绳牵引并联机构的研究概况与发展趋势

总结了近20年来关于绳牵引并联机构的研究概况和研究内容；论述了绳牵引并联机构的构型、工作空间、刚度和冗余性等方面的研究；分析了绳牵引并联机构的应用前景与发展趋势，指出了绳牵引并联机构在建筑机器人、虚拟现实的力反馈装置和触觉装置、大型运动仿真器、大型射电望远镜、超高速机器人、超大工作空间的轻型机器人和风洞试验等领域的应用前景，展望了绳牵引并联机构的预期研究内容。     

Type synthesis of 4-DOF parallel kinematic mechanisms based on Grassmann line geometry and atlas method

Many methods are proposed to deal with the type synthesis of parallel kinematic mechanisms（PKMs）, but most of them are less intuitive to some extent. Thus, to propose a concise and intuitive type synthesis method for engineering application is a very challenging issue, which should be further studied in the field. Grassmann line geometry, which can investigate the dimensions of spatial line-clusters in a concise way, is taken as the mathematic foundation. Atlas method is introduced to visually describe the degrees of freedom（DOFs） and constraints of a mechanism, and the dual rule is brought in to realize the mutual conversion of the freedom-space and constraint-space. Consequently, a systematic method based on Grassmann line geometry and Atlas method is generated and the entire type synthesis process is presented. Three type 4-DOF PKMs, i.e., 1T3R, 2T2R and 3T1R（T： translational DOF; R： rotational DOF）, are classified according to the different combinations of the translational DOFs and rotational DOFs. The type synthesis of 4-DOF PKMs is carried out and the possible configurations are thoroughly investigated. Some new PKMs with useful functions are generated during this procedure. The type synthesis method based on Grassmann line geometry and Atlas method is intuitive and concise, and can reduce the complexity of the PKMs＇ type synthesis. Moreover, this method can provide theoretical guidance for other PKMs＇ type synthesis and engineering application. A novel type synthesis method is proposed, which solves the existing methods＇ problems in terms of complicated, not intuitive and unsuitable for practical application.     

并联运动机械结构综合及其优化设计研究的最新进展

综合评述了以德国为主的欧洲工业国在并联运动机械结构综合与设计方面的最新研究成果与进展,内容涉及：针对实际应用背景提出新机型并进行了设计;通过研制设计分析仿真软件,针对某种并联运动机械机型进行了结构综合改进与优化、尺度综合和优化以及性能评估与改善等工作;进一步地,在大量实践与理论探索的基础上,较系统地提出用于开发混合运动机械、冗余并联运动学以及可重构并联运动机械的设计方法学,这些内容都是并联运动机械设计研究领域内富有创造性的成果。

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Modular design of typical rigid links in parallel kinematic machines: Classification and topology optimization

Due to the demand of reconfigurable system in parallel kinematic machines (PKMs), modular design technology is significant and necessary. However, in earlier research, the core joint modules have been concerned about rather than the customized link modules. The modular design to the typical customized links from the point of seeking optimal structures with best mechanical performances is analyzed and processed in two steps: classification and optimization. Firstly, a brief introduction to the current research status and the aims of this paper are outlined. And then, how the typical customized links classified is proposed. Next, the technology method and the iterative formula derivation process of topology optimization are described in detail. Finally, calculation models for each group of classified ones are set up and their optimal structures are achieved through topology optimization technique. The results provide useful references for reconfigurable and modular design in engineering cases.     

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.     

一类带冗余支链并联机器的运动学自标定

利用冗余支链测量信息,对一类带冗余支链并联机器的运动学参数进行自标定。通过矢量闭环微分法,建立冗余支链运动学误差模型,并通过多个位姿处误差传递矩阵的组合,得到自标定的辨识雅可比矩阵。针对部分运动学参数误差辨识性差的问题,提出一种基于辨识雅可比矩阵各列线性相关性分析的辨识性分析方法,得到可辨识的运动学参数误差线性耦合式,并简化误差辨识方程使辨识性提高。最后利用冗余支链角度编码器测量信息,完成一个4RRR冗余并联机器的运动学自标定,仿真结果显示,基于冗余支链的运动学自标定能有效提高冗余支链和机构终端运动精度。     

