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.     

Step kinematic calibration of a 3-DOF planar parallel kinematic machine tool

This paper presents a novel step kinematic calibration method for a 3 degree-of-freedom (DOF) planar parallel kinematic machine tool, based on the minimal linear combinations (MLCs) of error parameters. The method using mapping of linear combinations of parameters in error transfer multi-parameters coupling system changes the modeling, identification and error compensation of geometric parameters in the general kinematic calibration into those of linear combinations of parameters. By using the four theorems of the MLCs, the sets of the MLCs that are respectively related to the relative precision and absolute precision are determined. All simple and feasible measurement methods in practice are given, and identification analysis of the set of the MLCs for each measurement is carried out. According to the identification analysis results, a step calibration including step measurement, step identification and step error compensation is determined by taking into account both measurement costs and observability. The experiment shows that the proposed method has the following merits: (1) the parameter errors that cannot influence precision are completely avoided; (2) it reflects the mapping of linear combinations of parameters more accurately and enhances the precision of identification; and (3) the method is robust, efficient and effective, so that the errors in position and orientation are kept at the same order of the measurement noise. Due to these merits, the present method is attractive for the 3-DOF planar parallel kinematic machine tool and can be also applied to other parallel kinematic machine tools with weakly nonlinear kinematics. Supported by the “863” High-Tech Program of China (Grant Nos. 2006AA04Z204 and 2006AA04Z227), National Natural Science Foundation of China (Grant Nos. 50775118 and 50605041), the “973” Basic Research Project of China (Grant Nos. 2006CB705406 and 2007CB714000), and Tsinghua Basic Research Foundation (Grant No. JC200701)     

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)     

五轴数控机床综合误差建模评价方法研究

针对五轴数控机床精度综合评价分析的需要,提出了一种对机床几何误差和伺服误差进行综合评价的方法。该方法通过机床线性轴和旋转轴联动的方式,利用球杆仪进行圆度误差检测,根据所建立的误差分析评价模型,通过对机床运动过程中的各项误差对机床总误差的影响进行分析得知,随着进给速度的增加,机床的几何误差基本保持不变,而伺服误差在机床总误差中所占比重逐渐增大,当进给速度增大到10 000 mm/min时伺服误差占机床总误差的75%左右。实验结果表明本机床误差评价模型具有较高的准确性,分析结果可为机床的误差补偿提供计算依据。     

Accuracy Analysis for 6-DOF PKM with Sobol Sequence Based Quasi Monte Carlo Method

To improve the precisions of pose error analysis for 6-dof parallel kinematic mechanism (PKM) during assembly quality control, a Sobol sequence based on Quasi Monte Carlo (QMC) method is introduced and implemented in pose accuracy analysis for the PKM in this paper. The Sobol sequence based on Quasi Monte Carlo with the regularity and uniformity of samples in high dimensions, can prevail traditional Monte Carlo method with up to 98.59％ and 98.25％ enhancement for computational precision of pose error statistics. Then a PKM tolerance design system integrating this method is developed and with it pose error distributions of the PKM within a prescribed workspace are finally obtained and analyzed.     

Nonlinearity for a parallel kinematic machine tool and its application to interpolation accuracy analysis

This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvature. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.     

Approach to joint translational and rotational phase auto-focusing

In high-resolution inverse synthetic aperture radar imaging, the rotational motion of the targets tends to introduce the time-variant Doppler modulation in the echo, which acts as the range-variant phase errors in phase history. Moreover, the performance of translational phase error compensation may be dramatically degraded without properly considering the range-variant phase errors. In this paper, an approach to joint translational and rotational phase auto-focusing is proposed. In the procedure, the joint phase error correction is modeled as range-invariant and range-variant phase errors using a metric of minimum entropy. Then the minimum-entropy optimization is solved by employing a coordinate descend method based on the quasi-Newton solver. Finally, experiment based on simulated data is performed to confirm the effectiveness of the proposed algorithm.     

