制造误差对过约束机构性能影响的研究

针对平面闭链机构为超静定的过约束结构和制造误差的非平面性，将结构力学中处理超静定结构的力分析法与平面连杆机构的动力分析相结合，以构件的扭转变形和弯曲变形为变形协调条件，建立了考虑非运动平面过约束的平面加杆机构动力学分析模型，仿真结果揭示了制造误差对过约束机构性能的影响。     

基于运动副自由度优化配置的机构自调性设计研究

针对机构动力性能对形位误差敏感的问题，通过约束分析，发现普遍使用的平面闭链机构在理想平面约束条件下存在对机构工作性能不起作用的过约束，并导致机构系统对制造误差很敏感，要求很高的制造精度。为此，以曲柄导杆机构为例，阐述如何配置机构的约束和自由度，设计自调性机构。结果表明所得到的自调机构可大幅度降低机构对误差的敏感度，降低生产成本，减轻装配难度，提高机构的传动效率、使用寿命和对环境的适应能力。从机构的结构因素上消除了误差对机械品质的影响，大大提高了其稳健性。     

平面5R并联机器人约束误差影响分析

少自由度并联机器人中的过约束构型,具有结构简单、刚度大的优点,但其依赖运动副轴线间的特殊几何约束关系,如平行、垂直、汇交于一点等,来实现预期的动平台自由度。此类机构有对几何约束条件敏感的缺点,约束误差的存在将对机构产生一系列不良影响。基于此,以平面5R并联机器人为对象,在分析其过约束特性基础上,研究运动副轴线几何约束误差导致的回路封闭变形协调条件。应用矩阵力法计算强制装配引起的机构附加内力以及连杆的变形,从而分析动平台的寄生运动以及机构的应变能波动。对一种具体的5R并联机器人进行仿真分析,计算结果揭示了过约束机构对运动副轴线几何约束误差的敏感性以及约束误差与过约束共同作用下对并联机器人性能的影响机理。     

具有重复结构的平面连杆机构的过约束分析

给出空间平面过约束和理论平面过约束的定义，分析了这两种过约束对机构误差的敏感特性。提出具有重复结构的平面连杆机构的过约束分析方法，得到该粪机构存在的过约束的数量和类型。从而为该类机构消除或减小过约束影响的措施的采取指明了方向。     

平面连杆机构的自调及其允差的分析研究

以V－V－Ⅳ-Ⅲ运动副配置的无过约束平面曲柄滑块机构为研究对象，分析了机构自调的机理及其自调时圆柱副中的位移协调规律，根据移动副中的自锁条件导出机构能够实现自调的条件，在此基础上，得到机构能够实现自调的允许误差角，为消除或减小过约束机构结构的采用以及机械的精度设计提供了理论依据。     

平面闭链六杆机构的自调结构及允差的研究

分析了串联watt型六杆机构的无过约束结构、自由度配置及在此配置下的自调与允差。结果表明:多回路机构只有按每一回路的零过约束配置设计,才能确保整个机构的无过约束,且每一回路内存在自调构件时,机构较易实现无过约束配置;公共铰链采用V级副时,机构能同时保持平面运动特性;公共铰链的形位误差会直接影响两个回路的平面约束不确定性。     

具有重复结构的平面连杆机构的过约束分析

给出空间平面过约束和理论平面过约束的定义,分析了这两种过约束对机构误差的敏感特性.提出具有重复结构的平面连杆机构的过约束分析方法,得到该类机构存在的过约束的数量和类型,从而为该类机构消除或减小过约束影响的措施的采取指明了方向.     

