航天机械臂逆动力学的完全笛卡尔坐标方法

运用多体系统完全笛卡尔坐标方法研究安装在航天器上的刚性机械臂平面运动逆动力学问题，建立自由漂浮状态下系统的一阶微分方程组，通过算例求出各坐标及转角变化规律．     

链状柔性多体机器人系统动力学研究

本文基于Ｊｏｕｒｄａｉｎ变分原理建立了具有链状拓扑结构柔性多体机器人系统动力学通用模型，用在一致质量有限单元法及正则模态分析基础上引入的模态坐标描述构件的弹性形，用独立坐标描述相邻板件间的大位移运动，每个铰容许１－６个自由度，组强非线性惯性耦合的封闭形式的系统动力学微分方程组，文末对单弹性臂和双弹性臂机器人操作手进行动力学仿真。     

柔性多体系统的递推组集建模与仿真软件的实现

简要地阐述多体系统动力学单向递推组集建模方法，介绍根据这种方法开发而成的仿真软件系统ＤＡＦＭＢ及它的功能与特点。通过双摆算例指出本文提出的模型在计算效率与计算精度方面优于笛卡尔坐标的微分－代数方程。     

刚柔耦合约束多体系统的动力分析

本文提出了描述柔性多体系统的牵连坐标系统。该系统由惯性参考系，牵连坐标系，物体坐标系及单元坐标系组成，实现了对刚体平动。刚体转动及弹性运动的连续分解，最大限度地消除了由于铡体大角度转动导致的非线性特性。以有限元法为基础，应用拉格朗日方程建立了在该坐标下的刚柔耦合约束多体系统的动力学控制方程，该方程具有耦合程度小，易于推导，编程及求解等优点，为大规模约束多体系统的动力分析提供了新的途径。本文还讨论了     

弹性杆-刚性体系统动力学分析的广义逆矩阵方法

将多刚体系统的广义逆矩阵方法推广到含弹性杆与刚性体的混合系统的动力学分析中,建立了以节点坐标表示的基于全局惯性坐标系的刚体-柔性体混合系统动力学方程.首先以两端节点坐标为变量推导了弹性杆的动力学方程,以刚性体节点坐标为变量推导了刚性体节点速度约束方程和刚性体动力学方程,最后得到弹性杆与刚性体混合系统的动力学方程和速度约束方程.本方法在同一个惯性坐标系对刚柔多体系统进行描述,具有方法简洁、便于计算建模的特点.论文最后给出两个数值算例,检验了方法的有效性.     

多柔体系统动力学建模与优化研究进展

多柔体系统是由柔性部件和运动副组成的力学系统,在航空、航天、车辆、机械与兵器等众多工程领域具有广泛的应用前景, 其典型的代表包括柔性机械臂、直升机旋翼、卫星的可展开天线、太阳帆航天器等. 近年来,随着工程技术的发展,多柔体系统动力学问题日益突出,尤其是含变长度柔性部件的多柔体系统,不仅涉及其动力学 建模与计算,还涉及其动力学优化设计. 事实上,部件柔性对多柔体系统的动力学行为影响很大,直接影响到优化结果,因此需要发展基于多柔体系统动力学的优化设计方法. 本文首先阐述了多柔体系统动力学优化的研究背景及意义,简要回顾了多柔体系统动力学建模的3类方法:浮动坐标方法、几何 精确方法和绝对节点坐标方法,并介绍了含变长度柔性部件的多柔体系统动力学建模方法. 系统概述了多柔体系统动力学响应优化、动力学特性优化和动力学灵敏度分析3个方面的研究进展,并从尺寸优化、形状优化和 拓扑优化 3 个方面综述了多柔体系统部件优化的研究进展. 本文最后提出了在多柔体系统动力学优化研究中值得关注的若干问题.      

用点系笛卡尔坐标表示的刚体模型

本文叙述刚体的一种非传统模型,即利用刚体内若干参考点的笛卡尔坐标表示刚体的空间位置和姿态.与利用欧拉角或欧拉参数表示姿态的传统刚体模型比较,点系模型的主要优点是所有约束方程的Jacobi矩阵均为坐标的线性函数,从而使数值计算的效率明显提高,尤其适合应用于多体系统的建模.     

