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.

A Finite and Instantaneous Screw Based Approach for Topology Design and Kinematic Analysis of 5-Axis Parallel Kinematic Machines

Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non?redundant screws in quasi?vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two?translational and three?rotational(2T3R)5?axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthe?sized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.

Comparison of Parallel Kinematic Machines with Three Translational Degrees of Freedom and Linear Actuation

The development of new robot structures, in particular of parallel kinematic machines（PKM）, is widely systematized by different structure synthesis methods. Recent research increasingly focuses on PKM with less than six degrees of freedom（DOF）. However, an overall comparison and evaluation of these structures is missing. In order to compare symmetrical PKM with three translational DOF, different evaluation criteria are used. Workspace, maximum actuation forces and velocities, power, actuator stiffness, accuracy and transmission behavior are taken into account to investigate strengths and weaknesses of the PKMs. A selection scheme based on possible configurations of translational PKM including different frame configurations is presented. Moreover, an optimization method based on a genetic algorithm is described to determine the geometric parameters of the selected PKM for an exemplary load case and a prescribed workspace. The values of the mentioned criteria are determined for all considered PKM with respect to certain boundary conditions. The distribution and spreading of these values within the prescribed workspace is presented by using box plots for each criterion. Thereby, the performance characteristics of the different structures can be compared directly. The results show that there is no ＂best＂ PKM. Further inquiries such as dynamic or stiffness analysis are necessary to extend the comparison and to finally select a PKM.

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 DESIGN OF A RECONFIGURABLE MINIATURE PARALLEL KINEMATIC MACHINE

The kinematic design of a reconfigurable miniature parallel kinematic machineis dealt with. It shows that the reconfigurability may be realized by packaging a tripod-basedparallel mechanism with fixed length struts into a compact and rigid frame with which the differentconfigurations can be formed. Utilizing a dual parameter model, the influences of the geometricalparameters on the dexterous performance and the workspace/machine volume ratio are investigated. Anovel global performance index for the dimensional synthesis is proposed and optimized, resulting ina set of dimensionless geometrical parameters.

Running Accuracy Analysis of a 3-RRR Parallel Kinematic Machine Considering the Deformations of the Links

Parallel kinematic machines have drawn considerable attention and have been widely used in some special fields.However,high precision is still one of the challenges when they are used for advanced machine tools.One of the main reasons is that the kinematic chains of parallel kinematic machines are composed of elongated links that can easily suffer deformations,especially at high speeds and under heavy loads.A 3-RRR parallel kinematic machine is taken as a study object for investigating its accuracy with the consideration of the deformations of its links during the motion process.Based on the dynamic model constructed by the Newton-Euler method,all the inertia loads and constraint forces of the links are computed and their deformations are derived.Then the kinematic errors of the machine are derived with the consideration of the deformations of the links.Through further derivation,the accuracy of the machine is given in a simple explicit expression,which will be helpful to increase the calculating speed.The accuracy of this machine when following a selected circle path is simulated.The influences of magnitude of the maximum acceleration and external loads on the running accuracy of the machine are investigated.The results show that the external loads will deteriorate the accuracy of the machine tremendously when their direction coincides with the direction of the worst stiffness of the machine.The proposed method provides a solution for predicting the running accuracy of the parallel kinematic machines and can also be used in their design optimization as well as selection of suitable running parameters.

