Design and analysis of a novel 6-DOF redundant actuated parallel robot with compliant hinges for high precision positioning

This paper presents the design and modeling of a new 6-DOF 8-PSS/SPS compliant dual redundant parallel robot with wide-range flexure hinges. This robot can achieve either high accurate positioning or rough positioning as well as a 6-DOF active vibration isolation and excitation to the payload placed on the moving platform. Adopting a kind of wide-range flexure hinge, we establish the kinematics model of the macro parallel mechanism system via the stiffness model and Newton–Raphson method, then we build up the dynamics model using Kane’s method for the micro-motion system. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for a novel compliant dual redundant parallel mechanism in order to achieve the feature of larger workspace, higher motion precision and better dynamic characteristics. The results will be helpful in modifying the structure of the prototype platform to enhance its high kinematics and dynamics properties.     

A CONSTITUTIVE MODEL FOR TRANSFORMATION, REORIENTATION AND PLASTIC DEFORMATION OF SHAPE MEMORY ALLOYS

A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys (SMAs). It is based on the concept that an SMA is a mixture composed of austenite and martensite, the volume fraction of each phase is transformable with the change of applied thermal-mechanical loading, and the constitutive behavior of the SMA is the combination of the individual behavior of its two phases. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. Making use of the Tanaka’s transformation rule modified by taking into account the effect of plastic deformation, the constitutive model of the SMA is obtained. The ferroelasticity, pseudoelasticity and shape memory effect of SMA Au-47.5 at.%Cd, and the pseudoelasticity and shape memory effect as well as plastic deformation and its effect of an NiTi SMA, are analyzed and compared with experimental results.     

Design and analysis of a compliant parallel pan-tilt platform

In combination of the advantages of both parallel mechanisms and compliant mechanisms, a compliant parallel mechanism with two rotational degrees of freedom is designed to meet the requirement of a lightweight and compact pan-tilt platform. Firstly, two commonly-used design methods i.e. direct substitution and Freedom and Constraint Topology are applied to design the configuration of the pan-tilt system, and similarities and differences of the two design alternatives are compared. Then inverse kinematic analysis of the candidate mechanism is implemented by using the pseudo-rigid-body model, and the Jacobian related to its differential kinematics is further derived to help designer realize dynamic analysis of the 8R compliant mechanism. In addition, the mechanism’s maximum stress existing within its workspace is tested by finite element analysis. Finally, a method to determine joint damping of the flexure hinge is presented, which aims at exploring the effect of joint damping on actuator selection and real-time control. To the authors’ knowledge, almost no existing literature concerns with this issue.     

Phenomenological constitutive model for a CNT turf

Carbon nanotubes (CNT), grown on a substrate, form a turf – a complex structure of intertwined, mostly nominally vertical tubes, cross-linked by adhesive contact and few bracing tubes. The turfs are compliant and good thermal and electrical conductors. In this paper, we consider the micromechanical analysis of the turf deformation reported earlier, and develop a phenomenological constitutive model of the turf. We benchmark the developed model using a finite element implementation and compare the model predictions to the results two different nanoindentation tests.The model includes: nonlinear elastic deformation, small Kelvin–Voigt type relaxation, caused by the thermally activated sliding of contacts, and adhesive contact between the turf and the indenter. The pre-existing (locked-in) strain energy of bent nanotubes produces a high initial tangent modulus, followed by an order of magnitude decrease in the tangent modulus with increasing deformation. The strong adhesion between the turf and indenter tip is due to the van der Waals interactions.The finite element simulations capture the results from the nanoindentation experiments, including the loading, unloading, viscoelastic relaxation during hold, and adhesive pull-off.     

