力矩载荷下的柔顺机构2R伪刚体动力学模型

柔顺机构的研究在结构学及运动学方面取得了大量成果,但是在动力学方面的成果却很少。本文首次以柔顺杆为研究对象,建立其在力矩载荷下的2R伪刚体动力学模型,并应用拉格朗日方程推导出动力学方程,进行了动力学响应分析,给出了相应的动态位形图。同时与1R伪刚体动力学模型做比较,从方程、响应曲线等方面分析2R伪刚体动力学模型的特点,表明此模型的优越性。     

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.     

A parameter optimization framework for determining the pseudo-rigid-body model of cantilever-beams

This paper focuses on developing a framework for determining the optimal pseudo-rigid-body (PRB) model of 2D cantilever beams. PRB models are commonly used in design and analysis of compliant mechanisms since they significantly reduce the number of degrees of freedom compared with the finite element approach. Although a number of PRB models are available in literature, there is not a unified method to determine the most suitable pseudo-rigid-body model for a specific application. In this work, we first study a modified Timoshenko beam equation which accommodates shear forces and axial deformation. The numerical solution to the Timoshenko beam equation provides a baseline for comparing various models. A novel concept of “PRB matrix” is proposed for representing topologies of all PRB models in a uniform way. The optimal set of kinematic parameters (characteristic lengths and spring constants) of PRB models are determined by minimizing the error of tip deflection and comparing with the solution of the Timoshenko beam equation. To validate this formulation, we compare the results with existing PRB models and obtained equivalent if not a more accurate set of PRB parameters. At last, a case study of a compliant slider mechanism is provided to demonstrate the accuracy of two PRB models in this particular application.     

基于伪刚体模型法的柔顺机构驱动特性研究

本文对不同载荷下大变形柔性杆件的末端轨迹进行了分析,给出不同情况下柔性杆件伪刚体模型中各参数的确定方法.在此基础上,对一个大变形曲柄滑块机构分析了已知从动件规律,如何用伪刚体模型法求解主动件的驱动问题,其结果证明了伪刚体模型法在柔顺机构研究中的有效性.     

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。     

大变形柔顺机构的驱动特性研究

基于“伪刚体模型法” ,分析研究了当给定从动件的变形或给定其运动规律时大变形柔顺机构原动件的驱动问题。首先对柔顺机构中不同柔性元件的运动轨迹进行了分析 ,给出了其“伪刚体模型”中主要结构参数的确定方法。在此基础上 ,研究了当从动件产生预期的变形或满足给定的运动规律时 ,求解原动件驱动力矩的一般方法。最后通过算例说明了方法的有效性。     

Modeling of large-deflection links for compliant mechanisms

The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.     

Modeling of large-deflection links for compliant mechanisms

The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.     

仿袋鼠跳跃机构伪刚体模型的动力学分析

为解决袋鼠大长脚的柔性和肌肉的储能作用,根据袋鼠的跳跃特点,提出了仿袋鼠跳跃机构伪刚体动力学模型。建立了机构在跳跃过程中的运动学和动力学方程,讨论了袋鼠起跳时解除地面约束的条件和柔性机构的引入对各关节输入的影响。通过实例给出了跳跃过程模型底部受力的变化规律及其相应解释,用Matlab进行了仿真验证,证明柔性机构的引入有效地降低了关节最大输入扭矩,很好地模拟了袋鼠长脚的柔性和肌肉的储能作用。     

仿袋鼠柔性跳跃机器人的驱动力特性研究

依据袋鼠生物体的运动结构和跳跃运动特点，利用扭转弹簧模拟其关节柔性和肌肉的储能作用，提出仿袋鼠柔性跳跃机器人的伪刚体机构模型。应用凯恩法建立仿袋鼠跳跃机器人的动力学方程。基于MATLAB6．5，结合实例对机器人的运动和驱动力特性进行了仿真分析。分析结果表明：利用柔性机构可降低仿生跳跃机器人跳跃运动所需关节驱动力和能量消耗，同时也揭示了袋鼠跳跃运动快而耗能低的规律。     

A new type of compliant spatial four-bar (RSSR) mechanism

This paper presents a novel study on the analysis and design of a new type compliant spatial four-bar (RSSR) mechanism. To the best of our knowledge, any research on compliant spatial mechanisms which possesses out of plane motions is not available in the literature. This study introduces enumeration and novel approach for the analysis and design of such mechanisms. The analysis and design are performed with the pseudo-rigid-body model (PRBM). Since there are numerous applications of rigid spatial four bar mechanisms, it is strongly believed that a compliant version of such mechanisms may find many applications.     

