Pseudo-rigid-body Model for Corrugated Cantilever Beam Used in Compliant Mechanisms

Common compliant joints generally have limited range of motion, reduced fatigue life and high stress concentration. To overcome these shortcomings, periodically corrugated cantilever beam is applied to design compliant joints. Basic corrugated beam unit is modeled by using pseudo-rigid-body method. The trajectory and deformation behavior of periodically corrugated cantilever beam are estimated by the transformation of coordinate and superposition of the deformation of corrugated beam units. Finite element analysis（FEA） is carried out on corrugated cantilever beam to estimate the accuracy of the pseudo-rigid-body model. Results show that the kinetostatic behaviors obtained by this method, which has a relative error less than 6%, has good applicability and corrugated cantilever beam has the characteristics of a large range of motion and high mechanical strength. The corrugated cantilever beam is then applied to design a flexible rotational joint to obtain a larger angle output. The paper proposes a pseudo-rigid-body model for corrugated cantilever beam and designed a flexible rotational joint with large angle output.

Stiffness Analysis of Corrugated Flexure Beam Used in Compliant Mechanisms

Conventional flexible joints generally have limited range of motion and high stress concentration. To overcome these shortcomings, corrugated flexure beam（CF beam） is designed because of its large flexibility obtained from longer overall length on the same span. The successful design of compliant mechanisms using CF beam requires manipulation of the stiffnesses as the design variables. Empirical equations of the CF beam stiffness components, except of the torsional stiffness, are obtained by curve-fitting method. The application ranges of all the parameters in each empirical equation are also discussed. The ratio of off-axis to axial stiffness is considered as a key characteristic of an effective compliant joint. And parameter study shows that the radius of semi-circular segment and the length of straight segment contribute most to the ratio. At last, CF beam is used to design translational and rotational flexible joints, which also verifies the validity of the empirical equations. CF beam with large flexibility is presented, and empirical equations of its stiffness are proposed to facilitate the design of flexible joint with large range of motion.

Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the crosssection(i.e., the thickness and the width). After reviewing the available equations, two thickness-to-width ratio Independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design Insights are obtained. These equations, together with the previous work on symmetric equations for calculating torsional compliance, provide a convenient and effective way for designing and optimizing torsional beams in compliant mechanisms.

Simulation optimal design of a compliant mechanism with circular notch flexure hinges based on the equivalent beam methodology

This paper presents an in-depth study of Equivalent beam model (EBM).Firstly three-dimensional (3D) finite element analysis (FEA) model for circular flexure hinge developed by Zettl et al.was verified by the comparison with Smith's experimental results and the 3D FEA model was feasible within 5.5% error.Then the accuracy of Timoshenko short-beam due to shear force was verified based on finite element method.The results showed that the EBM has good accuracy within 5% error for 1≤r/t≤3.Finally the EBM methodology was applied for the simulation optimal design of a bridge-type compliant mechanism.The results showed that the EBM methodology has very high numerical efficiency and satisfactory accuracy for simulation optimal design of planar compliant mechanism with flexure hinges.

微流体装置力源机构的优化设计

为解决微流控系统中流体介质贮存装置输出压力不稳定等问题,设计了一种柔顺机构作为装置的力源机构。该柔顺机构基于正负刚度叠加理论设计,由四根固定导向梁和两根平面弹簧组成。首先,利用链式梁约束模型和广义打靶法分别求解出固定导向梁和平面弹簧的位移-载荷特性,建立优化模型,得到了满足设计要求的最优解。然后,为验证计算模型的准确性,使用ANSYS对柔顺梁进行大变形分析,结果显示该计算模型和有限元分析相比,误差小于1%。最后,通过实验发现该柔顺机构输出力的实验值和理论设计值存在误差,经过分析发现是加工精度、材料弹性模量误差以及只考虑了中性轴的变形等原因所导致的。

Enabling the transfer matrix method to model serial-parallel compliant mechanisms including curved flexure beams

Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.

Free flexural vibration of a partially wet tapered Timoshenko beam with intermittent mass and stiffness variations, eccentric tip mass and non-classical foundation

A compliant tower is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with parallel linear and torsional dampers(Kelvin-Voigt model). The superstructure adds to the kinetic energy of the system without affecting the potential energy, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its natural frequencies further. The empty space factor due to the truss-type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes satisfying the end condition. The weights are evaluated by the Rayleigh-Ritz(RR) method, and verified using finite element method(FEM). The weight of the superstructure acts as an axial compressive load on the beam. Kelvin-Voigt model of structural damping is included.A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. A parametric study is done for various magnitudes of tip mass and various levels of submergence. The computational efficiency and accuracy of the Rayleigh-Ritz method, as compared to the FEA, has been demonstrated. The advantage of using closed-form trial functions is clearly seen in the efficacy of calculating the various energy components in the RR method.