Deformation of a fluid-filled compliant cylinder in a uniform flow

We investigated surface compliance effects of a fluid-filled object in flow on its shape and internal flow through numerical simulation. A two-dimensional compliant cylinder containing fluid in a flow is a simple model of a cell, e.g. an erythrocyte, leukocyte or platelet. The thin membrane of the cylinder consisted of a network of mass-spring-damper (MSD) systems, representing its mechanical characteristics. We assumed that the stiffness and damping coefficients were those of latex gum. The two-dimensional flow inside and outside the membrane was obtained by solving the two-dimensional Navier–Stokes equations by using the finite element scheme at Re=400, based on the external flow velocity and diameter of an initial circular cylinder. The deformation of the membrane was calculated by solving the equation of motion for an MSD system by using the fourth-order Runge-Kutta method. The compliant cylinder deformed more if its stiffness was smaller than that of latex gum. The initial circular section of the cylinder became oval, with a flat front and a convex rear. The aspect ratio of the lateral to streamwise axis length of the oval became larger than unity, and increased with decreasing stiffness. The drag coefficient of the oval cylinder became larger than that of the circular cylinder, and increased with decreasing stiffness. The partial vibration at the rear, caused by shedding vortices, induced oscillating internal flows between two antinodes of the vibrating membrane. Since the object with smaller stiffness had higher ductility, velocity fluctuations of the external flow influenced the internal flow of the compliant object through deformation of the membrane.     

基于超导的全张量重力梯度敏感头设计

基于超导的迈斯纳效应与超导量子干涉技术,结合柔性并联机构理论,设计一种基于超导的全张量重力梯度敏感头。敏感头采用6个完全相同的同时具有移动与转动自由度的敏感结构,对称的布置在正六面体外,对称面的两个敏感结构相对旋转90°成垂直状态。轴向间距使两个敏感结构直接测量重力梯度轴向分量,相互垂直使两个敏感结构既可以测量重力梯度交叉分量,也可以测量共模角加速度。利用超导线圈的电感变化响应质量块位移,进一步通过超导回路将其转变为磁场变化,并由超导量子干涉器进行检测。敏感结构采用8分支的柔性并联机构支承,构成空间对称的形式,可以实现对称的力学特性,保证各处的柔性铰链产生均匀变形,减少非对称的偏移,避免单一铰链的应力集中,具有沿轴移动刚度与绕轴转动刚度小、非设计的寄生误差方向刚度大的优势。在惯性系下的全张量重力梯度值可由坐标变换得到,可以预期得到1E的测量精度。     

单自由度超弹性SMA减振结构随机振动控制理论研究

利用形状记忆合金（Shape Memory Alloy,简称SMA）丝的超弹性,提出了一种具有复位功能的阻尼器。在SMA丝的Graesser本构模型基础上,建立了阻尼器恢复力的滑移双线性模型;假定滞回面积相等,提出了恢复力的滑移刚塑性模型以近似简化滑移双线性模型。采用等价线性化法建立了单自由度超弹性SMA减振结构在高斯白噪声激励下的平稳随机振动分析公式。通过一算例,考虑不同激励谱密度和结构阻尼比：比较了等价线性法和蒙特卡罗（Monte Carlo）模拟法计算的结构振动响应（位移标准差和速度标准差）,证明了SMA减振结构随机振动控制理论的有效性;比较了等价线性减振结构和无控结构的动力特性（刚度和阻尼比）和振动响应,说明了SMA阻尼器能提高结构的刚度和阻尼比,因而可有效抑制结构的振动。     

Bending actuation in polyurethanes with a symmetrically graded distribution of one-way shape memory alloy wires