Synchronous tracking control of 6-DOF hydraulic parallel manipulator using cascade control method

The synchronous tracking control problem of a hydraulic parallel manipulator with six degrees of freedom (DOF) is complicated since the inclusion of hydraulic elements increases the order of the system. To solve this problem, cascade control method with an inner/outer-loop control structure is used, which masks the hydraulic dynamics with the inner-loop so that the designed controller takes into account of both the mechanical dynamics and the hydraulic dynamics of the manipulator. Furthermore, a cross-coupling control approach is introduced to the synchronous tracking control of the manipulator. The position synchronization error is developed by considering motion synchronization between each actuator joint and its adjacent ones based on the synchronous goal. Then, with the feedback of both position error and synchronization error, the tracking is proven to guarantee that both the position errors and synchronization errors asymptotically converge to zero. Moreover, the effectiveness of the proposed approach is verified by the experimental results performed with a 6-DOF hydraulic parallel manipulator.     

交叉杆型并联机床误差模型建立与分析

基于交叉杆型并联机床的并联机构特点,利用空间矢量法建立了几何误差的数学模型,由此得出了动平台中心点位姿误差与铰链点位置误差和驱动杆长度误差的关系表达式。并针对BJ-04-02(A)型交叉杆并联机床的初始位置误差进行了计算分析,所得结论对并联机床的性能评价有一定的指导意义。     

一种新型五轴并串联机床的工作空间分析

针对6自由度Stewart型并联机床工作空间小的问题,提出一种新型5自由度并串联机床,该机床由一个2-TPR/2-TPS空间四自由度并联机构串联一个可转动的部件组成,具有空间三维移动和两维转动5个自由度.介绍了该机床的结构布局特点,用解析法推导了位置反解方程和输出参数间的解耦关系.采用数值分析的方法生成了该机床的工作空间,分析了结构参数的变化对工作空间的影响.分析的结果表明,该机床机床结构简单,其工作空间较Stewart型并联机床工作空间大,能够完成对具有空间复杂曲面的工件的加工.同时也为该机床的进一步设计和研究提供了理论依据.     

BKX-I型并联机床动力学分析

应用子结构法建立了一种UPS型6自由度并联机床及其部件的有限元实体模型,并通过模态实验和有限元模态分析对有限元实体模型进行了验证.应用有限元法对机床模型进行了谐响应分析,获得了机床各节点沿机床虚拟x、y、z轴向的位移谐响应曲线.在此基础上,对该并联机床谐响应规律进行了分析,明确了该机床谐响应的特点和响应幅度的数量级,为该类机床的结构优化设计提供了理论依据.     

某型六自由度运动系统误差建模

基于多体系统运动学理论的基本原理,结合六自由度运动系统,阐述了多体系统的拓扑结构,分析了多体系统有误差运动的基本规律,推导了特征矩阵构建方法,研究了根据特征矩阵得到六自由度运动系统空间误差模型.本方法可为其他类型的多自由度运动系统的误差建模及误差补偿提供理论参考.     

高速扫描CMM的几何动态误差

利用有限元软件研究了CMM在快速探测时导轨几何误差的动态模型。研究表明,X导轨的绕y和z方向的角误差εy（x）与εz（z）能产生显著的动态效应。它们的动态误差造成CMM,尤其是低刚度CMM中对应测端静态分量大的改变。由此,提出一个能提高CMM快速探测时误差补偿精度的简单方法,即根据探测速度及y坐标值对几何误差曲线进行平滑化。     

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.     

