小齿轮自调位装置的运动学建模及分析

利用多刚体系统笛卡儿运动学方法对小齿轮自调位装置进行建模。根据铰的性质建立邻接刚体的坐标问的约束方程。约束方程中描述空间刚体姿态的最基本参数为方向余弦阵,基于连体基的基点坐标与方向余弦坐标构成的最基本的笛卡儿坐标,导出一般形式的邻接刚体的基本约束方程。通过建立系统的位置、速度、加速度约束方程求解对系统运动学进行分析。     

基于完全笛卡尔坐标的机构动力学计算机分析

介绍了一种用于平面和三维机构运动学和动力学分析的新方法 ,该方法基于完全笛卡尔坐标的参考基点和参考基矢量描述系统的位置和姿态 ,而不需要角度坐标。约束方程可以通过系统的各构件刚体条件和联接构件的关节铰或运动副的约束条件获得。由于约束方程仅是二次代数式 ,因而雅可比矩阵是线性的 ,可以大大提高计算效率。通过仿真算例表明 ,该方法解决机械系统机构动力学问题是有效的。     

一种新型凸轮-连杆组合分度机构的运动学分析

针对自动化机械要求实现高速分度的需求,提出一种新型的凸轮-连杆组合分度机构。在系统分析该机构的结构与传动原理的基础上,将其在运动学上等效为以组合分度机构的输入、输出构件为驱动构件的五杆机构。在此基础上,采用多刚体运动学分析方法,推导了系统的约束方程,进而建立等效机构的运动学分析模型,得到了各构件在一个分度周期内的运动规律。文中研究可为该机构的运动学设计及动力学分析奠定基础,采用的多体运动学分析方法可为同类机构的运动分析提供借鉴。     

基于完全笛卡尔坐标的机构动力学计算机分析

介绍了一种用于平面和三维机构运动学和动力学分析的新方法,该方法基于完全笛卡尔坐标的参考基点和参考基矢量描述系统的位置和姿态,而不需要角度坐标,约束方程可以通过系统的各构件刚体条件和联接构件的关节铰或运动副的约束条件获得,由于约束方程仅是二次代数式,因而雅可比矩阵是线性的,可以大大提高计算效率,通过仿真算例表明,该方法解决机械系统机构动力学问题是有效的。     

基于机构运动学分析的人体下肢几何参数提取

由关节中心(轴)位置所确定的下肢几何参数是步态运动测量与分析的关键参数。已有的基于三维运动捕捉系统的步态运动测量应用中,人工干预因素较多,存在一定的主观性,从而对步态运动的测量信度产生显著的不利影响。针对这一问题,在对下肢环节和关节进行合理机构学简化的基础上,建立人体下肢多刚体运动学模型;通过下肢机构运动学分析,改进标志点设置方案;通过构造下肢运动的约束方程,充分利用大量的采样数据,推导了关节位置、模型几何参数的拟合算法。并通过试验验证测量方案及算法的有效性。     

3-PRC三维平移并联机器人机构的运动学分析

讨论了具有三平移自由度的3—PRC并联机器人机构的运动分析。基于机构运动约束方程,得到机构位置逆解的解析表达式;通过对刚体平面运动和点的合成运动分析,建立机构控制构件与动平台速度和加速度关系,并以显函数的形式表示;运动学解形式简单,便于实时控制。     

基于ADAMS/car的双横臂悬架运动学和弹性运动学分析

利用多体动力学方法建立了基于ADAMS软件平台的双横臂悬架动力学仿真分析模型.采用轮跳方法、加载地面侧向力和纵向力方法,对该悬架系统进行运动学和弹性运动学仿真对比分析,探讨了悬架橡胶衬套弹性对车辆性能的影响.结果表明:多柔体悬架模型对车身的侧倾和纵倾、车轮定位参数等比多刚体悬架模型具有较好的抑制作用,有利于提高汽车操纵稳定性.     

