Reciprocal Screw Theory Based Singularity Analysis of a Novel 3-DOF Parallel Manipulator

Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.

Gravity-Based Kinetostatic Modeling of Parallel Manipulators Using Screw Theory

The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.

Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory

The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.

INSTANTANEOUS KINEMATIC CHARACTERISTICS OF ASPECIAL 3-UPU PARALLEL MANIPULATOR

The instantaneous kinematics of a special 3-UPU parallel platform manipulator is discussed. First, the instantaneous motions of the 3-UPU manipulator in four kinds of positions and a special manipulator are studied by reciprocal screw theory. Then, the principal screws in one of four positions are obtained. It is shown that the moving platform has five degrees of freedom （DOF） in the initial position or after a translation along the z-axis; In the generic position, the mechanism only has three DOF, moreover the three DOF characteristics are different in different position. The instantaneous kinematic characteristics of alike 3-UPU mechanisms are very different in different position and special structure. The results presented are important to the use of alike 3-UPU parallel manipulator and contribute to the mechanism theory .

KINEMATICS OF 3-DOF PYRAMID MANIPULATOR BY PRINCIPAL SCREWS

Kinematics of a 3 RPS parallel pyramid manipulator are investigated by principal screw. Firstly, the principal screws are identified by quadric degeneration. The planar conics representing the relations between the pitches and the three linear inputs are described, and the three dimensional distribution of the axes of all the twists is illustrated. Finally, a numerical example is given successfully.

Kinematics of a Trinal-Branch Space Robotic Manipulator with Redundancy

This paper presents a trinal-branch space robotic manipulator with redundancy, due to hash application environments, such as in the station. One end-effector of the manipulator can be attached to the base, and other two be controlled to accomplish tasks. The manipulator permits operation of science payload, during periods when astronauts may not be present. In order to provide theoretic basis for kinematics optimization, dynamics optimization and fault-tolerant control, its inverse kinematics is analyzed by using screw theory, and its unified formulation is established. Base on closed-form resolution of spherical wrist, a simplified inverse kinematics is proposed. Computer simulation results demonstrate the validity of the proposed inverse kinematics.

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.

Dynamic modeling and analysis of the 3-PRS power head based on the screw theory and rigid multipoint constraints

This study presents a dynamic modeling and analysis methodology for the 3-PRS parallel mechanism.First,an improved reduced dynamic model of component substructures is proposed using the dynamic condensation technique and the rigid multipoint constraints at the joint/interface level,leading to a minimum set of generalized coordinates for external nodes.Next,the mapping between interface constraint stiffness and global stiffness is illustrated,resulting in an analytical stiffness model of joint substructures.Subsequently,the derived component and joint substructures are synthesized into the entire mechanism based on the Lagrange equation.Finally,a case study illustrates that the lower-order dynamic performances predicted within the proposed approach have the same trend as those obtained from a complete-order finite element model.The root mean square discrepancy of the lower-order natural frequencies between the two models is less than 5.92%,indicating the accuracy and effectiveness of the proposed model.The developed approach can highly and efficiently predict the dynamic performance distributions across the entire workspace and guide the optimal functional design under the virtual machine framework.

DYNAMICS ANALYSIS OF 2-DOF SPHERICAL PARALLEL MECHANISM

The analytical formulations of the velocity and the acceleration of a 2-DOF spherical parallel mechanism are derived by the screw theory. Based on building its dynamics model by the principle of virtual work and reciprocal product of the screw, the equation of the motor moment is obtained. Through the transformation of dynamics model, the configuration space method of the dynamics equation and the corresponding coefficients are presented. Finally, the result of an example shows that the inertia moment and the gravity play a more important role than the coriolis and centrifugal moment, and the former is ten times of the latter in the magnitude. So, the latter can be neglected only when the velocity of mechanism is very slow.