单自由度吊丝配重式重力补偿机构的精度分析

以单自由度吊丝配重式系统为研究对象,建立系统误差模型。为评估各类几何误差及惯性力对补偿精度的影响,将起吊点和悬挂点的偏离量作为误差评估指标,选定同步误差对应的误差评估指标进行误差匹配,可分析各类误差的影响。研究发现吊丝长度与补偿精度成正相关,各类几何误差对评估指标的影响有差异。惯性力引起的误差可等效成求解悬链线问题,经分析发现,其导致起吊点方向偏转为最大影响因素。算例表明,角加速度过大时,系统对吊丝长度有更高的要求。     

伺服阀阀口棱边几何精度的研究

液压伺服控制部件电液伺服阀的核心是由阀芯阀套组成的滑阀副,而滑阀副阀口棱边的几何精度直接影响着它的工作性能。在对阀口棱边的几何精度检测方法研究的基础上提出了在宏观和微观上检测阀口棱边几何精度的两种新方法,分析了伺服液棱边加工精度的现状及造成误差的因素,提出棱边质量标准应该包括棱边的几何形状误差即棱边的粗糙度,棱边的圆角以及棱边的宏观几何形状即棱边端向跳动误差等方向,指出建立科学的棱边几何形状精度质     

一种基于旋量理论的机器人关节结构 误差对其精度影响的分析方法

为提高工业机器人的定位精度,应用旋量理论,提出了一种分析关节误差源对机器人精度影响的分析方法。该方法通过分析机器臂关节两轴线在不同几何误差作用下的空间位置关系,将关节误差表示成旋量的形式,结合POE公式,给出了包含关节误差的机器人正向运动学显式表达式,并以一个三关节机械臂为例,用Adams仿真验证了该方法的正确性。     

Kineto-static analysis of a novel high-speed parallel manipulator with rigid-flexible coupled links

A novel high-speed parallel kinematic machine (PKM) named Delta-S parallel manipulator is proposed,which consists of a fixed base connected to a moving platform through three limbs with identical topology.Each limb is composed of one driving arm and one follower arm,herein,the latter includes two strings and one middle rod,all located in a same plane.Compared with similar manipulators with uniform parameters,the novel and unique topology as well as the addition of two strings of Delta-S manipulator can remo...     

新型三平移并联机构的工作空间和运动灵活度分析

文章通过位置逆解公式,描述了机构输入与输出速度关系的逆雅可比,对该并联机构作业空间和运动灵活性进行了分析,给出了一尺度参数下机构作业空间及运动灵活性的分布规律。分析表明,该机构具有几何形状规则的作业空间及较好的运动灵活性,是一种较为理想的能实现三维移动操作的并联机构选型,获得的结果可应用于该并联机构的设计之中。     

五轴机床旋转轴几何误差分析与补偿

五轴机床旋转轴之间装配所导致的位置无关几何误差（PIGEs—Position independent geometric error）是决定机床精度的关键因素,如何量化PIGEs对位姿精度的影响程度以及误差项之间的耦合作用强弱,从而合理地确定补偿值的权重系数是目前机床误差补偿技术所关注的热点问题。为降低五轴机床装配导致的PIGEs对机床精度的影响,首先,基于多体系统理论及齐次坐标变换方法建立了混合式五轴机床几何误差综合模型,表征了空间误差向量与几何误差项之间的映射关系。其次,考虑几何误差的分布特性,引入Morris全局灵敏度分析方法量化几何误差的作用效果及误差参数间的耦合强弱,通过灰色关联度分析表征误差的敏感性系数与位置向量、姿态向量间的关联程度,基于分析结果确定位置无关几何误差补偿值的权重系数。最后,以摆头-转台为特征的混合式五轴机床为例,进行基于球杆仪(DBB-Double ball bar)的几何误差测量辨识实验,利用辨识值进行虚拟圆锥台轨迹测量、误差补偿和复杂曲面零件加工实验。结果显示：十项几何误差对姿态误差的直接作用效果最为明显,利用基于敏感性分析的修正补偿值进行误差补偿后,虚拟圆锥台测量轨迹的半径偏差减小了65.1%,圆度误差降低了58.8%。基于误差分析实施误差补偿后,“S”型工件的轮廓精度平均提升了49.9%,误差补偿结果验证了误差分析结果的准确性和有效性。