Structures are being actuated by embedding shape memory alloy (SMA) wires into compliant materials, such as polyurethane. To achieve bending actuation, these wires are placed in opposing wire configurations, where multiple wires are often employed to enhance the amplitude of the bending actuation response. In this investigation, a procedure has been developed for fabricating polyurethanes with a symmetrically graded distribution of SMA wires. The effects of grading the distribution of one-way SMA wires have been characterized using full-field displacement deformation measurements obtained with the digital image correlation (DIC) technique. These measurements have been used in a one-dimensional (1D) model of bending actuation to determine the “equivalent two-way shape memory effect (SME)” of the graded wire distribution. To utilize the 1D actuation model, the constitutive properties of the polyurethane structure predicted by rule-of-mixture formulations were reduced to account for the differences in strain between the SMA wires and the polyurethane matrix. The graded wire distribution was also found to significantly stiffen the polyurethane structure. The level of equivalent two-way SME therefore became limited by the maximum recovery stress of the SMA wires, with a maximum level that was approximately 75% less than previously measured levels in an opposing wire configuration. However, the bending actuation behavior was more symmetric, and the actuated bending deflections were similar to those observed when using more compliant materials. It was also predicted that the symmetrically graded wire distribution would exhibit a better balance between actuation amplitude and uniformity, which combined with the more symmetric actuation behavior makes the graded wire distribution potentially more desirable for achieving higher actuation frequencies with distributed actuation concepts in new applications, such as miniaturized double diaphragm pumping devices.     

Reprint of “Size dependence and orientation dependence of elastic properties of ZnO nanofilms” [In. J. Solids Struct. 45 (2008) 1730–1753]

The elastic properties of ZnO nanofilms with different film thickness, surface orientations and loading directions are investigated by using molecular mechanics (MM) method. The size dependence of elastic properties is relevant to both the film surface crystallographic orientation and loading direction. Both atomic structure analysis and energy calculation are employed to identify the mechanisms of the size-dependent elastic properties, under different loading directions and surface orientations. Upon small axial deformation, the relationship between intralayer and interlayer bond length variation and film elastic stiffness is established; it is found that the atomic layers with larger bond length variation have higher elastic stiffness. The strain energies of atomic layers of ZnO nanofilm and bulk are decoupled, from which the stiffness of film surface, intralayers, and interlayers are derived and compared with their bulk counterparts. The surface stiffness is found to be much lower than that of the interior layers and bulk counterpart, and with the decrease of film thickness, the residual tension-stiffened interior atomic layers are the main contributions of the increased elastic modulus of ZnO nanofilms.     

仿鸡脖子刚柔耦合结构的仿生机理及大变形建模

观察表明,禽类颈部普遍具有刚柔耦合的特点,在运动过程中,可以辅助身体运动,使得头部产生大变形.在机器人、航空航天等领域普遍需要具有大变形、变刚度等特征的结构实现相关功能.受禽类脖子结构的启发,提出了一种仿鸡脖子刚柔耦合结构,阐明仿鸡脖子的仿生机理并建立大变形模型.首先,从鸡颈部的生物解剖出发,发现仿鸡脖子结构势必具有多自由度刚柔耦合的特征,因此,根据鸡脖子骨骼的构型构造出单节仿生标准单元,根据肌肉的连接方式厘清节间弹性连接,建立起仿鸡脖子刚柔耦合结构的力学模型;然后,通过定义连接矩阵描述节间弹性元件的分布和作用,由此得到任意运动下的标准单元的力平衡方程;最后,选取了几种具有代表性的工况,通过有限元分析验证理论建模方法的准确性并展示结构的非线性变刚度特征;在4种典型平面弯曲工况下得到不同变形与发力肌肉群的对应关系.文章提出的仿鸡脖子刚柔耦合结构建模具有仿生机理清晰、适合大变形计算及结构具有非线性刚度特征等特点,也解释了禽类颈部变形机理.     

Size dependence and orientation dependence of elastic properties of ZnO nanofilms

The elastic properties of ZnO nanofilms with different film thickness, surface orientations and loading directions are investigated by using molecular mechanics (MM) method. The size dependence of elastic properties is relevant to both the film surface crystallographic orientation and loading direction. Both atomic structure analysis and energy calculation are employed to identify the mechanisms of the size-dependent elastic properties, under different loading directions and surface orientations. Upon small axial deformation, the relationship between intralayer and interlayer bond length variation and film elastic stiffness is established; it is found that the atomic layers with larger bond length variation have higher elastic stiffness. The strain energies of atomic layers of ZnO nanofilm and bulk are decoupled, from which the stiffness of film surface, intralayers, and interlayers are derived and compared with their bulk counterparts. The surface stiffness is found to be much lower than that of the interior layers and bulk counterpart, and with the decrease of film thickness, the residual tension-stiffened interior atomic layers are the main contributions of the increased elastic modulus of ZnO nanofilms.     

