多刚体系统运动学分析的自然坐标法及在悬架运动学分析中的应用

本文介绍了一种适用于计算机分析的多刚体系统运动学分析的自然坐标法。利用自然坐标描述多刚体系统时,只需要一些点和一些单位向量,刚体的约束方程和运动副的约束方程组成了多刚体系统的运动学约束方程。约束方程均为线性或二次方程,因此求解方便。文中利用该方法分析了Maepherson悬架的轮胎横向滑移量、主倾内倾角等与车轮上、下跳动距离的关系。     

渐开线圆柱齿轮系统运动精度可靠性分析

为确定齿轮系统在随机因素影响下满足精度要求的概率,基于齿轮运动精度理论与鞍点逼近技术,提出一种渐开线圆柱齿轮系统运动精度可靠性分析方法,用以确定齿轮系统在随机因素影响下满足精度要求的概率。分析了齿轮加工误差、轴的径向跳动以及装配偏心对齿轮系统运动误差的影响,推导了齿轮系统运动误差的均值、方差、三阶和四阶原点矩的函数表达式,利用鞍点逼近方法拟合了齿轮系统运动误差的概率密度函数与概率分布函数。结合国家标准建立了齿轮系统运动精度可靠性分析模型。数值算例表明,该方法具有较高的求解精度和效率。     

机械振动系统的电路模拟与分析

在机械振动实验中,经常要建立机械实验系统,而建立机械实验系统本身有很多困难,比如说设备多,成本高,费时.这样,我们想到用其它模型来模拟机械模型.电路模型无疑是最适合的.本文用电路模型来模拟简单的隔振模型和动力吸振模型.分析及数值结果证明该电路模型实现了机械振动控制系统的本身的规律,可以实现预期的功能.这样,我们可用电学实验去实现机械振动控制实验.     

The derivation of general kinematic equations of spatial constrained mechanical systems with the aid of a computer

The kinematic solution of constrained spatial mechanical systems esp., of spatial mechanisms with nonconstant velocity ratio is usually carried out numerically with the aid of a computer. As far as the analytical solution is concerned, we are still forced to use hand computation although there exist general methods and procedures which enable us to obtain the starting kinematic equations of motion. This step is a frequent source of errors, because essentially we must multiply a great number of matrices of the type (4 × 4) whose elements are, in general, trigonometric expressions. The aim of this paper is to introduce a method that enables us to obtain the mathematical model automatically with the aid of a computer using only basic information about dimensions and variables. The procedure is based on the application of the transformation matrices of basic motions [1,2] and of the programs for symbolic operations with matrices [3].     

Functional process capability analysis in mechanical systems

Functional quality in the mechanical products is governed mainly by the degree of satisfaction of the design requirements, which itself depends on the variations in the effective variables. The functional parameters cannot be easily measured in mass production, and thus, are not usually considered as a direct inspection objective. Process capability indices are useful tools for evaluating the ability of a process to produce the dependent variables of a product that meet certain specifications. In this paper, the conventional process capability concept is extended to develop a computational tool for analysis of the functional quality of a mechanical product. Through defining new proper indices called functional process capability indices (FPC_p, FPC_pk, FPC_pm, and FPC_pmk), a statistics-based process capability analysis method is used to estimate the ability of a manufacturing process for meeting the functional requirements of a mechanical system. Using this approach for statistical design of a mechanical product, the effects of variations in manufacturer’s dimensions on the functional requirements of a product can be evaluated. A parameter is introduced which quantifies the contribution of variables that reduce the functional process capability. The applications of the proposed method are demonstrated through implementing it on two case studies and the results are discussed.     

Non-linear flexible body analysis for mechanical systems

Component mode synthesis method considers only small deformation problems and cannot handle large deformation problems. This paper presents an improved mode synthesis method. Mild geometric nonlinear problems have been solved by considering nonlinear effects in the stiffness matrix.     

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.     

基于状态空间方法的机械运动方案设计的理论基础

为解决机械运动方案的设计问题,提出了机械运动方案设计的状态空间方法,以基本变换单元为功能载体,构建了状态特征矢量,并推导获得了状态方程;提取了状态矩阵内非零元素的运动特征值,讨论了对偶矢量及状态空间的相关性质,得到了状态空间中运动变换特征矢量的运算规则,为应用状态空间方法实现方案设计的可计算自动求解提供了理论基础。     

基于状态空间方法的机械运动方案设计的综合求解及算法实现

依据机械运动方案设计的状态空间理论,实现了把串联机械系统的运动方案设计问题转化为对偶矢量的分解,进而转化为状态矩阵的分解,通过组合状态矩阵对应的基本变换单元获得相应的运动方案设计可行解。在此基础上,建立了方案设计的知识库,并转换为相应的数据结构,提出了求解过程中运动的类型方向、变换特征分解及综合求解算法。最后,通过一个设计实例验证了状态空间方法的有效性。     

Topology and kinematic analysis of color-changing ball

The color-changing ball has two stable configurations. Its mechanism is a multiple loop and polygonal mechanism. This paper investigates the mechanism typology and analyzes its structure and configurations during motion. A three-legged mechanism is extracted from this mechanism. The kinematics model of the mechanism is presented and singularity is discussed. The paper further decomposes the mechanism and investigates the platform structure of the intersection between loops. This leads to investigation of the offset of joint intersection at the intersection and its relevant geometry and kinematics. The paper further focuses on the configuration change between two states of the mechanism and investigates kinematics and singularity between two configurations. Based on the analysis, simulation of the color-changing ball is carried out. The topology and kinematics analysis in this paper helps the analysis of this kind of polyhedral linkage mechanism with radial motion. The research could potentially lead to the development of kinematics for design of this kind of mechanism.     