基于半圆型波纹周期梁的柔顺恒力机构优化设计

为了解决柔顺恒力机构中正刚度模块的几何非线性问题,基于半圆型波纹周期梁设计了正刚度模块,负刚度模块采用双稳态梁,利用正负刚度叠加原理设计了柔顺恒力机构。采用莫尔积分法和柔度矩阵法建立了正刚度模块的理论模型,采用椭圆积分法建立了负刚度模块的理论模型,并通过ANSYS有限元仿真软件分析了柔顺恒力机构的力-位移曲线以验证理论模型,两者相对误差在10%以内。为了扩大恒力区间范围,采用响应面法对柔顺恒力机构的几何参数进行优化,并对影响恒力范围的几何参数进行了灵敏度分析。利用3D打印技术加工柔顺恒力机构样机进行实验验证,实验结果表明,机构能在输入位移1.1~6.2 mm的范围内保持约18.8 N的恒力,验证了所设计的柔顺恒力机构的可行性、优化方法的有效性和理论模型的准确性。

一种新型柔顺机构设计方法的研究

大变形柔顺机构的设计由于几何非线性的关系,需要利用有限元软件分析研究,而不同宽度的梁单元在有限元建模时并不符合实际机构的设计。提出一种柔顺机构连接器,通过连接器与不同梁单元的连接可以构成不同的柔顺机构,而对同一种柔顺机构由于不同的输入与输出,也会发生不同的变形。其次,对柔顺机构连接器进行有限元建模。最后,对设计域内的柔顺机构建立了拓扑优化设计的数学模型,从而可以通过数学模型的求解找到设计域内最优的设计方法。

具有单拐点大变形梁的柔顺机构伪刚体模型

为了分析柔顺机构中具有单拐点的大变形梁,基于伪刚体模型原理,提出一种用于模拟具有单拐点大变形梁的柔顺机构4R伪刚体模型.以伪刚体模型拐点位置误差最小为目标函数,运用优化方法得到模型的最优特征半径系数,应用线性回归方法得出模型的刚度系数.数值计算结果说明:提出的模型能够很好地模拟具有单拐点的柔顺杆末端及拐点位置.

部分浸入水中的柔性梁非线性自由振动

研究了浸入水中的柔性梁非线性自由振动,假设其底端具有线弹性扭转弹簧支撑,顶端附有不计体积的集中质量块。推导了梁的运动控制方程和边界条件,由于考虑了大挠度,法向运动和轴向运动是非线性耦合的,使用Morison方程给出了流体力的表达式,利用有限差分法和Runge-Kutta法数值分析了梁在真空中和在水中的自由振动,讨论了参数对振动模态、固有频率等的影响。

Design of Passive Constant‑Force End‑Effector for Robotic Polishing of Optical Reflective Mirrors

Polishing plays an indispensable role in optical processing,especially for large-aperture optical reflective mirrors with freeform surfaces.Robotic polishing requires effective control of the contact force between the robot and the mirror during processing.In order to maintain a constant contact force during polishing,traditional polishing robots rely on closed-loop control of air cylinders,whose performances heavily rely on high-fidelity force sensing and real-time control.This paper proposes to employ a compliant constant-force mechanism in the end-effector of a polishing robot to passively maintain a constant force between the robot and the mirror,thus eliminating the requirement for force sensing and closed-loop control.The compliant constant force mechanism utilizing the second bending mode of fixed-guided compliant beams is adopted and elaborated for the passive end-effector.An end-effector providing a constant contact force of 40 N is designed and prototyped.The polishing experiment shows that the passive constant-force end-effector provides stable contact force between the robot and the mirror with fluctuation within 3.43 N,and achieves RMS(Root Mean Square)lower thanλ/10(λ=632.8 nm)of the polished surface of the largeaperture optical reflective mirror.It is concluded that the constant-force compliant mechanism provides a low-cost and reliable solution for force control in robotic polishing.

柔性微抓取器的机构分析及设计优化

以实现对微小零件的装配为目标,通过对运用单轴柔性铰链位移放大机构的柔性微抓取器进行理论和有限元分析,指出柔性铰链的缺陷.在改进设计中提出并利用柔性梁替代柔性铰链作为抓取器的运动副.通过理论、有限元对改进后的柔性微抓取器进行分析,并通过实验证明了该抓取器的可行性.