空间6R串联机械手逆运动学分析的新方法研究

为了解决空间6R串联机械手的逆运动学问题使用矩阵方法建模时,需要进行矢量运算或投影运算的问题,基于四维旋转矩阵和倍矩阵,提出了一种建模新方法。根据三维空间刚体变换的四维旋转矩阵和倍矩阵表示,建立空间6R串联机械手的正运动学方程。通过变量分离,直接得到14个逆运动学基本约束方程;通过线性消元和Sylvester结式消元,将其转化为求解一个16阶矩阵的特征值问题,得到该问题的16组解。采用数值实例和SolidWorks仿真验证了新方法的正确性。新方法的优势在于可以直接得到14个逆运动学约束方程,不需要进行矢量运算或者投影等,并且由于新方法将三维空间中的平移变换近似为四维空间中的旋转变换,故而可以统一求解含有R、P和C副的空间串联机械手逆运动学问题。     

基于ANSYS的曲柄滑块机构运动学分析

结合新型公交车车门（滑块）的实例,介绍了利用ANSYS对曲柄滑块机构进行运动学分析的方法、步骤和过程,并使用解析解对有限元分析结果进行验证。结果表明使用ANSYS软件可准确地进行多刚体运动学分析。     

人体跳跃机理运动学动力学分析

在分析人体下肢生理结构与跳跃运动特征的基础上,将人体下肢的跳跃模型简化为一个平面多刚体运动系统;对简化模型运用正运动学分析方法,建立了在跳跃过程中的下蹲相和起跳相时下肢各构件关节点、质心与总质心的位置、速度和加速度模型;在运动学分析的基础上通过采用Lagrange方法进行动力学分析,得到了跳跃过程中力与位置关系的动力学方程。为各种仿人跳跃机构设计提供理论基础。最后,用Workbench对在不同相时的脚部构件进行了静力学分析,得到不同相时脚掌的变形和应力分布。     

Sensitivity analysis approach to multibody systems described by natural coordinates

The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.     

3D geometric constraint solving using the method of kinematic analysis

In this paper, an approach based on kinematic method for solving 3D geometric assembly constraints is presented. The relative generalized coordinates and generalized recursive formulations used in kinematic analysis are utilized to reduce the size of constraint equations. Based on the cut-constraint method, this approach can be used to solve all kinds of configurations. In the case of an open-loop constraint system, the geometric constraints can be satisfied by sequentially determining the values of relative generalized coordinates. With respect to a closed-loop constraint system, the proposed approach converts it to a spanning tree structure by cutting constraints and introducing cut-constraint equations. Furthermore, a topological analysis method is also developed to obtain the spanning tree with the minimal number of cut-constraint equations, and the analytical Jacobian matrix of cut-constraint equations is derived to enhance computational efficiency. In the end, the proposed approach is demonstrated and validated using two examples of closed-loop geometric constraint system.     

作大范围运动柔性梁的一种碰撞动力学求解方法

研究作大范围运动柔性梁的碰撞动力学问题。针对梁碰撞前、碰撞过程、碰撞后三个阶段,分别建立各阶段的动力学方程。基于柔性多体系统刚柔耦合动力学理论,建立梁无碰撞时的刚柔耦合动力学方程。结合冲量动量法和接触约束法提出一种碰撞动力学求解方法,先以冲量动量法实现运动转换得到协调的碰撞初始条件,再以接触约束法求解碰撞过程。导出系统的刚柔耦合碰撞动力学方程,给出了接触、分离判据,实现三个不同阶段的转换与动力学求解。编制仿真软件,对实例进行动力学仿真,得到系统不同阶段的动力学响应。研究表明,所提碰撞求解方法可以较方便地用于计算柔性多体系统的碰撞问题。梁的柔性、大范围运动及碰撞效应相互耦合,碰撞行为对于柔性多体系统碰撞过程和碰撞后的全局动力学性态均产生较大的影响。     

Multibody approach for tolerance analysis and optimization of mechanical systems

A multibody approach is suitable for tolerance analysis of mechanical systems since multibody formulation can directly consider part-level tolerance variables. In this study, procedures for performing tolerance analysis and corresponding sensitivity analysis for spatial multibody systems are proposed. First, statistical formulation for performing multibody system tolerance analysis is developed to obtain system level tolerance for given part-level tolerances. One very useful aspect of the proposed formulation is that in the process of computing system tolerance, the sensitivity of system tolerance with respect to part-level tolerances can be additionally obtained. The kinematics of spatial multibody systems has been redefined in terms of both generalized coordinates and part-level tolerance variables. Tolerances in geometry of a body are specified in terms of the variations in relative locations of joint definition points and relative distance between them. Tolerances in the joint kinematics are defined through variations in vector closure equations and orthogonality equations that are two fundamental constraint equations for most kinematic joints. To demonstrate the validity and effectiveness of the proposed tolerance analysis procedure, tolerance analysis of a spatial 4-bar mechanism and tolerance optimization are performed.     

