Stiffness estimation of a parallel kinematic machine

This paper presents a simple yet comprehensive approach to quickly estimating the stiffness of a tripod-based parallel kinematic machine. This approach can be implemented in two steps. In the first step, the machine structure is decomposed into two substructures associated with the machine frame and parallel mechanism. The stiffness models of these two substructures are formulated by means of virtual work principle. This is followed by the second step that enables the stiffness model of the machine structure as a whole to be achieved by linear superposition. The 3D representations of the machine stiffness within the usable workspace are depicted and the contributions of different component rigidities to the machine stiffness are discussed. The result is compared with that obtained through finite element analysis.     

Calibration of a Parallel Kinematic Machine Tool

The parallel kinematic machinetool(PKMT)is anew-style machine tool[1].Though it has an advan-tage over traditional NC machine tool due to a seriesof characteristics such as si mple structure,fast re-sponse speed and non cumulative errors[2,3],its abso-lute accuracy is not sufficient for a machine tool re-quiring high accuracy.A mainfactor reducingthe ac-curacy is kinematic parameter errors caused by ma-chining and assembling errors[4].Calibration is a solution to this problem.It ismore prac…     

An approach to error elimination for multi-axis CNC machining and robot manipulation

The geometrical accuracy of a machined feature on a workpiece during machining processes is mainly affected by the kinematic chain errors of multi-axis CNC machines and robots, locating precision of fixtures, and datum errors on the workpiece. It is necessary to find a way to minimize the feature errors on the workpiece. In this paper, the kinematic chain errors are transformed into the displacements of the workpiece. The relationship between the kinematic chain errors and the displacements of the position and orientation of the workpiece is developed. A mapping model between the displacements of workpieces and the datum errors, and adjustments of fixtures is established. The suitable sets of unit basis twists for each of the commonly encountered types of feature and the corresponding locating directions are analyzed, and an error elimination (EE) method of the machined feature is formulated. A case study is given to verify the EE method. Recommended by Prof. XIONG YouLun, Member of Editorial Committee of Science in China, Series E: Technological Sciences Supported by the National Natural Science Foundation of China (Grant Nos. 50475141, 50436010), the “973” Research Foundation of China (Grant No. 2005CB724103) and the Program for New Century Excellent Talents in University (Grant No. NCET-05-0651)     

Kinematic calibration of a class of parallel kinematic machines (PKM) with fewer than six degrees of freedom

The accuracy of parallel kinematic machines (PKM), particularly machine tools is an important performance index. It has been acknowledged that kinematic calibration is a practical and economical way for enhancing the accuracy of PKM systems. The procedure usually involves four steps, i.e. error modeling, measurement, identification and implementation[1,2]. So far, most work on the kinematic calibration of PKM systems has focused upon the objects with six degrees of freedom (DOF)[3—13]. A…     

Theory of loop algebra on multi-loop kinematic chains and its application

Based on the mathematic representation of loops of kinematic chains, this paper proposes the " ⊕ " operation of loops and its basic laws and establishes the basic theorem system of the loop algebra of kinematic chains. Then the basis loop set and its determination conditions, and the ways to obtain the crucial perimeter topological graph are presented. Furthermore, the characteristic perimeter topo-logical graph and the characteristic adjacency matrix are also developed. The most important characteristic of this theory is that for a topological graph which is drawn or labeled in any way, both the resulting characteristic perimeter topological graph and the characteristic adjacency matrix obtained through this theory are unique, and each has one-to-one correspondence with its kinematic chain. This character-istic dramatically simplifies the isomorphism identification and establishes a theoretical basis for the numeralization of topological graphs, and paves the way for numeralization and computerization of the structural synthesis and mechanism design further. Finally, this paper also proposes a concise isomorphism identifica-tion method of kinematic chains based on the concept of characteristic adjacency matrix.     

Inverse dynamics and servomotor parameter estimation of a 2-DOF spherical parallel mechanism

A novel reconfigurable 5-DOF hybrid manipulator—TriVariant-B is composed of a 2-DOF spherical parallel mechanism which is serially connected with a 3-DOF open-loop kinematic chain undergoing one translation and two rotations by a prismatic joint. The merit of this design is that a relatively large workspace/limb-stroke ratio can be achieved thanks to the decomposition of the fixed point rotation and the relative translation. In this paper, on the basis of inverse dynamic formulation of the 2-DOF spherical parallel mechanism, an approach is proposed for estimating the servomotor parameters including moment of inertia, rated speed and the maximum torque in a quick manner. The approach has been employed for the development of a prototype for frame cutting process. Supported by the National Natural Science Foundation of China (Grant Nos. 50535010 and 50510488)     