一种变截面片弹簧骨架柔顺关节的变形研究

提出一种以变截面片弹簧为骨架的气动柔顺关节,可构成柔性自适应机械手。片弹簧的变形等效于自由端受特殊变载荷(方向和大小都随气缸内压力而变化)作用的弹性悬臂梁的大扰度变形。文中采用非线性变系数并带有未知参数的微分方程组建立静态模型,借助ode45和fmincon函数得到不同压力下片弹簧任意位置的转角位移、坐标位移的数值解,变载荷明确后利用ANSYS建模仿真验证模型与数值解法的正确性,最后与等截面片弹簧骨架关节进行对比,说明变截面片弹簧骨架关节具有柔性好、节省能源的优点。

柔顺杆大变形分析的A-T-S方法

柔顺机构是一种新型机构,其中杆状柔顺机构占据了很大的比重。对大变形杆状柔顺机构的设计和分析,关系到整个柔顺机构的设计成功率。将链式算法和二分法应用于柔顺杆分析中,依据角度等量递变原则对柔顺杆进行分段,每一段的相对转角相等而长度不等,运用一个刚杆和一个扭簧连接来近似替代此小段,进而依据力的平移定理推出了相邻两段之间的长度关系,据此计算传统柔顺杆各部分受力后的变形、位移、转角,并根据所得结果推导出柔顺杆各部分应变能分布情况,从而为柔顺杆大变形分析提供了一种新的方法。经过与传统椭圆积分进行对比,验证了此方法的可行性。

基于几何精确Euler-Bernoulli梁单元的柔顺机构动力学分析

基于几何精确梁理论(GEBT),研究大变形柔顺机构的动力学建模与仿真求解问题:依据Euler-Bernoulli梁变形假设,构造严格满足梁截面与形心线切向垂直关系的大变形梁单元变形场;利用虚功率原理推导几何精确Euler-Bernoulli梁单元的节点力、质量矩阵及广义外力,对柔顺四连杆机构和空间圆弧导向柔顺机构两种典型柔顺机构建立精确动力学模型,并进行仿真对比.仿真结果表明,与绝对节点坐标(ANCF)梁单元模型和ADAMS的数值结果相比,采用几何精确Euler-Bernoulli梁单元进行柔顺机构动力学仿真分析在计算效率和计算精度上均具有优越性.

基于固支-简支屈曲梁的旋转驱动双稳态柔顺机构

与传统刚体机构不同,柔顺机构通过构件变形可实现位移和力的传递与转换,这可大大减少摩擦、润滑和装配。由于具有结构简单、变形大、易于加工等特点,双稳态屈曲梁成为常见的柔顺机构设计单元,在能量吸收、软体机器人、能量收集等领域被广泛应用。以固支-简支双稳态屈曲梁为研究对象,设计一种新型旋转驱动的双稳态柔顺机构。首先,基于能量法建立分析模型,用于分析双稳态屈曲梁在简支端旋转驱动下的跳变特性,预测屈曲梁的力矩-角度曲线和变形过程,并通过有限元模型和实验结果验证了分析模型的有效性;其次,利用分析模型、有限元模型和实验分析了预压缩量和几何参数对于双稳态屈曲梁力矩-角度曲线和最大力矩的影响;最后,基于双稳态屈曲梁的研究结果设计旋转驱动的双稳态柔顺机构并对其跳变行为进行有限元分析和实验验证。

A closed-form nonlinear model for spatial Timoshenko beam flexure hinge with circular cross-section

Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.

具有连续多行程恒力柔顺机构设计

为实现多段恒力功能,提出一种基于并联负刚度结构的多行程恒力柔顺机构设计方法。以一种新型余弦形曲梁作为负刚度结构,其负刚度行程大、线性度高,与具有正刚度特性的复合梁组合后,以实现连续两段恒力输出性能。采用伪刚体法和基于能量法的瑞利一里兹法建立多行程恒力柔顺机构的理论分析模型,有限元仿真结果验证理论模型的准确性。以提高恒力范围为目标,分析主要尺寸参数对力学特性的影响,优化初始尺寸参数。制作且测试优化后的恒力机构样机,实验结果表明恒力机构两段恒力范围分别为1mm~6.8mm、8.8mm~14.4mm,输出恒力分别约为7.7N、19.7N,证明了设计方法的有效性。

柔顺机构中大变形柔性梁的2自由度伪刚体模型

针对柔顺机构中的大变形柔性梁,提出了一种新的伪刚体模型,即"两自由度伪刚体模型"。通过对模型末端倾角的进行参数化近似得出了模型最优特征半径系数,然后应用线性回归方法得到了模型的刚度系数。该模型能精确模拟柔顺机构中大变形柔性梁的变形轨迹和变形角度。最后通过末端轨迹的对比说明了该模型的优越性。