Homing Strategy for a 4RRR Parallel Kinematic Machine

Returning home is the most important process of a parallel kinematic machine （PKM） with incremental encoders.Currently,most corresponding articles focus on the accuracy of homing process,and there lacks the investigation of the operation＇s safety.For a 4RRR PKM,all servoaxes would be independently driven to their zero positions at the same time based on the traditional homing mode,and that can bring serious interfere of the kinematic chains.This paper systemically investigates this 4RRR PKM＇s safety of homing process.A homing strategy usually contains three parts which are the home switches＇ locations,the platform＇s initial moving space,and each links＇ homing direction,and all of them can influence the safety of homing operation.For the purpose of evaluating and describing the safety of the homing strategy,some important parameters are introduced as follows：Safely homing ratio （SHR） is used to evaluate the probability of a machine＇s successfully returning home from an initial moving space;Synchronal rotational angle （SRA） is the four links＇ largest synchronal rotational angle with given directions from a given pose.Whether a machine can safely return home from a given pose can be judged by comparing the SRA with all four home switches＇ mounting angles.By meshing the initial moving space and checking the safeties of returning home from all the initial poses on the nodes,the SHR of this initial moving space can be calculate.For the sake of convenience,the platform＇s initial moving space should be as large as possible,and in this 4RRR PKM,a square zone in the center of the workspace with a giving initial rotation range is selected as the platform＇s initial moving space.The forward direction is selected as each link＇s homing direction according to custom,and the platform＇s initial rotational angle is selected as larger than 0° based on this 4RRR PKM＇s kinematic characteristics.The platform＇s initial moving space can be defined only by the side length of the initial moving square.By setting a probable searching step and calculating the SHR of the initial moving square,an optimal procedure of searching for the largest side length of the platform＇s initial moving square is proposed.The homing strategy proposed is based on a systemic research on the safety of homing process for PKM,and the two new indexes SHR and SRA can clearly describe the safety of homing operation.The homing operation based on this strategy is fast and safe,and the method can also be used in other PKMs with the situation of serious components＇ interference.

The Kinematic Analyses of the 3-DOF Parallel Machine Tools

A 3-degree-of-freedom （3-DOF） parallel machine tool based on a tripod mechanism is developed and studied. The kinematics analysis is performed, the workspace is derived, and an analysis on the number of conditions of the Jacobian matrix and manipulability is carried out. A method for error analysis and manipulability is introduced. Hence, the manipulability analysis of the parallel machine tool is accomplished.

Calibration of a Parallel Kinematic Machine Tool

A calibration method is presented to enhance the static accuracy of a parallel kinematic machine tool by using a coordinate measuring machine and a laser tracker. According to the established calibration model and the calibration experiment, the factual 42 kinematic parameters of BKX-I parallel kinematic machine toot are obtained. By circular tests the comparison is made between the calibrated and the uncalihrated parameters and shows that there is 80 % improvement in accuracy of this machine tool.

Research on postprocessing of seven-axis linkage parallel kinematics machine with complicated surfaces

Because of restriction of workspace of parallel kinematics Machine (PKM), 6 DOF PKM can’t finish machining of workpiece with complicated surfaces under only once locating. It is necessary to fit workpiece beyond twice and to lead to low machining precision. Therefore the seven-axis linkage PKM is implemented by fixing a turntable on the worktable of the six-axis linkage PKM. However, the turntable angle decomposing problem from the CL file should be well considered. If the traditional decomposing methods are adopted, the nutation angle usually goes beyond the workspace of the machine. Therefore, according to the relation of the machine coordinate system and the workpiece coordinate system, the turntable angle decomposition algorithmic of the consistent coordinate system and the turntable angle decomposition algorithmic of the non-consistent coordinate system are developed to resolve the problem mentioned above. The turntable angle decomposition of the non-consistent coordinate system processes the decomposition which is based on the consistent coordinate system again. It calculates the initial angle of the locating workpiece, and the decomposed angle of the turntable at the machine coordinate system results in the nutation angle not going beyond workspace of the machine, thereby the decomposition process can be simplified.

A numerical error analysis method and its application on a 4RRR parallel kinematic machine

To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.

Calibration of parallel kinematics machine using generalized distance error model

This paper focus on the accuracy enhancement of parallel kinematics machine through kinematics calibration. In the calibration processing, well-structured identification Jacobian matrix construction and end-effector position and orientation measurement are two main difficulties. In this paper, the identification Jacobian matrix is constructed easily by numerical calculation utilizing the unit virtual velocity method. The generalized distance errors model is presented for avoiding measuring the position and orientation directly which is difficult to be measured. At last, a measurement tool is given for acquiring the data points in the calibration processing. Experimental studies confirmed the effectiveness of method. It is also shown in the paper that the proposed approach can be applied to other typed parallel manipulators.