Mobility,Constraint Singularity and Isotropy of the 3-R Translational Parallel Mechanism

The non-overconstrained 3-degrees of freedom（DOF） translational parallel mechanism（TPM） has received much attention due to its advantages in reduced cost of fabrication and assembly. Researches are being conducted in the area of type synthesis, kinematic analysis and dimensional synthesis. Mobility, constraint singularity and isotropy of a 3-PRRRR non-overconstrained TPM are studied, where P denote the prismatic pair, R the revolute pair and the overline indicates the same axis direction of the kinematic pair The different arrangements of the three limbs affect the kinematic performance of this kind of TPM. First, the mobility analysis, actuation selection, and the constraint singularity of the general 3-PRRRR TPM are conducted based on screw theory. For a general 3-PRRRR TPM, the three prismatic pairs cannot be chosen as actuators and two kinds of constraint singularities are identified. In the first constraint singularity, the moving platform has four instantaneous DOFs. In the second constraint singularity, the moving platform has five instantaneous DOFs. Then, an orthogonal 3-PRRRR TPM is proposed, which can be actuated by three prismatic pairs and has no constraint singularities. Further, the forward and inverse kinematic analysis of the orthogonal TPM are presented. The input-output equations of the orthogonal TPM are totally decoupled. The full isotropy of the orthogonal TPM is proved by establishing the Jacobian matrix , which is an identity 3x3 diagonal matrix in the whole workspace. The orthogonal 3-PRRRR TPM has great potential in application like fast pick-and-place manipulator, parallel machine and micro-motion manipulator.

一种新型3-R(4r)(4r)R并联机构及运动学分析

本文提出了一种3-R(4r)(4r)R型全对称三平移并联机构,运用螺旋理论分析了该并联机构实现三平移的机构学原理,进行了驱动输入的选取,分析了机构平台奇异、驱动奇异和支链奇异的特性,建立了机构运动学模型,获得了运动学正、逆解析解,并通过数值仿真验证了正逆解模型的正确性。研究结果表明,该并联机构无平台奇异,运动学模型简单且正解唯一。

机械臂运动学和动力学的李群表述

D-H参数法已经被广泛应用到机械手运动建模及分析中,但其所描述的运动都是围绕着x轴和z轴,而不能反映出y轴的运动。为了解决这个问题,采用旋量理论的方法,用旋量来表述出将机械臂的位置和姿态,并进一步分析机械臂的运动学和动力学。相较于传统的D-H法计算运动学正解,旋量理论是从整体上对机械臂的运动进行表述,且不需要中间参考系,几何意义清晰。利用Paden-Kahan子问题分析肘机械臂的逆运动学问题,计算出其运动学逆解,并利用旋量理论和李群-李代数,通过Newton-Euler法建立了高效的递归动力学模型。最后对于用旋量理论求出的肘机械臂运动学逆解进行仿真验证,并计算出其工作空间,结果表明用旋量理论的方法更加简洁、精确、高效。

基于螺旋理论的3自由度并联机构运动学分析

【目的】满足汽车表面加工与车漆喷涂的任务需求,利用机器人进行协同甚至自主完成加工、美化工作,提高工作效率。【方法】设计了一款具备多自由度的汽车车身制造与喷漆机器人,采用3-RPS并联机构作为执行部件支撑件,针对机器人的结构设计特点,主要对机器人末端3-RPS并联机构支撑部分的机构构型和整体运动采用螺旋理论进行分析,利用闭环支链建立机构运动学模型。【结果】利用MATLAB和Admas View软件分别完成了运动学方程求解和运动学仿真,两者结果误差在3%以内。【结论】仿真值与分析值的误差较小,在可忽略范围内,所建立的设计机构运动学方程有效可行,可以利用此结果进行进一步的机器人运动控制设计与相关研究。

一种3自由度并联抛磨机械臂的运动学分析

针对百叶窗叶片的仿形抛磨要求,研究了一种可为末端执行器提供X向、Y向的移动和Z向转动的3自由度并联机械臂。为了验证机械臂的运动学性能,首先,描述了其机构特征,并基于螺旋理论进行了机构自由度分析;其次,基于闭环矢量法构建了机构运动学方程,对其进行了位置正、逆解分析,并通过具体算例对分析结果进行了初步验证;最后,构建了机构的数值仿真模型和虚拟样机模型,进行了位置、速度的逆运动学仿真分析。仿真结果表明,两种模型的分析结果一致,逆解理论分析结果可信;机械臂各支链可协调运动,运动过程平稳,位移、速度曲线平滑、无突变,可为后续机械臂的尺寸优化和运动控制提供依据。

