计及动力刚化的柔体动力学

提出两种计及动力刚化影响的动力学建模方法；有限段方法和一致线性化动力学方法。分析了这两种动力不主动力刚化的机理，有限段方法将柔体动力学问题转化为带有柔性的多刚体体系统动力学问题，计及了几何非线性的影响，适合于解决梁式结构的动力学问题；一致线性化动力学方法将变形场描述成为变形广义坐标的非线性形式，在适当的阶段线性化，可得到一致线性化动力学方程，自然计及了动力刚化项，适合于柔体的小变形问题。     

多体动力学的休斯敦方法及其发展

介绍多体动力学休斯敦方法的核心内容（含低序体阵列、变换矩阵、广义坐标及其导数、运动参数计算和动力学方程等）及其发展,即柔性体的有限段方法及综合模态分析方法。将变形表示为二阶小量形式,基于小变形原理,适时进行线性化,以获取动力刚化项和一致线性化动力学方程。     

计及环境特征的柔性多体系统动力学理论

对柔性体非线性变形场进行了描述,将柔性体变形场表达为直至变形广义坐标的二阶小量的形式,基于Kane方程建立了任意形状柔性体动力学方程。采用Huston的低序体阵列描述多体系统的拓扑结构,以此为基础进行系统的动力学分析,同时依据Kane方程建立了一般柔性多体系统的动力学方程。在建立一般柔性多体系统动力学方程的基础上,研究了计及环境特征的柔性多体系统,将环境特征作为外部约束引入柔性多体系统,建立了带有约束的一般柔性多体系统动力学方程。     

三维大变形梁系统的动力学建模与仿真*

对三维大变形柔性梁系统的动力学建模和仿真进行了研究。采用绝对节点坐标法描述柔性体的大变形和大位移运动,并由此建立三维大变形柔性梁系统的动力学模型。在此动力学模型基础上,编制动力学仿真软件,实现了对三维大变形柔性梁系统的动力学仿真。给出了两个动力学仿真算例。第一个对柔性单摆自由下落进行了动力学仿真,并与现有文献结果相比较,验证了模型的正确性。第二个对空间柔性双摆的自由下落过程进行了动力学仿真,并将模型计算的结果与使用ADAMS软件计算的结果进行比较。研究结果表明,ADAMS在计算大变形物体动力学时具有局限性,而所得的模型能够有效地对三维大变形柔性梁系统的动力学进行仿真解决这类动力学问题。     

计及非线性变形的刚-柔耦合动力学建模

考虑变形产生的几何非线性效应对运动柔性梁的影响，在柔性梁的纵向、横向变形位移中均考虑横向弯曲以及轴向伸缩的耦合作用，从非线性应变-变形位移的原理出发，说明增加耦合变最后，剪应变为零，由此得出的变形模式更符合工程实际和简化需要。并采用有限元离散，通过Lagrange方程导出系统的动力学方程。最后对一带有中心体的柔性梁，在大范围运动为自由和大范围运动为已知两种情况下进行仿真计算，结果表明，在结构有初始变形的情况下，仅在纵向变形中计及变形二次耦合量的一次动力学模型，与考虑完全几何非线性变形的文中模型具有一定的差异。     

旋转悬臂梁动力学的B样条插值方法

采用B样条插值方法对旋转悬臂梁的动力学特性进行研究。考虑柔性梁的纵向拉伸变形和横向弯曲变形,计入由于横向弯曲变形引起的纵向缩短,即非线性耦合项。利用B样条插值方法对柔性梁的变形场进行离散。采用Lagrange方程建立系统的动力学方程,并编制旋转悬臂梁动力学仿真软件。进行动力学仿真,将B样条插值方法的仿真结果与假设模态法、有限元法进行比较分析,验证了提出的方法的正确性,并表明B样条插值方法作为变形体离散法在柔性多体系统动力学中具有优良性能和应用价值。     