带有约束的3-TPS并联机床位姿误差分析

针对并联机床运动副数量多,结构复杂,误差分析难度大等问题,以一种带有约束机构的3-TPS并联机床为研究参考,将并联机构部分和约束机构部分分别进行建模,研究单一几何误差对末端位置的影响,并用蒙特卡洛法对多个误差源进行统计分析,结果表明来自约束机构部分的误差源对末端位置误差的影响更为明显。     

平面闭链机构中过约束分析的研究与应用

由于不可避免的制造误差，平面闭链机构中广泛存在的过约束，导致对机械性能的一系列有害影响。因而越来越受到机械结构设计者的重视，提出了多种机构过约束的分析方法。但是，这些方法还存在一些不足，还需进一步发展完善。因此在深入、系统研究这些方法的基础上，重点介绍了其中两种较好的方法，提出了一些新的见解，并总结出了一些完善过约束分析方法及其在消除或减小过约束影响设计、应用方面的结论和原则。     

含运动副间隙平面轨迹机构的可靠性设计

针对平面轨迹机构,提出一种同时考虑尺寸公差和运动副间隙的机构可靠性设计方法。首先应用截尾降维方法处理机构运动误差函数中的运动副间隙变量,以此建立机构各输出分量的误差概率模型,并以各运动分量误差的联合概率密度函数求解机构运动的综合可靠度。在此基础上,建立以机构结构误差最小为目标和机构运动的综合可靠度为约束的机构可靠性设计模型。最后给出数值实例对所提方法的有效性进行验证。     

平面连杆机构运动误差综合的研究（Ⅰ）──运动误差综合的单位向量法

以运动误差分析为基础，从机构输出运动误差最小出发，给出了机构输出运动误差极值理论，提出了机构运动误差综合的单位向量法。该法具有公差分配合理，简单为行，无需优化，适用空间机构等优点，最后给出了算例．     

Kinematic analysis of geared linkage mechanisms

A general approach to the kinematic analysis of planar geared linkage mechanisms (GLMs) is presented based on their structural topological characteristics. Firstly, a systematic method for decomposing a GLM into a series of sequential independent kinematic units, such as the simple links and the dyad link groups is proposed. The concept of tricolored graph and its mathematic expressions are introduced to describe the topological relationship between the kinematic pairs and the links in a GLM. The criteria and process for the structural decomposition and for choosing circuits using the theory of type transformation are established. Then the kinematic equations and the analytic solutions for the kinematic units are derived, and the method for the kinematic analysis of position, velocity and acceleration of GLMs is obtained in an algorithmic fashion. Finally, an application program has been developed, by which the whole work from the structural decomposition to the kinematic analysis can be accomplished automatically for any one of the GLMs. Some examples are used to illustrate the procedures.     

Design and accuracy analysis of a metamorphic CNC flame cutting machine for ship manufacturing

The current research of processing large size fabrication holes on complex spatial curved surface mainly focuses on the CNC flame cutting machines design for ship hull of ship manufacturing. However, the existing machines cannot meet the continuous cutting requirements with variable pass conditions through their fixed configuration, and cannot realize high-precision processing as the accuracy theory is not studied adequately. This paper deals with structure design and accuracy prediction technology of novel machine tools for solving the problem of continuous and high-precision cutting. The needed variable trajectory and variable pose kinematic characteristics of non-contact cutting tool are figured out and a metamorphic CNC flame cutting machine designed through metamorphic principle is presented. To analyze kinematic accuracy of the machine, models of joint clearances, manufacturing tolerances and errors in the input variables and error models considering the combined effects are derived based on screw theory after establishing ideal kinematic models. Numerical simulations, processing experiment and trajectory tracking experiment are conducted relative to an eccentric hole with bevels on cylindrical surface respectively. The results of cutting pass contour and kinematic error interval which the position error is from –0.975 mm to +0.628 mm and orientation error is from –0.01 rad to +0.01 rad indicate that the developed machine can complete cutting process continuously and effectively, and the established kinematic error models are effective although the interval is within a ‘large' range. It also shows the matching property between metamorphic principle and variable working tasks, and the mapping correlation between original designing parameters and kinematic errors of machines. This research develops a metamorphic CNC flame cutting machine and establishes kinematic error models for accuracy analysis of machine tools.     

