance against physical impacts, but also implements the variable stiffness actuator principle in a compact finger without adding supererogatory actuators. It achieves finger stiffness adjustability according to the biologically inspired stiffness variation principle of discarding some mobilities to adjust stiffness. The mechanical design of the finger and its stiffness adjusting methods are elaborated. The stiffness characteristics of the finger joint and the actuation unit are analyzed. Experimental results of the finger joint stiffness identification and finger impact tests under different finger stiffness presets are provided to verify the validity of the model. Fingers have been experimentally proven to be robust against physical impacts. Moreover, the experimental part verifies that fingers have good power, grasping, and manipulation performance.     

Error analysis of a parallel mechanism considering link stiffness and joint clearances

In order to utilize a parallel mechanism as a machine tool component, it is important to estimate the errors of its end-effector due to the uncertainties in parts. This study proposes an error analysis for a new parallel device, a cubic parallel mechanism. For the parallel device, we consider two kinds of errors. One is a static error due to link stiffness and the other is a dynamic error due to clearances in the parts. In this study, we propose a stiffness model for the cubic parallel mechanism under the assumption that the link stiffness is a linear function of the link length. Also, from the fact that the errors of u-joints and spherical joints are changed with the direction of force acting on the link, they are regarded as a part of link errors, and then the error model is derived using forward kinematics. Lastly, both the error models are integrated into the total error, which is analyzed with a test example that the platform moves along a circular path. This analysis can be used in predicting the accuracy of other parallel devices.     

Design and stiffness analysis of a compliant spherical chain with three degrees of freedom

This paper introduces and investigates a compliant spherical 3R open chain that is obtained by the in-series connection of three identical circularly-curved beam flexures with coincident centers of curvature and mutually orthogonal axes of maximum rotational compliance. The considered open chain is intended to be used directly as a spherical mechanism in pointing devices or as a complex spherical flexure for the development of spatial parallel manipulators. The compliance matrix of the proposed chain is first determined via an analytical procedure. After finite element validation, the obtained equations are used in a parametric study to assess the influence of circularly-curved beam flexure geometric parameters on the overall stiffness performances of the considered compliant spherical 3R open chain. In addition, comparison with an equivalent compliant spherical chain employing straight beam flexures is reported to highlight the added benefits of using circularly-curved beam flexures in terms of reduced parasitic motions.     

含有柔性铰链并联机器人的刚度分析及刚度优化配置

以一类含有柔性铰链的并联机器人为研究对象，在位置分析的基础上，导出摄动位移间映射关系，为其建立了刚度分析模型。此外，还探讨了有关刚度性能指标的问题，最后以该性能指标为目标函数对其进行了刚度优化配置。     

Effective elastic properties of damaged isotropic solids

In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two- and three-dimensional isotropic solids.     

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     

Global stiffness and natural frequency analysis of distributed compliant mechanisms with embedded actuators with a general-purpose finite element system

Distributed 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 modeling approach for analysis of system stiffness and natural frequency behavior of a distributed compliant mechanism with embedded actuators such as lead zirconate titanate (PZT) actuators with a general-purpose finite element system, in particular ANSYS. Use of a general-purpose system has a great practical significance to designers in manufacturing systems. The paper also includes a comparison of the proposed approach with other three approaches in literature to demonstrate the unique feature of the proposed approach. Finally, a particular distributed compliant mechanism with three embedded PZT actuators, which has been used as a part of the cell manipulator system, is analyzed to provide us with some insight of the vibration and stiffness behavior of the system. Such knowledge is important on the control of a distributed compliant manipulator.     

Synthesis and stiffness modeling of XYZ flexure parallel mechanisms with large-motion and decoupled kinematic structure

This paper systematically studies structure synthesis and dimension optimization of XYZ flexure parallel mechanisms (FPMs) with large-motion and decoupled kinematic structure. Different from structure synthesis of rigid-body mechanisms, structure synthesis of flexure mechanisms is constrained by the limitations inherent in flexure mechanisms. These limitations are investigated and summarized as the structure constraints. With consideration of these structure constraints, the configurations of the decoupled XYZ-FPMs are synthesized using the Screw Theory. The synthesized XYZ-FPMs also possess large motion range, due to integration of a new type of large-motion prismatic joint designed in this paper. The stiffness models of the synthesized XYZ-FPMs are formulated. A 3-PPP XYZFPM is developed as the case of the studies of structure synthesis and stiffness modeling.     

Multi-objective optimization of a 3-DOF translational parallel kinematic machine

In this paper, stiffness modelling and analysis of a typical 3-DOF parallel kinematic machine (PKM) that provides translational motion along X, Y and Z axes is presented. The mechanism consists of three limbs each having an arm and a forearm with prismatic-revoluterevolute-revolute joints (PRRR). The joint arrangement is in such a way that the moving or tool platform maintains same orientation in the entire workspace. Through inverse kinematics, the joint angles for a given position of tool platform necessary for the stiffness modelling and analysis are obtained. The stiffness modelling is based on the compliance matrices of arm and forearm of each limb. Typical non-dimensional performance indices, namely, workspace volume index (WVI), global translational stiffness index (GTSI), and global rotational stiffness index (GRSI), are introduced and used to study the influence of dimensions. Attempts are also made to find the optimal dimensions of the translational PKM using multi-objective optimization based on the genetic algorithms (MOGA) in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the PKM under study.     

The development of pivot bearing with multiple degrees of freedom: 1st report: Prototype of pivot bearing with two degrees of freedom

This paper deals with the prototype of a new pivot bearing having two degrees of freedom. The idea of the pivot bearing is based on a continuous velocity joint (CVJ). The experimental axial stiffness and contact pressure are compared with those determined by theoretical analysis. Then, it is confirmed that the pivot bearing swings smoothly with a range of ±25°. Furthermore, the stiffness of the bearing increases as the swinging angle becomes larger. Therefore, this newly developed pivot bearing may be applied to a parallel mechanism, a joint of robot and so on.     

3-RRR平面并联机构刚度分析

刚度是并联机构重要性能指标,为了评价并联机构刚度,提出了一种刚度评价方法.基于3-RRR机构的逆运动学模型,推导出其雅可比矩阵.在力雅可比矩阵的基础上,给出了刚度评价指标,该指标不仅适用于3-RRR并联机构,而且可以应用于其它并联机构.将提出的刚度指标应用于3-RRR并联机构,数值仿真结果表明3-RRR机构在工作空间中具有对称的刚性.     

解耦球面转动并联机构的运动分析与验证

详细分析了一种解耦球面转动并联机构的运动特性,利用速度关系证明该机构具有3个完全解耦的转动自由度,并具有工作空间大、刚度均匀一致、误差分布全局各向同性的优点.针对机构约束冗余的不足,进一步提出了避免过约束的改进机型.     

Improved Stiffness Modeling for An Exechon-Like Parallel Kinematic Machine(PKM) and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy, stiffness and workspace of machining equipment. Therefore, a 5-DOF(degrees of freedom) parallel kinematic machine(PKM) with redundant constraints is proposed. Based on the kinematics analysis of the parallel mechanism using intermediate variables, the kinematics problems of the PKM are solved through equivalent kinematics model. The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM, where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis. And the stiffness model of the parallel mechanism is improved by correction coefficient matrix, each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism. The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively. The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism. To enhance the machining accuracy of the PKM, the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece. A plate workpiece taken as example is examined in the case study section, which demonstrates the effectiveness of optimization method.