一种高效的数值计算方法在柔性并联机构动力学中的应用

首先利用自然坐标法和绝对广义坐标法构建了刚柔混合3-RRRU空间并联机器人的非线性逆动力学模型,该模型可描述柔性空间梁单元的大范围非线性弹性变形,同时考虑了弹性构件的剪切效应。为了避免连续介质力学中泊松闭锁现象的发生,对弹性矩阵和应变能进行了合理分割,给出了高效计算弹性力及其雅克比矩阵的新方法。最后结合Generalized-α法和牛顿法,并以圆周运动轨迹为例,对柔性并联机构逆动力学模型的解进行了研究,验证了数值计算方法的有效性与正确性。     

平面柔性连杆3-RRR并联机器人动力学建模

为了描述包含柔性连杆的平面柔性3-RRR并联机器人的运动学、动力学特性,需要建立机器人的弹性动力学模型.采用一种适用于刚体、柔体混合的复杂机械系统有限元建模方法,通过分析柔性连杆与刚性动平台的运动学耦舍关系,推导出单元弹性广义坐标相对于系统弹性广义坐标的转换矩阵,利用运动弹性动力学理论,建立了平面柔性3-RRR并联机器人的弹性动力学方程.避免了采用运动学、动力学约束方程的弊端,缩小了方程的规模,缩短了计算时间.用SAMCEF软件验证了模型的准确性.计算实例表明,该模型反映了机器人的弹性振动特性,杆件的弹性变形对机器人的运动误差具有重要影响.     

考虑变形耦合的受冲击柔性机械臂动力学建模

将刚-柔耦合体动力学的新建模理论应用于受冲击柔性机械臂的研究。将柔性机械臂简化为弹性梁,在梁的纵向变形中考虑了变形耦合量,计及了这种耦合对大范围运动的影响。利用Lagrange方程建立了机械臂的动力学方程。将受碰撞冲击后柔性机械臂的瞬态响应,作为求解动力学方程组的初始条件。针对刚体模型和柔性耦合模型进行了数值仿真计算,表明柔性耦合模型更加符合实际情况,为柔性机械臂的动力学分析与控制提供了依据。     

5R柔性并联机器人系统运动微分方程

为了描述平面5R柔性并联机器人的运动学和动力学特性,需要建立机器人的运动微分方程。针对刚性活动平台和柔性杆件的运动学耦合特点,改进了一套适用于刚体、柔性体耦合的有限元建模方法,推导出单元弹性广义坐标相对于系统弹性广义坐标的转换矩阵,综合考虑了科氏阻尼、离心刚度和几何非线性的影响,利用运动弹性动力学理论,建立了平面5R柔性并联机器人的运动微分方程,避免了采用运动学和动力学约束方程的弊端,提高了建模精度。计算实例表明,该方程反映了机器人的弹性振动特性,杆件的弹性变形对机器人的运动误差具有重要影响。     

机械系统动力刚化机理分析

采用计及变形约束的非线性运动学分析方法及传统分析方法建立简单柔性机械臂线性化的动力学方程。笔者认为：运动的柔性机械构件春变形运动的耦合产生动力刚化，传统分析方法失去了刚体运动与弹性振耦合的动力刚化项；如果在建立运动学方程时，计及运动学的非线性项，至少要计及振动坐标的二阶小量，将非线性保留到适当阶段，再线性化，熊猫是到一致化性化的动力学方程，这种方法适合于机械系统件的小变形问题，对动力刚化的研究实际     

Investigation on steady state deformation and free vibration of a rotating inclined Euler beam

The steady state deformation and infinitesimal free vibration around the steady state deformation of a rotating inclined Euler beam at constant angular velocity are investigated by the corotational finite element method combined with floating frame method. The element nodal forces are derived using the consistent second order linearization of the nonlinear beam theory, the d'Alembert principle and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The rotating element coordinates rotate about the hub axis at the angular speed of the hub. The equations of motion of the system are defined in terms of an inertia global coordinate system, which is coincident with a rotating global coordinate system rigidly tied to the rotating hub. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady state deformation and natural frequency of the rotating inclined beam.     