曲壁蜂窝夹层板的振动特性研究

曲壁蜂窝具有负刚度特性,可以在大变形过程中吸收能量、抗冲击,并且在冲击过后可以自我恢复而不像传统蜂窝被压溃。本文将曲梁构成的负刚度蜂窝作为芯层,建立夹层板的动力学模型;推导出了曲壁负刚度蜂窝胞元的等效弹性参数,将其周期性排列为蜂窝芯,应用Reddy高阶剪切变形理论、Von-Karman大变形关系和Hamilton原理推导了负刚度蜂窝夹层板的非线性动力学方程;应用Navier法计算了四边简支边界条件下的固有频率。并利用有限元软件ABAQUS建立模型,计算固有频率,与理论计算结果进行比较,结果显示二者的计算结果具有较好的一致性,验证了芯层等效弹性参数及模型的有效性。探讨了在蜂窝胞元具有较高吸能情形下,夹层板在不同芯层厚度、不同芯厚比以及不同胞元曲壁厚度时的固有频率的变化特性。     

Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers

Thermal post-buckled vibration of laminated composite doubly curved panel embedded with shape memory alloy (SMA) fiber is investigated and presented in this article. The geometry matrix and the nonlinear stiffness matrices are derived using Green–Lagrange type nonlinear kinematics in the framework of higher order shear deformation theory. In addition to that, material nonlinearity in shape memory alloy due to thermal load is incorporated by the marching technique. The developed mathematical model is discretized using a nonlinear finite element model and the sets of nonlinear governing equations are obtained using Hamilton’s principle. The equations are solved using the direct iterative method. The effect of nonlinearity both in geometric and material have been studied using the developed model and compared with those published literature. Effect of various geometric parameters such as thickness ratio, amplitude ratio, lamination scheme, support condition, prestrains of SMA, and volume fractions of SMA on the nonlinear free vibration behavior of thermally post-buckled composite flat/curved panel been studied in detail and reported.     

Mechanical activation of the transfer process in polymer systems

Mechanical activation (change in reactivity or activation energy) of polymer systems with a locally nonequilibrium (relaxation) response to mechanical perturbations is studied. Mechanical activation in such systems is caused by deviation of the medium microstructure from the state of local thermodynamic equilibrium. A system of equations for shear and uniaxial (elongation) deformation modes is formulated. The influence of local nonequilibrium in the medium microstructure on the mechanism and regular features of the macroscopic transfer process and also the effect of the stressed state of the polymer system and structural, kinetic, and orientation (steric) factors on the reactivity of polymer systems are analyzed. It is demonstrated that the reactivity of systems with a complicated internal structure has an energetic entropic character and depends on the reaction zone size (effect of a “nanoreactor”). The ranges of mechanical activation parameters affecting the reactivity and activation energy of polymer systems are determined for the shear and uniaxial modes of their deformation.     

CONTINUUM TOPOLOGY OPTIMIZATION FOR MONOLITHIC COMPLIANT MECHANISMS OF MICRO-ACTUATORS

A multi-objective scheme for structural topology optimization of distributed compliant mechanisms of micro-actuators in MEMS condition is presented in this work, in which mechanical flexibility and structural stiffness are both considered as objective functions. The compliant micro-mechanism developed in this way can not only provide sufficient output work but also have sufficient rigidity to resist reaction forces and maintain its shape when holding the work-piece. A density filtering approach is also proposed to eliminate numerical instabilities such as checkerboards, mesh-dependency and one-node connected hinges occurring in resulting mechanisms. SIMP is used as the interpolation scheme to indicate the dependence of material modulus on element-regularized densities. The sequential convex programming method, such as the method of moving asymptotes (MMA), is used to solve the optimization problem. The validation of the presented methodologies is demonstrated by a typical numerical example.     