空间并联机构运动学与动力学分析的新方法

空间并联机构的运动学与动力学分析具有相当的复杂性。将Dynamic Designer／Motion仿真模块和Solidworks三维建模软件结合，提出了一种进行空间并联机构运动学与动力学分析的新方法——仿真分析法，并给出了其在六自由度八面体变几何桁架机构设计中的应用实例。文中给出了实现仿真分析所涉及的主要技术方法和详细步骤。     

非线性方程组解集边界求解方法及其在并联机构分析中的应用

并联机构的结构使其输入和输出运动之间具有复杂的非线性关系,在该类机构的运动学、动力学、作业空间、误差分析及运动控制中均涉及大量的非线性方程组求解。介绍一种含参数的非线性方程组的解集边界求解方法,基于流形理论和数值化连续算法,可直接搜索出一个非线性系统的解集边界,计算速度快、效率高。利用上述算法,对一台实际的4自由度并联机床进行了作业空间边界的求解和分析,验证了算法的实用性和有效性。     

Axis geometrical errors analysis through a performance test to evaluate kinematic error in a five axis tilting-rotary table machine tool

Geometrical work piece errors in milling process are commonly generated by different error sources. Axis geometrical errors, such as the straightness error for linear axis and the offset location error of the origin of rotary axis, introduce kinematic error in the tool path. Direct measurement of kinematic error requires special devices such as laser interferometers, grid plate encoders or double ball bars, which impose production stop and specialized staff. These problems could be analyzed using indirect measurements obtained by means of a cutting performance test that is already a standard for three axis machine tools. Because of the different architectures of five-axis milling machines these tests are hardly standardizable, therefore this paper proposes a devised easy-to-use and time efficient cutting performance test to identify and quantify axis geometrical errors for a five axis tilting-rotary table machine tool. This test can be performed as a periodical checkup or, in case of production, as a re-start test. The main goal of this study is to develop a kinematic analytical model capable of correlating the work-piece geometrical errors to the axis geometrical errors of the machine tool. The model has been implemented on a multi-body software in order to simulate the axes motion sequence of the performance test and validated to decouple the kinematic error into the geometrical axis errors. The developed models have demonstrated to be capable of correcting a generic five axis tool path by predicting the tool-path error displacement. The overall validation of this approach has been carried out by comparing the simulated and experimentally measured profile of the NAS 979 standard five axis contouring cone frustum profile.     

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.     

Mathematical models for analysis and synthesis of spatial mechanisms—I: Four-link spatial mechanismsMathematische modelle zur analyse und synthese von räumlichen mechanismen. Teil 1: Räumliche 4 gliedrige mechanismen

In this paper mathematical models of links connecting all possible combinations of lower kinematic pairs are described simply by determining direction cosines of various joint axes using Plücker line coordinates. These models can be used in conjunction with the decomposition method [4] to analysis and synthesis single and multi-loop spatial mechanisms.     

Error analysis and auto-calibration for a Cartesian-guided tripod machine tool

This paper focuses on the error analysis and calibration methodologies for a parallel kinematic machine (PKM) called a Cartesian-guided tripod (CGT). The CGT volumetric error due to the geometric error, kinematic parameter error and nonlinear machine stiffness were studied. It is well known that the PKM nonlinear machine stiffness can produce significant volumetric errors from several tens to several hundreds of micrometres depending on the averaged value and deviation range for the machine stiffness. For most PKMs, joint level sensors are used to estimate the virtual Cartesian movements of the cutting tool. The nonlinear stiffness effect is not detected by this indirect metrology method and must be compensated for by a calibration methodology. A solution for the nonlinear stiffness effect implemented on the CGT involves using a passive Cartesian guiding/metrology leg that is independent of the driving legs to directly measure the Cartesian movement of the motion platform. Because the metrology loop of the Cartesian guiding/metrology leg is separated from the kinematic loops of the driving legs, the volumetric accuracy of the CGT is immunised against thermal errors and load deformations on the drive mechanisms. The passive Cartesian guiding/metrology leg is also used for the auto-calibration of the CGT kinematic parameters. The auto-calibration methodology and simulation results were studied and reported.     

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.