复杂刚—柔混合机构的动力学分析方法

本文应用柔性多体系统理论分析了复杂刚－柔混合机构的动力学问题，用单项递推组集方法建立了系统的动力学模型，用模态综合方法描述柔性的变形，对空间四连杆机构进行了动力这仿真。讨论了安装误差对系统动力学性态的影响。     

柔性机械臂动力学方程单向递推组集方法

本文基于Jourdain变分原理提出一种柔性机械臂动力学方程的单向递推组集方法。用规则标号法描述系统中物体和铰的邻接关系;用铰相对坐标和模态坐标分别描述物体的大位移运动和弹性变形。文末以三连杆机器人操作手为例说明本文建模的过程。     

双面约束多点摩擦多体系统的建模和数值方法

提出了一种建立具有固定双面约束多点摩擦的多体系统动力学方程的方法. 用笛卡尔坐标阵描述系统的位形,根据局部方法的递推关系建立系统的约束方程,应用第一类Lagrange方程建立该系统的动力学方程,使得具有摩擦的约束面的法向力与Lagrange乘子一一对应,便于摩擦力的分析与计算,并用矩阵形式给出了摩擦力的广义力的一般表达式. 应用增广法将微分-代数方程组转化为常微分方程组,并用分块矩阵的形式给出,以便于方程的编程与计算.给出了一种改进的试算法,可提高计算效率. 最后给出了一个算例,应用试算法和RK法对算例进行了数值仿真.      

基于自然坐标的自由浮动空间机械臂动力学分析

利用一种新方法研究自由浮动空间机械臂动力[学问题,这种方法基于一种称为“自然坐标”的新坐标体系,导出用自然坐标表示的无力矩状态下空间机械臂初积分形式动力学方程,根据臂端设计轨迹,对空间机械臂进行逆动力学仿真计算,结果表明该方法是一种简便,高效的可行方法。     

A velocity transformation method for the nonlinear dynamic simulation of railroad vehicle systems

The solution of the constrained multibody system equations of motion using the generalized coordinate partitioning method requires the identification of the dependent and independent coordinates. Using this approach, only the independent accelerations are integrated forward in time in order to determine the independent coordinates and velocities. Dependent coordinates are determined by solving the nonlinear constraint equations at the position level. If the constraint equations are highly nonlinear, numerical difficulties can be encountered or more Newton–Raphson iterations may be required in order to achieve convergence for the dependent variables. In this paper, a velocity transformation method is proposed for railroad vehicle systems in order to deal with the nonlinearity of the constraint equations when the vehicles negotiate curved tracks. In this formulation, two different sets of coordinates are simultaneously used. The first set is the absolute Cartesian coordinates which are widely used in general multibody system computer formulations. These coordinates lead to a simple form of the equations of motion which has a sparse matrix structure. The second set is the trajectory coordinates which are widely used in specialized railroad vehicle system formulations. The trajectory coordinates can be used to obtain simple formulations of the specified motion trajectory constraint equations in the case of railroad vehicle systems. While the equations of motion are formulated in terms of the absolute Cartesian coordinates, the trajectory accelerations are the ones which are integrated forward in time. The problems associated with the higher degree of differentiability required when the trajectory coordinates are used are discussed. Numerical examples are presented in order to examine the performance of the hybrid coordinate formulation proposed in this paper in the analysis of multibody railroad vehicle systems.     

On the use of linear graph theory in multibody system dynamics

Multibody dynamics involves the generation and solution of the equations of motion for a system of connected material bodies. The subject of this paper is the use of graph-theoretical methods to represent multibody system topologies and to formulate the desired set of motion equations; a discussion of the methods available for solving these differential-algebraic equations is beyond the scope of this work. After a brief introduction to the topic, a review of linear graphs and their associated topological arrays is presented, followed in turn by the use of these matrices in generating various graph-theoretic equations. The appearance of linear graph theory in a number of existing multibody formulations is then discussed, distinguishing between approaches that use absolute (Cartesian) coordinates and those that employ relative (joint) coordinates. These formulations are then contrasted with formal graph-theoretic approaches, in which both the kinematic and dynamic equations are automatically generated from a single linear graph representation of the system. The paper concludes with a summary of results and suggestions for further research on the graph-theoretical modelling of mechanical systems.     

A Fully Symbolic Model of Multibody Systems Containing Flexible Plates

The modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multi-body dynamics and the area of structural mechanics and vibration theory. As regards the multibody approach, recursive formulations in relative coordinates are quite suitable and efficient for a large variety of applications. Such a formalism is developed here for a general multibody system containing flexible plates and in such a way that its full symbolic generation is possible within the ROBOTRAN program [1].     

