含间隙平面连杆机构运动分析的杆组法 (Ⅱ)应用杆组法进行含间隙机构运动误差分析的基本方法

采用连续接触模型,编制了求解含间隙杆组的通用子程序和辅助子程序,结合应用无间隙机构和含间隙机构的杆组法,提出了考虑运动副间隙影响的平面连杆机构运动误差分析的基本方法和步骤。     

含间隙平面连杆机构运动精度的稳健优化设计

考虑杆长制造误差和运动副间隙的影响,提出一种平面连杆机构的稳健设计方法。对运动副间隙引起的回转副偏心距及其对平面机构位姿的影响进行分析,用位置矢量方程描述考虑运动副间隙后平面机构的位姿。根据构件两端回转副要素的实际结构,把构件分成两孔型、孔销型、两销型三种类型。把回转副偏心距的大小及其方向视为两个随机变量,建立三种相应的有效杆长计算模型。采用复数矢量法,推导出三种有效杆长计算公式。对所建立的有效杆长计算模型的计算精度进行数值仿真,结果表明其计算精度可满足工程设计要求。基于所建立的有效杆长计算模型,给出再现函数的曲柄滑块机构的稳健优化设计实例,验证了文中方法的有效性和实用性。     

含间隙平面连杆机构运动分析的杆组法──(1)求解含间隙基本二级杆组的数学模型

建立了考虑运动副间隙的五种基本类型二级杆组的数学模型,并据此编制了求解含间隙二级杆组的通用子程序和一些辅助子程序,从而使传统的杆组法能够应用于含间隙平面连杆机构的运动误差分析。     

Workspace analysis of positioning discontinuities due to clearances in parallel manipulators

Clearances at joints produce a loss of accuracy when positioning a mechanism. The end-effector pose error due to clearances depends on the mechanism configuration, the magnitude of the clearance itself and applied external wrenches. Sudden changes which occur in the actual posture of the mechanism owing to a change of contact mode at joints can be detected in the neighbourhood of some configuration. These sudden changes lead to positioning discontinuities on certain trajectories, or on the workspace. In this paper, a methodology for analysing the location of the discontinuities by means of a dynamic or kinetostatic analysis is presented. The advantages of choosing either the dynamic or the kinetostatic approach are analysed, making use of the 5R planar mechanism.     

用连续接触模型预测平面连杆机构转动副的分离

本文采用平面连杆机构有间隙转动副的连续接触模型，来计算机构周期运动时的间隙副的运动反力，由间隙杆受压来预测实际的含间隙的运动副在机构周期运动时是否会发生分离。本文以一平面四杆机构为例说明了该方法。     

平面连杆机构运动误差及可靠性分析

为获得考虑运动副间隙和杆长误差的平面连杆机构运动规律，采用复数矢量法，推导出运动误差计算公式，在此基础上建立了曲柄滑块机构运动精度可靠性分析模型，编制了相应的计算机软件，并计算出算例机构位置参数和输出运动误差的方差和可靠度。     

Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network

Clearance is inevitable in the joints of mechanisms due primarily to the design, manufacturing and assembly processes or a wear effect. Excessive value of joint clearance plays a crucial role and has a significant effect on the kinematic and dynamic performances of the mechanism. In this study, effects of joint clearances on bearing vibrations of mechanism are investigated. An experimental test rig is set up, and a planar slider-crank mechanism having two imperfect joints with radial clearance is used as a model mechanism. Three accelerometers are positioned at different points to measure the bearing vibrations during the mechanism motion. For the different running speeds and clearance sizes, this work provides a neural model to predict and estimate the bearing vibrations of the mechanical systems having imperfect joints. The results show that radial basis function (RBF) neural network has a superior performance for predicting and estimating the vibration characteristics of the mechanical system.     

A simple method for the allocation of appropriate tolerances and clearances in linkage mechanismsEine einfache methode zur auswahl von toleranzen und lagerspiel in koppelgetrieben

A method for the calculation of appropriate tolerances on the link lengths and clearances in the joints of linkage mechanisms is presented. Account is taken of the variation of the sensitivity of the output of the mechanism to variations in mechanism parameters which arises from the change in geometry of the mechanism throughout its cycle of operation. To demonstrate the applicability of the method to a wide range of planar linkage mechanisms, two examples are given: a 4-bar function generator (the results for which are compared with those of previous investigations) and a 10-bar linkage from the textile industry.     