6-PUS/UPU并联机器人运动学及工作空间分析

提出和研究了一种新型6-PUS/UPU并联机器人,该机器人结构对称,刚度大,可用于视觉测量、力控制研究、冗余控制研究。首先利用螺旋理论对6-PUS/UPU并联机器人进行了自由度分析,然后根据该机构的几何特点和D-H法对该并联机器人进行了运动学分析,得出了6-PUS/UPU并联机器人的运动学反解,并在此基础上对该并联机器人的工作空间进行了分析。该研究结果对此种机器人的深入研究及该并联机器人的实际应用具有重要理论意义。

基于改进蚁群算法的3-PPR并联机构位置正解研究

针对3-PPR并联机构位置正解问题,运用螺旋理论计算其自由度,并分析其运动特性,同时通过解析法构建该并联机构的完整运动学逆解。将并联机构运动学正解问题的求解转化为对目标函数优化问题的求解,并基于此建立该并联机构正解的目标函数优化模型。通过对基本蚁群算法进行有效的改进,构建了可用于求解连续优化问题的改进蚁群算法。运用该算法求解3-PPR并联机构的运动学正解并进行Matlab仿真分析,对比传统数值方法和改进蚁群算法,证实该算法具有良好的全局寻优能力,并能避免初值和局部最优值对计算结果的影响,可有效应用于求解并联机构的位置正解问题。

一种新型3-RPR并联机构及其运动学分析

提出了一种能实现沿Y、Z轴平移和绕X轴转动的3-RPR型三自由度并联机构,运用螺旋理论分析了该并联机构实现二维平移和一维转动的机构学原理,计算了机构自由度,进行了驱动输入选取与论证,并进行了奇异分析,提出了减少奇异的参数设计条件,运用多体系统运动学理论建立了运动学模型,研究了运动学正反求解,并进行了数值仿真验证,最后分析了机构的工作空间。该并联机构是一种支链完全相同的半对称并联机构,结构较为简单,是对2T1R并联机构的重要补充,可应用于工业装配机器人、姿态调节器、并联机床、工作台等领域。

4自由度并联机器人刚度分析

少自由度并联机构应用于机床上时要求具有很高的刚度,而少自由度并联机器人的刚度和机器人雅可比矩阵有很密切的关系。采用螺旋理论方法求出了4-RUC 4自由度并联机构的雅可比矩阵,推导出4自由度并联机器人的刚度计算公式和条件指数计算公式,分析了少自由度并联机器人在某一位置时(z=0)最大和最小刚度所在的方向,给出了这种4自由度并联机器人的最大和最小刚度曲线,通过曲线可以评价出此并联机构在各个方向上刚度大小,为这种机器人的应用和开发提供了有力的依据。

线驱动拟人臂机器人逆向运动学分析

基于最新人臂仿生理论和并联机器人研究的成果,提出一种线驱动7-DOF冗余手臂的设计方案。线驱动机构具有高刚度、高精度、高负载能力的优点,可以克服常规串联机构的缺点。介绍这种新型线驱动拟人臂机器人具体的结构,利用旋量理论描述机器人运动,在绳索张力条件的约束下,分析肩关节的工作空间。针对7-DOF机器人的逆运动学求解问题,先采用关节速度再分配法求关节速度逆解;然后与Paden-Kahan子问题法相结合,取得具有冗余控制的位置逆解,求出在给定位姿时各关节角的角度;再由关节角与绳长的关系解出各关节处驱动绳索的长度,并分析肩关节运动对腕、肘关节的耦合影响。最后在ADAMS下进行仿真,采用直线插补算法,动画图形实时显示机器人的运动情况,证明逆向运动学算法的正确性。

欠秩空间并联机器人输入选取的理论与应用

提出一种基于螺旋系线性相关性和约束反螺旋概念的空间并联机器人输入原动件选取合理性的判别方法。这种方法的原理是首先求取机构的结构及刚化机构主动副映射到动平台的反螺旋系，然后判断刚化输入映射到动平台上的反螺旋系及其与结构约束反螺旋系的线性相关性，从而确定空间并联机器人输入选取的机构学合理性。以３－ＲＲＣ和４－ＴＲＴ两种新型并联机器人机构模型为例进行了验证。