Comparative study on multibody vehicle dynamics models based on subsystem synthesis method using Cartesian and joint coordinates

The subsystem synthesis method has been developed in order to improve computational efficiency for a multibody vehicle dynamics model. Using the subsystem synthesis method, equations of motion of the base body and each subsystem can be solved separately. In the subsystem synthesis method, various coordinate systems can be used and various integration methods can be applied in each subsystem, as long as the effective mass matrix and the effective force vector are properly produced. In this paper, comparative study has been carried out for the subsystem synthesis method with Cartesian coordinates and with joint relative coordinates. Two different integration methods such as an explicit integrator and an explicit implicit integrator are employed. In order to see the accuracy and computational efficiency from the different models based on the different coordinate systems and different integration methods, a rough terrain run simulations has been carried out with a 6 × 6 off-road multibody vehicle model.     

柔性多体系统动力学实验研究综述

介绍了国内外柔性多体系统动力学实验研究现状,分为三个方面,即理论模型验证实验、动力学特性的实验研究和其它实验.柔性多体系统动力学建模理论的发展经历了3个阶段:运动-弹性动力学(KED)方法、传统混合坐标方法和计及了动力刚化效应的各种非线性理论.关于这些理论的模型验证实验均在本文中作了重点介绍.文中还对柔性多体系统动力学性态的研究实验也作了介绍,包括系统模态特性和共振等非线性力学行为.关于机械臂控制和碰撞研究实验虽有提及,但不作为重点.随后,着重介绍了柔性体弹性振动位移的测量和阻尼因素的处理这两个在实验不可避免但又难以解决的问题,尤其是结构阻尼和大范围运动引起的空气阻力.最后指出了今后的研究方向.文中对一些较为重要的实验装置也着重予以介绍,并给出了部分实验图片及数据曲线,以给读者一个更好的理解和参考.      

RESEARCH ON MODELING AND NUMERICAL METHOD OF FREE STANDING BODY ON PLANAR RIGID MULTIBODY DYNAMICS

采用非光滑多体系统动力学的方法研究浮放物体与基础平台组成的多体系统,建立其非光滑接触的动力学方程与数值算法.浮放物体由主体部分和支撑腿组成,其间通过含黏弹性阻力偶的转动铰连接.支撑腿与基础平台间的接触力简化为接触点的法向接触力和摩擦力,采用扩展的赫兹接触力模型描述接触点的法向接触力,采用库伦干摩擦模型描述其摩擦力.采用笛卡尔坐标系下的位形坐标作为系统的广义坐标.首先,将基础平台运动看作非定常约束,用第一类拉格朗日方程建立系统的动力学方程,并采用鲍姆加藤约束稳定化的方法解决违约问题.随后给出基于事件驱动法和线性互补方法的数值算法.当相对切向速度为零时,构造静滑动摩擦力的正负余量和正、负向加速度的互补关系,从而将接触点黏滞——滑移切换的判断以及静滑动摩擦力的计算转化为线性互补问题进行求解,并采用Lemke算法求解线性互补问题.最后,通过数值仿真选择合适的步长;通过仿真结果说明浮放物体运动中存在的黏滞-滑移切换现象以及基础平台运动、质心位置对浮放物体运动的影响.     

On the numerical solution of tracked vehicle dynamic equations

In this investigation, the solution of the nonlinear dynamic equations of the multibody tracked vehicle systems are obtained using different procedures. In the first technique, which is based on the augmented formulation that employes the absolute Cartesian coordinates and Lagrange multipliers, the generalized coordinate partitioning of the constraint Jacobian matrix is used to determine the independent coordinates and the associated independent differential equations. An iterative Newton-Raphson algorithm is used to solve the nonlinear constraint equations for the dependent variables. The numerical problems encountered when one set of independent coordinates is used during the simulation of large scale tracked vehicle systems are demonstrated and their relationship to the track dynamics is discussed. The second approach employed in this investigation is the velocity transformation technique. One of the versions of this technique is discussed in this paper and the numerical problems that arise from the use of inconsistent system of kinematic equations are reported. In the velocity transformation technique, the tracked vehicle system is assumed to consist of two kinematically decoupled subsystems; the first subsystem consists of the chassis, the rollers, the sprocket and the idler, while the second subsystem consists of the track which is represented as a closed kinematic chain that consists of rigid links connected by revolute joints. It is demonstrated that the use of one set of recursive equations leads to numerical difficulties because of the change in the track configuration. Singular configurations can be avoided by repeated changes in the recursive equations. The sensitivity of the predictor-corrector multistep numerical integration schemes to the method of formulating the state equations is demonstrated. The numerical results presented in this investigation are obtained using a planner tracked vehicle model that consists of fifty four rigid bodies.