任意分布参数平面连杆机构运动精度可靠性灵敏度设计

将可靠性设计理论与灵敏度分析方法相结合,讨论了任意分布参数平面连杆机构运动精度可靠性灵敏度设计问题。首先,结合机构精确度理论和可靠性理论,提出任意分布参数平面机构运动精度可靠性评估方法。然后,引入灵敏度设计理论,推导出任意分布参数平面机构运动精度可靠性灵敏度设计方法。最后,以平面四杆机构为例,详细阐述了设计参数的改变对平面连杆机构运动精度可靠性的影响,为平面连杆机构的运动精度可靠性设计和可靠性维护提供了理论依据。     

Accuracy modeling,analysis and radical error distribution of 3-RPR planar parallel mechanism

Output accuracy performance is directly determined by geometric errors and working poses of a mechanism. Accuracy sensitivity as geometric error transmission coefficient, closely relates to pose configuration and geometric parameters. This research focuses on accuracy of a 3-RPR planar parallel mechanism: firstly, established 3 models in an analytic form, to describe relationship between output errors and geometric ones, then they are mutually verified statistically. Secondly, the anisotropy and periodic fluctuation of position errors, independently contributed by each category of geometric errors, are illustrated; and mirror symmetric trajectories and poses generating output errors with mirror symmetry, are also revealed by numerical simulation. Finally, the radical accuracy model in an analytic form, was established through variance and covariance analysis on output errors. We concluded that the radical error of the movable platform in central symmetric poses, follows Rayleigh distribution pattern. Through statistical comparison with Monte Carlo simulation, the radical error model was demonstrated, that provided a reference for accuracy design for other planar parallel mechanism.

     

高速压力机机构运动精度可靠性研究

利用矩阵分析理论建立了平面连杆机构精度分析的一般模型,利用可靠性状态函数建立了连杆机构运动精度可靠性指标计算模型,以高速压力机机构为具体对象,建立了曲柄滑块机构运动输出精度模型及其可靠性分析计算模型。算例分析表明:在给定的设计精度下,高速压力机机构在不同的运动状态有着不同的运动误差和不同的运动可靠度。该模型可以定量地给出机构在不同运动状态下的失效概率,对机构的设计与制造具有应用价值。     

Error analysis of a parallel mechanism considering link stiffness and joint clearances

In order to utilize a parallel mechanism as a machine tool component, it is important to estimate the errors of its end-effector due to the uncertainties in parts. This study proposes an error analysis for a new parallel device, a cubic parallel mechanism. For the parallel device, we consider two kinds of errors. One is a static error due to link stiffness and the other is a dynamic error due to clearances in the parts. In this study, we propose a stiffness model for the cubic parallel mechanism under the assumption that the link stiffness is a linear function of the link length. Also, from the fact that the errors of u-joints and spherical joints are changed with the direction of force acting on the link, they are regarded as a part of link errors, and then the error model is derived using forward kinematics. Lastly, both the error models are integrated into the total error, which is analyzed with a test example that the platform moves along a circular path. This analysis can be used in predicting the accuracy of other parallel devices.     

含非规则粗糙间隙表面铰链关节的平面柔性多连杆传动系统动态误差与运动副磨损周期行为分析

传统旋转间隙关节接触模型假定销轴和衬套接触面形状是规则的并忽略了磨损效应的影响,降低了机构动力学模型预测精度。提出了一种含非规则粗糙间隙表面铰链关节的平面柔性多连杆机构多体动力学建模、磨损预测和动态误差分析方法。为准确描述运动副元素间碰撞行为,考虑滑动轴承间隙关节的磨损效应,提出了一种非规则粗糙间隙表面铰链关节的改进接触模型。在此基础上,考虑柔性杆的影响,基于绝对节点坐标法建立了含非规则粗糙间隙表面铰链关节的平面柔性多连杆传动系统多体动力学模型。与基于传统光滑间隙模型的结果相比,基于非规则粗糙间隙改进模型的多连杆机构动态响应更接近于试验值,验证了所提出计算方法的有效性。仿真结果表明,选用CuSn10P和CuPb30作为铰链衬套材料能够有效降低多连杆机构滑块动态响应偏差和提高机构的运动精度;表面粗糙度过高会导致运动副磨损加剧,过低则会降低间隙表面微凸体对碰撞能量的吸收。此外,磨损加剧了间隙表面轮廓不规则度,导致机构动态响应的不稳定性增大,运动精度降低。     