Analysis of kinematic systems: a generalized approach

The goal of the designer of kinematic systems is a deterministic and stable design. An analysis method must, therefore, be able to quantify both aspects. The generalized approach to the analysis of kinematic systems presented herein reduces the analysis of kinematic systems to simple matrix analysis. The system matrix containing the geometry of the system is introduced as the key to the analysis of kinematic systems. The procedure calculates the magnitudes of the contact forces from the external forces. Then Hertz's theory is used to estimate the deflections at the contact points, from which global error motions are computed. The method has been developed for two-body systems with an arbitrary number of unconstrained degrees of freedom. From these elementary building blocks, more complex systems can be assembled. We show how friction can be included in the model, based on simplifying assumptions. The quality/performance of the design can be checked at various points throughout the analysis. We show that the stability of kinematic systems is closely linked to the eigen values of the system matrix. The general formulation naturally includes previous work on such special cases as couplings and linear motion systems.     

The kinematic analysis of axial-piston pumps

This investigation describes the kinematics of axial hydraulic pumps with spherical ended pistons. The results, however, apply to the basic kinematics of all axial piston pumps. The current hypothesis is that sliding at the piston/swash plate interface contributes to the wear of these parts. The analysis concludes that sinusoidal sliding is inherent at the piston/swash plate contact point, and that its magnitude is a function of the pump design variables. Therefore, manipulation of the basic design variables of the pump is the key to controlling the amount of sliding and related wear at the contact point.     

随机因素对机加过程的涉扰性分析

分析了对机械加工过程产生涉扰的工艺系统部分随机因素以及该类随机因素对加工过程涉扰的机理,给出了估计涉扰程度的方法,同时提出了减少工艺系统部分随机因素对加工过程涉扰的对策。     

A kinematic analysis of disk motion in a double sided polisher for chemical mechanical planarization (CMP)

Double sided polishers are commonly used for industrial applications, such as lapping of silicon substrates and chemical mechanical planarization (CMP) of rigid disks. Whereas a kinematic analysis of a single sided polisher, extensively used for IC wafer CMP, is well known, available sources of such an analysis are limited for a double sided polisher, due to its more complicated design.The present work demonstrates a kinematic analysis for obtaining trajectory and relative velocity of a single location on a work piece during double side polishing. Relative velocity is used to calculate travel distance to be compared with the amount removed experimentally obtained. This paper presents mathematical derivation of the analysis and its effectiveness/limitations in conjunction with comparison between the analytical and experimental results.     

Self-locking analysis in closed kinematic chains

Self-locking analysis in closed kinematic chains is sometimes likened to kinematic singularity analysis, especially when mechanisms are characterized by more than one degree of freedom. Although in singular configurations a mechanism is obviously locked-up since joint constraint reactions and friction forces rise to infinity, this approach identifies only a condition sufficient for self-locking, while the phenomenon actually occurs in a larger domain, the size of which depends on the values of friction coefficients.The paper proposes a definition of self-locking for multi degrees of freedom mechanisms and presents an algorithm for computing the geometrical locus that corresponds to a specific self-locking configuration. This methodology is then demonstrated on a simple parallel kinematic mechanism with two degrees of freedom.     

Sensitivity analysis for estimation of inertial parameters of multibody mechanical systems

As an important issue, we first address in this paper the problem of a regression matrix with non-homogeneous physical units in the parameter estimation of multibody systems. This matrix contains the most important information about the motion of the system. Attention must be paid to this before implementing any parameter estimation algorithm due to the unit inconsistency in matrix multiplication required in such algorithms. A procedure to treat this problem in a proper way will be proposed. An experiment on a six degrees of freedom (DOF) robotic device, whose reference link follows a desired trajectory, is performed. The data collected from the experiment are then used for sensitivity analysis of inertial parameters based on the unit-homogenized regression matrix of the system. In this way, we characterize the influence of each selected inertial parameter on the dynamics of the system using unit-consistent mathematical manipulations.     

Workspace optimization and kinematic performance evaluation of 2-DOF parallel mechanisms

This paper presents the kinematics and workspace optimization of the two different 2-DOF (Degrees-of-Freedom) planar parallel mechanisms: one (called 2-RPR mechanism) with translational actuators and the other (called 2-RRR mechanism) with rotational ones. First of all, the inverse kinematics and Jacobian matrix for each mechanism are derived analytically. Then, the workspace including the output-space and the joint-space is systematically analyzed in order to determine the geometric parameters and the operating range of the actuators. Finally, the kinematic optimization of the mechanisms is performed in consideration of their dexterity and rigidity. It is expected that the optimization results can be effectively used as a basic material for the applications of the presented mechanisms to more industrial fields.     

管外移动机器人运动学分析

本文简要地介绍了管外移动机器人的研究意义和应用，以及管外移动机器人的主要功能和结构特点，建立了管外移动机器人运动学Ａ、Ｂ双模型；并给出其正逆问题求解公式。