Compliance modeling and analysis of a 3-RPS parallel kinematic machine module

The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric complexities. By using the screw theory, this paper explores the compliance modeling and eigencompliance evaluation of a newly patented 1T2R spindle head whose topological architecture is a 3-RPS parallel mechanism. The kinematic definitions and inverse position analysis are briefly addressed in the first place to provide necessary information for compliance modeling. By considering the 3-RPS parallel kinematic machine（PKM） as a typical compliant parallel device, whose three limb assemblages have bending, extending and torsional deflections, an analytical compliance model for the spindle head is established with screw theory and the analytical stiffness matrix of the platform is formulated. Based on the eigenscrew decomposition, the eigencompliance and corresponding eigenscrews are analyzed and the platform＇s compliance properties are physically interpreted as the suspension of six screw springs. The distributions of stiffness constants of the six screw springs throughout the workspace are predicted in a quick manner with a piece-by-piece calculation algorithm. The numerical simulation reveals a strong dependency of platform＇s compliance on its configuration in that they are axially symmetric due to structural features. At the last stage, the effects of some design variables such as structural, configurational and dimensional parameters on system rigidity characteristics are investigated with the purpose of providing useful information for the structural design and performance improvement of the PKM. Compared with previous efforts in compliance analysis of PKMs, the present methodology is more intuitive and universal thus can be easily applied to evaluate the overall rigidity performance of other PKMs with high efficiency.     

Kinematic and Dynamic Analysis of a 3-■US Spatial Parallel Manipulator

Parallel Kinematic Machines(PKMs) are being widely used for precise applications to achieve complex motions and variable poses for the end effector tool. PKMs are found in medical, assembly and manufacturing industries where accuracy is necessary. It is often desired to have a compact and simple architecture for the robotic mechanism. In this paper, the kinematic and dynamic analysis of a novel 3-PRUS(P: prismatic joint, R: revolute joint, U: universal joint, S: spherical joint) parallel manipulator with a mobile platform having 6 Degree of Freedom(Do F) is explained. The kinematic equations for the proposed spatial parallel mechanism are formulated using the Modified Denavit-Hartenberg(DH) technique considering both active and passive joints. The kinematic equations are used to derive the Jacobian matrix of the mechanism to identify the singular points within the workspace. A Jacobian based sti ness analysis is done to understand the variations in sti ness for different poses of the mobile platform and further, it is used to decide trajectories for the end effector within the singularity free region. The analytical model of the robot dynamics is presented using the Euler-Lagrangian approach with Lagrangian multipliers to include the system constraints. The gravity and inertial forces of all links are considered in the mathematical model. The analytical results of the dynamic model are compared with ADAMS simulation results for a pre-defined trajectory of the end effector.     

温固耦合下轴对称推力矢量喷管驱动机构的运动精度分析

基于空间AVEN驱动机构的运动学方程,利用全微分理论建立了该机构运动精度分析的数学模型,研究了输入误差、构件加工误差、运动副间隙对机构输出的矢量角和喷口面积的影响;基于ANSYS软件,分析了主要构件收敛调节片、扩张调节片和拉杆在高温高压下的变形对机构输出的矢量角和喷口面积的影响,最后对各影响因素进行综合分析。得出机构的定位参数误差、A9转向环转动角误差及温固耦合作用是影响AVEN驱动机构运动精度的主要因素。     

6自由度绳牵引并联机构的运动轨迹规划

首先,基于6自由度绳牵引并联机构的运动学逆解模型,给出了可用于运动轨迹规划的绳的速度和加速度 的一般结论:绳的速度值始终不大于动平台上相应铰链点的速度值;而正的绳加速度值始终不大于动平台上相应 铰链点沿绳拉力方向的加速度值。接着,提出一种适用于大部分工作空间的绳拉力的计算算法。然后,选择一个 结构紧凑的6自由度完全约束定位机构,以末端执行器能实现空间螺旋∞型的轨迹为目标,进行运动规划,研究 绳的运动特性。仿真结果验证了以上所得到的一般性结论。同时表明,一些绳的拉力的变化不大;而另外一些绳 的拉力的变化很大。这些运动轨迹规划的仿真结果,能为以后该机构的运动控制方案的研究提供依据。提出的运 动轨迹规划方法对一般的6自由度绳牵引并联机构都适用。     