一种并联混合机的运动学分析与尺度优化设计

根据方位特征集(Position and Orientation Characteristics,POC),提出了一种单输入多维输出的2RRS-S并联机构。分析了其拓扑结构、自由度及耦合度;采用基于耦合度的拓扑特征运动建模方法,建立了机构的运动正解模型,并通过仿真模型进行了验证;根据物料混合要求,设计了基于2RRS-S并联机构的多维混合机三维模型,仿真模拟了其运动轨迹以及姿态角的运动特征;以增大动平台姿态角变化量为目标函数,采用差分进化算法对机构的尺度参数进行优化,所得机构比优化前具有更好的混合运动性能。

可重构PKM模块的选型原则——理论与实践

可重构与多功能是并联构型装备(PKM)的重要发展趋势,模块化设计是实现这类装备可重构性的使能技术。首先借助线性空间理论,简要论述了少自由度并联机构的组成原理。按照支链对动平台提供约束和驱动的作用不同,将支链分为四种类型,并据此得到少自由度并联机构的三种组合方案。基于对可重构性、多功能,以及速度、剐度特别是精度的考虑,提出可重构PKM模块的选型原则,认为含简式恰约束支链的并联机构较适于搭建兼顾上述需求的PKM模块,进而将可重构PKM模块的设计转化为恰约束支链的选型问题。在此基础上,提出一种含主动恰约束支链的5自由度混联机械手模块——TriVariant,其具有与Tricept机械手完全相同的自由度数目和类型, 且几乎继承了后者的全部优点。最后给出若干用TriVariant搭建可重构装备的应用示例。

并联坐标测量机研究进展

并联机构具有刚度大、承载力强、动力性能好、支链间误差平均效应等优势,在机器人、机床、微动器件等领域得到了广泛应用。然而,传统直角式坐标测量机和关节式坐标测量机采用串联结构,存在误差累积的固有缺陷。鉴于并联机构具有的互补优势,近二十年来并联坐标测量机得到了快速的发展。结合国内外技术现状和团队的研究成果,对并联坐标测量机机构学、运动学、动力学、机构性能和控制策略等方面进行了系统的回顾和分析,总结了目前并联坐标测量机研究中存在的主要问题,提出了进一步的解决方法与思路,并展望了未来的发展趋势。

多运动模式并联机构工作空间分析

面对行业对自动化装备的重大需求,引入一种由移动副驱动的并联机构,该机构具有多运动模式、大工作空间等特点,可用于钻孔、装配、检测等领域.为了分析并联机构的工作空间,采用闭环矢量法建立不同运动模式下系统通用的运动学模型;在此基础上,考虑滑块行程、关节转角等约束条件,提出空间搜索法搜索不同运动模式下并联机构的可达工作空间.结果表明:在不同的运动模式下,并联机构的工作空间连续无空洞,该结果为后续的机构设计及应用提供了理论依据.

Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

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

By taking a 3-DOF translational milling machine as an example, this paper investigates the kinematic calibration of PKM systems with fewer than 6-DOF. The error mapping function is formulated in such a way that the geometric errors affecting the compensatable and uncompensatable pose errors can be separated. Based upon the previous investigation, a hierarchical approach to the geometric error identification is proposed. The compensation strategy is developed which is particularly suitable for the PKM systems with translational moving capability. The experiment has been carried out to verify the effectiveness of the proposed approach and the results show that the accuracy can be significantly improved.

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.

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 ann 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 remove the clearance of the spherical joints, reduce the inertial load of components further, improve the positioning accuracy and dynamic performance, and so on. In order to formulate the kineto-static model of Delta-S manipulator, the kineto-static analyses and models of the driving arm, the generalized follower and the moving platform can be carried out by the D＇ALEMBERT principle. For the sake of obtaining the force analytic results of strings, the deformation compatibility condition of strings and the middle rod are determined. Furthermore, in virtue of the assumption of small deformation and the linear superposition principle, the minimal pre-tightening force of the strings is calculated. The main results include that the loads of the strings and the middle rod must be larger than ＂zero＂ and the pre-tightening force over the workspace must be larger than the minimal pre-tightening force at any time within the workspace, which lay the foundation for the dynamic analysis and the prototype manufacture of the Delta-S manipulator.