A nonlinear finite element model for dynamics of flexible manipulators

A general nonlinear dynamics model is developed for three-dimensional flexible manipulators. A manipulator link is modelled as a beam undergoing both large gross rigid body motion and elastic deformation. The beam is discretized by the finite element method with its inertia lumped at the nodes of each element. A nonlinear strain-displacement relationship is developed to retain the geometric nonlinearity resulting from the large relative elastic deflections. The geometric nonlinearity is specifically treated so that the significance of the geometric nonlinear effects can be easily included not only in the fully nonlinear model, but also in the linearized model. Numerical results are presented to demonstrate the significant effects of geometric nonlinearity on the dynamic response of a flexible manipulator.     

Gough-Stewart平台高效动力学建模研究

运用凯恩方法建立并联机构动力学模型,以并联机构动平台参考点的速度和角速度作为伪速度,推导各个驱动杆和动平台偏速度和加速度,建立各个构件的凯恩方程,并加以综合,得出系统的动力学模型。所得模型表达简洁,变量和方程的数目少,适用范围广,计算效率高,适于并行计算。该方法便于在任务空间建立控制模型,并为并联机床的动态分析与设计提供了基础。     

COMPUTER AIDED ANALYSIS OF FLEXI－BLE MEMBER IN CONSIDERATION OF THE EFFECTS OF DYNAMIC STI－FFEN－ING

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Recursive newton-euler formulation for flexible dynamic manufacturing analysis of open-loop robotic systems

The main objective of this paper is to develop a recursive formulation for the flexible dynamic manufacturing analysis of open-loop robotic systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields. These time invariant quantities represent the dynamic manufacturing couplings between the rigid body motion and elastic deformation. This formulation applies recursive procedures with the generalized Newton-Euler equations for flexible bodies to obtain a large, loosely coupled system equation describing motion in flexible manufacturing systems. The techniques used to solve the system equations can be implemented in any computer system. The algorithms presented in this investigation are illustrated using cylindrical joints for open-loop robotic systems, which can be easily extended to revolute, slider and rigid joints. The recursive Newton-Euler formulation developed in this paper is demonstrated with a robotic system using cylindrical mechanical joints.     

Model study and active control of a rotating flexible cantilever beam

For a dynamic system of a rotating flexible cantilever beam, the traditional model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zero-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of a flexible cantilever beam with a high rotational speed. In this paper, a first-order approximation coupling model is presented to analyze the dynamics of rotating flexible beam system, which is based on the Hamilton theory and the finite element discretization method. The proposed model for the system considers the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam. The dynamic characteristics of the rotating beam system when using the zero-order approximation coupling model are compared with those when using the first-order approximation coupling models through numerical simulations. In addition, the applicability of the two dynamic models for control design are studied by using the classical optimal control method. Simulation and comparison studies show that, for the case without control for the system, there exists big difference between the result using the zero-order approximation coupling model and that using the first-order approximation coupling model even for the case of small angular velocity of the system. The larger is the angular velocity, the bigger is the difference. Vibration frequency of the beam by using the first-order approximation coupling model is higher than that by using the zero-order approximation coupling model. When the angular velocity of the system is close to or is larger than the fundamental frequency of the beam without rotation motion, the zero-order approximation coupling results in a wrong result, while the first-order approximation coupling model is valid. For the case with control for the system, the applicability of the zero-order approximation coupling model can be much broadened. The critical angular velocity of the system for validity of the zero-order approximation coupling model is much larger than that without control for the system. The first-order approximation coupling model is available not only for the case of small angular velocity but also for the case of large angular velocity of the system, and is applicable to the cases with or without control for the system.