3-PRS并联机构位置正解分析

根据3-PRS并联机构具有2个转动自由度和1个移动自由度的结构特点,利用封闭矢量方法和简化坐标转换矩阵,得到该机构运动平台中心的运动方程,然后运用遗传算法并结合其运动方程给出并联机构运动学位置正解适应度函数和目标函数,将计算结果代入运动方程求出杆长,其误差小、精度高,为3-PRS并联机构的控制策略奠定了基础．该解法既不需要选取迭代初值,也不需要复杂的数学推导,容易实现而且通用性强．     

基于运动学方程的停车波模型

为描述连续交通流中的停车波现象,分析了停车波传播的运动学特性,基于运动学方程建立了停车波模型。研究表明,该模型与基本交通波模型推导的停车波模型一致。为验证该模型,设计了数据采集方案及参数标定方法。利用长春市的调查数据标定了模型,得到停车波波速理论值与实测值之间的相对误差为3.85%。结果表明,基于运动学方程的停车波模型可以描述连续交通流中的停车波现象,参数标定方法简单可行。     

基于逆运动学的6-UPS并联机构运动学参数辨识方法

为了提高6-UPS并联机构的定位精度,研究了一种基于逆运动学的6-UPS并联机构运动学参数辨识方法.首先基于逆运动学建立了6-UPS并联机构的运动学参数辨识模型,然后通过Levenberg-Marquardt最小二乘法对模型进行求解,最后对该算法进行了仿真验证.结果表明该算法可以很快收敛,在测量设备没有测量误差的理想状态下,参数辨识精度达到10-10mm.在测量设备存在1μm、1″的误差状态下,参数辨识精度达到10-3mm,足以满足大部分应用场合下6-UPS的位姿精度要求.     

Error modeling,sensitivity analysis and assembly process of a class of 3-DOF parallel kinematic machines with parallelogram struts

This paper presents an error modeling methodology that enables the tolerance design, assembly and kinematic calibration of a class of 3-DOF parallel kinematic machines with parallelogram struts to be integrated into a unified framework. The error mapping function is formulated to identify the source errors affecting the uncompensable pose error. The sensitivity analysis in the sense of statistics is also carried out to investigate the influences of source errors on the pose accuracy. An assembly process that can effectively minimize the uncompensable pose error is proposed as one of the results of this investigation.     

基于元动作单元的数控机床运动精度映射

为使数控机床精度设计有定量的理论数值供参考,从运动的角度出发,建立了基于元动作单元的数控机床运动精度映射模型. 采用“功能(Function)-运动(Motion)-动作(Action), FMA”的结构化分解方法得到元动作单元,并结合多体系统理论对数控机床拓扑结构进行了描述；运用旋量理论对数控机床误差建模,建立数控机床空间运动误差模型,并用螺旋理论得到空间运动误差综合值；以制造成本、空间运动误差螺距及其大小为设计准则,构建了运动精度映射模型,并应用NSGA-Ⅱ遗传算法对数控机床运动精度进行映射. 对某国产加工中心进行运动精度映射求解,说明了该模型的可行性和有效性.     

精密钢球环槽等速传动机构运动精度及可靠性分析

在分析精密钢球环槽等速传动机构结构基础上,利用其等效机构和误差分析理论,研究了钢球环槽等速传动机构结构参数对其机构传动精度的影响规律,应用机构可靠性理论,建立了钢球环槽等速传动机构的运动精度可靠性模型,并研究分析了机构的运动精度可靠性,研究结果为精密钢球行星传动的设计和应用提供了理论依据。     

晶圆传输机器人标定技术研究

为了提高高速高精度晶圆传输机器人的定位精度,建立了精度分析和运动学标定为一体的精度保障体系.针对机器人的特点,建立了误差模型,分析了各结构几何参数误差源的灵敏度,提出了结合几何误差迭代法和基于运动学逆解的非线性参数辨识的分步标定方法,对其进行了标定,并对几何结构参数进行了误差补偿.仿真分析以及实验证明:机器人定位误差达到0.07mm,有效地提高了机器人末端的定位精度.     