制造误差对四杆机构轨迹综合精度的影响分析

通过建立杆长制造误差对平面四杆机构轨迹综合精度影响的数学模型,确定了杆长制造误差的敏感系数,分析了杆长制造误差对轨迹综合精度的影响规律。设计实例说明,合理设计四杆机构杆长制造公差,可使机构既满足精度要求又降低制造成本。     

具有运动副间隙机构的动力学研究

在本论文中,依据Kane方法,建立了一种新的研究具有运动副间隙的机构动力学的数学模型。作为一个例子,研究了有一个运动副间隙的平面曲柄摇杆机构,所得到的数学模型比现有的模型准确而且简单,数值结果准确地揭示了由于存在运动副间隙在机构高速运转时所产生的动特性。这种方法容易推广用于有运动副间隙的空间机构的研究。     

VB在平面四连杆机构运动分析中的应用

介绍了基于VB实现对平面四连杆机构进行全面运动分析的方法.通过一种简单有效的方法建立了数学模型,采用计算机模拟技术,能动态演示机构的运动和自动绘制连杆上任意点的轨迹曲线,并能输出各运动构件的位移图、速度图和加速度图.为平面四连杆的运动分析提供了一条简单易行的途径.     

Reducing undesirable vibrations of planar linkage mechanism with joint clearance

An optimization design method is presented to reduce the undesirable vibrations caused by clearance for planar linkage mechanism. A clearance joint is defined and considered a contact/impact force constraint. Contact and impact force models for the clearance joint are established using a normal contact force model based on Hertz model with energy loss and a tangential friction model based on modified Coulomb model with dynamic friction coefficient, respectively. In view of the clearance joint, dynamic equations and optimization method for a planar four-bar mechanism are then presented as an application example. The optimization aims to minimize the maximum absolute acceleration peaks of the mechanism by determining the link lengths of the planar linkage mechanism. Finally, the optimization design is solved by a generalized reduced gradient algorithm. Results show evident decrease in vibration peaks of the mechanism and obvious reduction in the contact forces in the clearance joint, which contribute to a good performance of planar linkage mechanism systems.     

A new screw theory method for the estimation of position accuracy in spatial parallel manipulators with revolute joint clearances

This paper presents a novel method based on screw theory for the analysis of position accuracy in spatial parallel manipulators with revolute joint clearances. The method is general, and can tackle with an arbitrary pose error function, expressed as a quadratic function of the end-effector displacement.The method performs a maximization of the pose error function, based on a 2-step computational procedure. The first computational step is analytical and leads to a sub-optimal estimate of the maximum pose error. This analytical solution represents the exact maximum pose error for the calculus of the angular accuracy in the special case of fully translational parallel mechanisms. The second computational step is numerical, and starting from the previous solution, can converge to the exact maximum pose error in a limited number of iterations.The relevance of the method is demonstrated through some application examples, where the worst-case angular and linear position accuracy in translating fully parallel manipulators is determined. As a further contribution, this paper shows how the position accuracy due to joint clearances in parallel manipulators is strictly dependent of the mechanism pose and its association to kinematic isotropy.     

Modeling and simulation of joint clearance effects on mechanisms having rigid and flexible links

In this study, kinematic and dynamic characteristics of a planar four-bar mechanism having joint clearance and link flexibility are investigated. Assuming that joint clearance as a virtual massless link, artificial clearances are developed at crank-coupler and coupler-follower joints. Contact model in joints with clearance is established using the nonlinear spring-damper model and the friction effect is considered using the Coulomb friction model. Then the simulation is implemented and the kinematic and dynamic characteristics of model mechanism are investigated. The computational methodology can predict the effects of clearance on planar mechanism having rigid and flexible links. The results are evaluated for the case of stationary phase, and naturally show that extreme values occur in output of the mechanism with clearances. Due primarily to the suspension effect of the flexible link, values of these peaks in the flexible mechanism decrease relative to that of the rigid mechanism. In addition, the flexibility has a significant effect on the vibration response of the mechanism with joint clearance.     

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.