Dynamic Modeling and Eigenvalue Evaluation of a 3-DOF PKM Module

Due to the structural complexity, the dynamic modeling and quick performance evaluation for the parallel kinematic machines (PKMs) are still to be remained as two challenges in the stage of conceptual design. By using the finite element method and substructure synthesis, this paper mainly deals with the dynamic modeling and eigenvalue evaluation of a novel 3-DOF spindle head named the A3 head. The topological architecture behind the proposed A3 head is a 3-RPS parallel mechanism, which possesses one translational and two rotational capabilities. The mechanical features of the A3 head are briefly addressed in the first place followed by inverse position analysis. In the dynamic modeling, the platform is treated as a rigid body, the RPS limbs as the continuous uniform beams and the joints as lumped virtual springs. With the combination of substructure synthesis and finite element method, an analytical approach is then proposed to formulate the governing equations of motion of system using the compatibility conditions at interface between the limbs and the platform. Consequently, by solving the eigenvalue problem of the governing equations of motion, the distribution of lower natural frequencies of the A3 head throughout the entire workspace can be predicted in a quick manner. Modal analysis for the A3 head reveals that the distributions of lower natural frequencies are strongly related to the mechanism configuration and are axially symmetric due to system kinematic and structural features. The sensitivity analysis of the system indicates that the dimensional parameters of the 3-RPS mechanism have a slight effect on system lower natural frequencies while the joint compliances affect the distributions of lower natural frequencies significantly. The proposed dynamic modeling method can also be applied to other PKMs and can effectively evaluate the PKM's dynamic performance throughout the entire workspace.     

Calibration of parallel kinematic machine tools using mobility constraint on the tool center point

In the application of parallel kinematic machine tools (PKM), because of errors in the geometric parameters, it is necessary to calibrate the PKM to improve the positioning accuracy. In existing self-calibration methods, either some redundant sensors on passive joints or some mobility constraints on the kinematic chains are used. However, the mobility constraints imposed on kinematic chains might apply large forces during the test on legs and passive joints. Also, these kinds of calibrating are applicable only on PKMs in which their actuated joints can be used as passive joints. To overcome weaknesses of existing methods, a novel approach to calibration based on imposing position constraints on the tool center point (TCP) is introduced. In this method, only the data of encoders installed on the actuated joints in some sets of configurations are required. In each set, the position of the TCP is fixed, but orientations of the tool are different. Simulations and experimental studies on a Hexaglide PKM built in Sharif University of Technology reveal the convenience and effectiveness of the proposed robot calibration method.     

Selection of optimal machining parameters for hexapod machine tool

Parallel kinematic machine tools (PKM) have the advantages of higher stiffness, higher payload capacity and lower inertia. Still their penetration into the machine tool industry is very less. One of the difficulties in using PKMs such as hexapod machine tools is that the stiffness continuously varies with configuration change at every instant. This makes location of work piece and selection of machining parameters difficult and complicated. A methodology is presented in this article to select optimal machining parameters for hexapod machine tools. Particle swarm optimization is used as a tool in the optimization process. A profile-milling example is also presented to demonstrate the selection of machining parameters.     

一种高强度聚焦超声串并联机器人的误差模型与仿真

以一种高强度聚焦超声治疗串并联机器人为例,分析机构的各误差参数,利用机器人的正解建立了误差模型.通过计算机仿真,得出并比较了机构参数误差对机器人输出参考点的影响情况;定量分析了滑块的位置偏差对机器人输出参考点的影响.     

Motion error compensation of multi-legged walking robots

Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot’s locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot’s locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.     

并联运动机械误差建模及校正技术的最新进展

介绍了以德国为主的欧洲工业国在并联运动机械(PKM) 误差建模及校正技术方面的研究成果与最新进展,包括基于统计的方法 、冗余校正方法、最小线性组合法、神经网络法、固定点法、自我校正方法等新的运动学建模与参数识别方法,以及最新研制的实用测量装置或元件。目前,全世界共有40余种 PKM获得成功应用,主要应用于以德国为主的欧洲工业国的模具制造、航空制造、汽车及成形技术等领域。由于机械加工误差、安装误差等因素的影响,PKM必须进行标定校正,以达到较好的工作精度;较高的制造安装精度是PKM获得有效工作空间、良好工作精度以及动力学性能的前提,减小误差及标定校正是其成功应用的技术保证。     

Kinetostatic modeling and analysis of an exechon parallel kinematic machine(PKM) module

As a newly invented parallel kinematic machine(PKM), Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method(FEM). The equilibrium equations of the platform are derived with Newton’s 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system’s deflections. The platform’s elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.     

模块化并联机器的精度设计

在模块化并联机器的精度设计中,以模块化结构设计为基础,建立了一种标准化的误差模型,研究了模块的误差与末端执行器输出误差之间的关系。使用6-SPS构型的模块化并联机器进行实验,并与理论计算的结果进行比较。     

随机参数连杆机构的静动态运动精度可靠性分析

将平面连杆机构的杆长、截面尺寸、铰链间隙、质量密度、弹性模量等几何、物理参数均视为随机变量,对机构输出运动进行了静态和动态误差分析。应用微小位移的线性叠加原理分别对静态、动态误差进行综合分析,建立了机构输出运动精度可靠性分析模型。通过算例,考察了机构中各个随机参数对输出运动精度可靠度的影响,获得了一些有意义的结论。