Steady-state equilibrium analysis of a multibody system driven by constant generalized speeds

A formulation which seeks steady-state equilibrium positions of constrained multibody systems driven by constant generalized speeds is presented in this paper. Since the relative coordinates are employed, constraint equations at cut joints are incorporated into the formulation. To obtain the steady-state equilibrium position of a multibody system, nonlinear equations are derived and solved iteratively. The nonlinear equations consist of the force equilibrium equations and the kinematic constraint equations. To verify the effectiveness of the proposed formulation, two numerical examples are solved and the results are compared with those of a commercial program.     

Kinematic configuration analysis of planar mechanisms based on basic kinematic chains

According to the single-link transformation principle, and based on the topological characteristic investigations to planar closed kinematic chains (PCKCs), a general study of the kinematic configuration analysis of planar mechanisms with R-pairs is conducted in this paper. Firstly, two new concepts, contract link distance sequence and basic link group code sequence, are defined, and a novel approach for identification of multi-bar basic kinematic chains (BKCs) within the kinematic chain left from the single-link transformation is proposed. Then, another two concepts, weight code and similarity code, are defined for aid to link similarity judgment and two judgment theorems are proposed as well. As a further step, weight code or similarity code of the transformed single-link will be employed for kinematic configuration analysis situation judgment. Finally, corresponding unified constraint equations are set up and solved with coefficient homotopy method, on the basis of aforementioned analysis results. The study shows that the method is reliable and effective, and it is especially applicable for the kinematic configuration analysis problem of PCKCs with multi-bars and multi-freedoms.     

Numerical kinematic analysis of the standard macpherson motor-vehicle suspension system

In this paper, an efficient numerical algorithm for the kinematic analysis of the standard MacPherson suspension system is presented. The kinematic analysis of the suspension mechanism is carried out in terms of the rectangular Cartesian coordinates of some defined points in the links and at the kinematic joints. Geometric constraints that fix the distances between the points belonging to the same rigid link are introduced. The nonlinear constraint equations are solved by iterative numerical methods. The corresponding linear equations of the velocity and acceleration are solved to yield the velocities and accelerations of the unknown points. The velocities and accelerations of other points of interest as well as the angular velocity and acceleration of any link in the mechanism can be calculated.     

Joint coordinate method for analysis and design of multibody systems: Part 1. System equations

This paper presents a method, known as the joint coordinate method, for the computer aided design process of multibody systems. The relationship between joint and absolute velocities is described by a linear velocity transformation matrix representing the system kinematics. Joint coordinate method can generate a minimal set of equations of motion in terms of the generalized joint accelerations. This method can also yield reaction and actuator forces acting at the kinematic joints that are necessary for forward and inverse dynamics analyses. Applications of this method to static equilibrium and design sensitivity analyses are also studied. Comparisons between the absolute and joint coordinate formulations are given in terms of their computational efficiency.     

Computer-aided kinematic analysis of basic spatial mechanisms

Using the spherical coordinate system in conjunction with the principle of algebraic correspondence between the displacement equations of the plane, spherical and spatial four-bar mechanisms and the plane and spatial slider-crank mechanisms, an efficacious procedure has been developed to carry out kinematic analysis for the coupler and output link of the mechanisms. The iteration-free nature of the procedure precludes any non-convergence problem and the inherent complexity of the 3-dimensional analysis is mitigated substantially.     

多体系统理论在机构运动分析中的应用

本文将多体系统理论用于机构的运动分析,理论分析和计算实例表明：多体系统理论用于机构的运动分析是行之有效的。