3-RPS并联机床的标定建模及振动分析

并联机床在标定时所建立的位置参考系与运动参考系不一致产生系统误差,从而影响机床的结构性能。通过改进标定建模方式,将两个参考系统一,并用数值模拟该并联机床的标定过程,对比结果发现,改进后的模型可以完全消除测量时的系统误差对并联机床标定精度的影响。把标定过的模型导入ADAMS进行振动仿真分析,通过对比可以发现标定过模型的各项振动指标明显优于未标定的模型,从而进一步提高并联机床的结构性能。直接提高机械加工精度及安装精度能够提高并联机床的结构参数的精度,但其代价将是极大地增加加工成本,采用运动学标定并联机床的运动学建模的方法则只需要按普通精度要求进行机械加工,这种标定建模方式具有很高的实用价值。     

Optimal measurement configurations for kinematic calibration of six-DOF serial robot

An optimal measurement pose number searching method was designed to improve the pose selection method. Several optimal robot measurement configurations were added to an initial pre-selected optimal configuration set to establish a new configuration set for robot calibration one by one. The root mean squares (RMS) of the errors of each end-effector poses after being calibrated by these configuration sets were calculated. The optimal number of the configuration set corresponding to the least RMS of pose error was then obtained. Calibration based on those poses selected by this algorithm can get higher end-effector accuracy, meanwhile consumes less time. An optimal pose set including optimal 25 measurement configurations is found during the simulation. Tracking errors after calibration by using these poses are 1.54, 1.61 and 0.86 mm, and better than those before calibration which are 7.79, 7.62 and 8.29 mm, even better than those calibrated by the random method which are 2.22, 2.35 and 1.69 mm in directions X, Y and Z, respectively.     

A novel random phase-shifting digital holographic microscopy method

This paper proposes a new method that reconstructs the information of specimen by using random phase shift step in digital holographic microscopy (DHM). The principles of the method are described and discussed in detail. In practical experiment, because the phase shifter is neither perfectly linear nor calibrated, digital holograms with inaccurate phase shift step are recorded by the charge-coupled device (CCD). The phase could be accurately reconstructed from the recorded digital holograms by using the random phase-shifting algorithm, which makes up for reconstructed phase error caused by ordinary phase-shifting algorithm. The phase aberration compensation is also discussed. In order to verify the flexibility of the proposed method, numerical simulation of random phase-shifting DHM was carried out. The simulation results illustrated that the presented method is effective when the phase shift step is unknown or random in DHM. Supported by the National Basic Research Program of China (“973” Project) (Grant No. 2004CB619304), the National Natural Science Foundation of China (Grant Nos. 10625209, 10472050, 10732080), the Project of Beijing Natural Sciences Foundation (Grant No. 3072007), the Program for New Century Excellent Talents (NCET) in Chinese University Ministry of Education (Grant No. NCET-05-0059), and the Opening Funds from the State Key Laboratory of Explosion Science and Technology     

一种改进的移动机器人运动控制算法

在传统的控制系统中,控制器修正信号通常选取为跟踪误差的线性函数,虽然运算量较小,但在跟踪误差较大时,系统的响应速度较慢,为此,提出一种改进的运动算法,控制器修正信号选取跟踪误差的三次函数,并且为了克服在跟踪误差较大对高阶误差修正容易出现不稳定现象的问题,提出了修正信号增益分段线性化的方法计算机仿真结果证明,在跟踪误差较小时该算法与传统算法具有相似的跟踪特性,但在较大跟踪误差时,该算法既提高了系统的响应速度,又保证了系统的稳定性。     

解决约束平面偏移问题的机械臂闭环标定

基于平面约束的工业机械臂闭环标定,拟合平面与实际约束平面之间存在一定偏差,直接影响标定精度.针对此问题提出消除偏差的方法及误差模型.建立平面坐标系,得到约束平面的准确方程,通过接触式测量头对约束平面进行测量,在平面坐标系中描述测量点的位置;建立最小完整连续运动学模型,从而减少冗余参数的影响;利用双目视觉定位约束平面并规划理论测量点位置,实现自动化测量;通过改进的最小二乘法对参数误差进行辨识.实验结果表明,修正运动学参数后,机械臂绝对位置精度由1.234 mm提高到0.405 mm.该方法成本低、精度高、效率高,且简化了误差模型,适用于工业机械臂的现场标定,为机械臂生产厂家实现批量化标定及后期设备维护提供了思路.     

Optimal measurement configurations for kinematic calibration of six-DOF serial robot

An optimal measurement pose number searching method was designed to improve the pose selection method.Several optimal robot measurement configurations were added to an initial pre-selected optimal configuration set to establish a new configuration set for robot calibration one by one.The root mean squares (RMS) of the errors of each end-effector poses after being calibrated by these configuration sets were calculated.The optimal number of the configuration set corresponding to the least RMS of pose error wa...     

Delta并联机械手几何误差建模及灵敏度分析

以一类含平行四边形支链的Delta并联机械手为对象,利用空间矢量链分析方法,构造出机构末端位置和姿态误差与几何误差之间的映射关系,明确揭示出影响机构末端不可补偿误差的几何误差源,并借助灵敏度分析定量揭示几何误差对末端位姿误差的影响.研究成果对指导同类装备的设计与制造具有普遍的意义.