柔顺机构的疲劳可靠性优化设计

基于伪刚体模型，以可靠度最大为目标，综合概率、疲劳和优化等学科的知识，给出了一种对柔顺机构进行优化设计的方法。建立了基于可靠性的随机变量优化问题的一般模型，分析了将概率约束条件转化为确定形式约束条件的方法；考虑柔顺元件的变形特性，计算了其随机疲劳强度、最大应力，分析了典型的约束形式；通过算例验证了该方法的正确性，结果表明，柔顺元件的可靠性对尺寸或材料特性等方面的变化比较敏感。     

基于正负刚度匹配原理的大行程常力微动平台设计

为解决常力微动平台的正负刚度匹配问题,提出一种利用具有线性力学关系的正负刚度结构形成常力平台的设计思路。为了形成零刚度结构,分别设计了Z字型和梯形两种力—位移关系为线性的正刚度结构。将所设计的两种正刚度结构与具有线性负刚度力学特性的双稳态梁结构进行组合,设计了两种新型的常力微动平台。采用伪刚体方法建立了平台的力学模型,基于该模型采用正负刚度匹配原理确定平台的结构参数。制作样机并与具有非线性力学关系的正刚度结构平台进行比较分析,理论和实验结果表明所设计的平台的常力范围可达2.4 mm,比非线性结构组成的平台增大了1.3 mm,说明了常力平台设计的可行性。所提方法为常力微动平台设计提供了一种更为简易的设计思路。     

垂直型多级位移放大机构设计与力学解析建模

针对压电位移放大机构在垂直方向较难实现大行程、高频带宽度的问题,结合两个复合菱形机构、两个杠杆机构以及一个普通菱形机构,提出了一种垂直型多级位移放大机构.基于能量守恒方法和弹性梁理论建立了位移放大比和输入/输出刚度解析模型,根据拉格朗日方程推导了固有频率解析模型.通过有限元法对解析模型进行了验证,所建立的位移放大比解析...     

Partially compliant spatial slider-crank (RSSP) mechanism

In this study, a novel compliant mechanism, “partially compliant spatial slider-crank (RSSP)” is proposed. All possible configurations of compliant RSSP mechanisms are classified and discussed. A method is derived to determine deflection of the multiple-axis flexural hinge for all positions of the crank. A design procedure for partially compliant RSSP mechanisms is introduced. In order to prove the feasibility of the proposed mathematical model, a real model is built and it is shown that results are consistent.     

定常力输出柔性滑块机构的优化综合

定常力输出机构就是在一定的输入范围内输出一恒定力的机构。本文首先利用虚功原理建立了实现定常力输出柔性滑块机构中力与位移间的关系式 ,进而提出了当考虑和不考虑零件中的应力时柔性滑块机构的优化综合方法 ,最后给出了优化综合实例以证明该方法的正确性     

基于转动约束策略的柔顺机构拓扑优化

柔顺机构在航天航空、生物医疗、及仿生机器人等高新科技领域的精密微机械系统中拥有巨大的应用潜力。目前,拓扑优化是柔顺机构构型设计的主要方法之一。为了解决传统柔顺机构拓扑优化设计中存在虚铰的问题,首先,将旋转角引入柔顺机构构型设计中,以旋转角为观测指标,分析拓扑优化结果中存在虚铰的原因。其次,通过约束设计域内的旋转角平方的平均值不超过许用值,建立无铰链式柔顺机构拓扑优化模型,并且利用伴随法推导与之相应的灵敏度分析列式。最后,采用反向位移机构与柔性夹钳这两个经典算例的拓扑优化设计验证了所提优化模型的可行性和有效性。研究结果表明：基于转动约束策略获得的具有类桁架构型无铰链式柔顺机构,虽然在输入位移与输出位移方面表现出一定程度的减少,但避免了局部应变过大、应力集中问题的出现。     

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。     

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.     

A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules

This paper presents normalized, nonlinear and analytical models of spatial compliant parallel modules—multi-beam modules with a large range of motion. The models address the non-linearity of load-equilibrium equations, applied in the deformed configuration, under small deflection hypothesis. First, spatial nonlinear load-displacement equations of the tip of a beam, conditions of geometry compatibility and load-equilibrium conditions for a spatial three-beam module are derived. The nonlinear and analytical load-displacement equations for the three-beam module are then solved using three methods: approximate analytical method, improved analytical method and numerical method. The nonlinear-analytical solutions, linear solutions and large-deflection FEA solutions are further analyzed and compared. FEA verifies that the accuracy of the proposed nonlinear-analytical model is acceptable. Moreover, a class of multi-beam modules with four or more beams is proposed, and their general nonlinear load-displacement equations are obtained based on the approximate load-displacement equations of the three-beam module. The proposed multi-beam modules and their nonlinear models have potential applications in the compliant mechanism design. Especially, the multi-beam modules can be regarded as building blocks of novel compliant parallel mechanisms.