Shape memory elastic foundation and supports for passive vibration control of composite plates

The paper presents an approach to passive vibration control of shear deformable and thin plates. The first of two methods of vibration control employs prestressed shape memory alloy (SMA) wires embedded in sleeves attached to the surface of the plate. The spacing between the wires can be arbitrary and variable enabling the development of a SMA support system for maximum control with minimum additional weight. The other method considered in the paper utilizes SMA wires supporting the plate at strategically selected points. The mechanism of passive control includes two components: (1) SMA wires prestressed as a result of constrained phase transformation act as an elastic foundation with a variable stiffness and (2) energy dissipation occurs as a result of hysteresis in superelastic wires vibrating together with the structure. As follows from examples, it is possible to achieve a significant reduction of the vibration amplitude over a broad spectrum of driving frequencies using any of two methods considered in the paper.     

Thermo-Mechanical Model and Thermal Analysis of Hollow Cylinder Planetary Roller Screw Mechanism

Planetary roller screw mechanism (PRSM) is widely used for rapid and precise motion translation from rotary into linear motion due to its high stiffness and high position accuracy. However, a high speed PRSM drive system naturally generates significant amount of frictional heat at the contact interfaces, which causes thermal deformation and thermal error and reduces motion accuracy. Preload is usually applied to remove the axial backlash of the PRSM for achieving high accuracy and great stiffness. However, more frictional heat is produced by such preload. On the other hand, larger numbers of angular contact bearings are needed to support the heavy axial load. The friction heat generated in support bearings has also to be investigated. In order to estimate the thermal distribution and thermal error of the hollow cylinder PRSM, a thermo-mechanical model based on finite element method (FEM) is developed, where heat generation from the two main sources of the PRSM, the parameters calculation of heat transfer coefficient and other thermal boundary conditions were studied. The presented model is proven capable of investigating temperature distribution, thermal error, and cooling performances of coolants of the PRSM system.     

鲫鱼皮肤和肌肉的力学性能研究

鱼在水中游动时,参与鱼体弯曲变形的组织和器官与水媒介相互作用,形成了不同的游动模式和变形方式。为了更好地理解鱼体变形机制并为今后的流固耦合计算提供基础实验数据,本文采用万能试验机进行单轴拉伸试验,对鲫鱼皮肤和肌肉等生物材料的力学性能进行研究。通过破坏实验的方式确定其杨氏模量,通过松弛实验的方式确定其归一化松弛函数。针对皮肤和肌肉的生物材料粘弹性性质,给出本构方程。通过简化为标准线性固体模型进行讨论,得到的结论是:鲫鱼游动过程中以很小的能量损耗为代价,增加了其有效刚度。     

绳牵引并联机器人弹性变形对动平台位姿精度的影响Influence of elastic deformation on pose precision of moving platform for wire-driven parallel robot

针对六自由度绳牵引并联机器人在风洞试验中的应用,分析了牵引绳弹性变形对动平台位姿精度的影响,其实质是运动学正解问题。鉴于牵引绳只能受拉力的特点,以及风洞试验的目的,须考虑系统的刚度和绳拉力的优化。基于系统运动学和动力学方程,推导了系统刚度矩阵;以提高系统主方向刚度为目标函数,对绳拉力进行了动态优化分布,以求解弹性变形;采用L‐M数值方法进行运动学正解,量化分析了两种不同弹性模量的牵引绳对系统刚度的影响,以及弹性变形引起的动平台位姿误差。研究结果表明,以刚度增强为优化目标,有利于提高系统稳定性;采用弹性模量较大的牵引绳,可以有效提高系统的刚度,减小绳长变形引起的飞行器模型位姿误差,满足风洞试验的精度要求。上述结果可为后续机构的改善和系统高精度的力位混合控制提供依据和指导。