PROPERTY IDENTIFICATION OF SINGULARITY LOCI OF GOUGHSTEWART MANIPULATOR

The pro'blem of identifying the property of singularity loci of Gough-Stewart manipulators is addressed. After constructing the Jacobian matrix of the Gough-Stewart manipulator, a cubic polynomial expression in the mobile platform position parameters, which represents the constantorientation singularity locus of the manipulator, is derived. Graphical representations of the singularity locus of the manipulator for different orientations are illustrated with examples. Further, the singularity locus of the manipulator in the principal-section, where the mobile platform lies, is analyzed. It shows that singularity loci of the manipulator in parallel principal-sections are all quadratic expressions including a parabola, four pairs of intersecting straight lines and infinite hyperbolas. Their geometric and kinematic properties are also researched as well.     

绳牵引并联机构奇异性分析及无奇异机构设计

绳牵引并联机构是将驱动器的运动和力以绳为介质并行转换成动平台的运动和力的装置,其末端执行器的自由度数可定义为机构的结构矩阵的所有旋量正张成的实数空间的维数。指出绳牵引并联机构仅有过运动性的奇异类型,阐明该奇异是一种由于位姿几何的特殊导致动平台的力旋量集合的维数降秩的现象;以一个1R2T机构为例指出了机构的奇异性除了会导致机构失去控制,还会导致绳优化拉力分布的不连续性:以1-2-1型的1R2T 机构为例研究动平台的重力会对机构的奇异性所造成的影响,从而发现即便动平台重力无法消除机构的奇异点, 但却能使各根绳的拉力分布重新得以配置。提出用各个转动自由度相互解耦,而平动运动能得到完全控制的机构是无奇异的这个原理来构造无奇异性的1-2-1型的CRPM(1R2T)、2-3-2型的RRPM-7(2R3T)的方法;提出用对心抓取定理构造无奇异性的2-2型的CRPMs(1R2T)和3-3型的CRPM(2R3T)的方法;提出用3维力封闭抓取定理构造无奇异性的3-3-3型的RRPM-9(3R3T)的方法。     

平面并联机器人的奇异性分析及仿真

针对平面并联机器人,在理论上对其进行了奇异性分析,根据速度方程中的雅可比矩阵的行列式值将其分为三类:逆运动奇异、正运动奇异及综合奇异.文中以最为常见的曲柄滑块机构及3RRR并联机器人为例,分别进行了奇异性分析,然后利用ADAMS对奇异状态下的机构进行了运动仿真,验证了理论分析结果,使结果更为直观.     

All planar parallel manipulators with cylindrical singularity surface

In this article we give the complete list of all non-architecturally singular parallel manipulators of Stewart Gough type with planar base and platform, whose singularity set for any orientation of the platform is a cylindrical surface with rulings parallel to a given fixed direction p in the space of translations. The presented list has only two entries containing the necessary and sufficient geometric conditions of the corresponding manipulator designs possessing such a singularity surface. These manipulators have the advantage that their singularity set can easily be visualized as curve by choosing p as projection direction. Moreover the computation of singularity free zones reduces to a 5-dimensional task. We close the paper by formulating a conjecture for the non-planar case.     

Singularity analysis with respect to the workspace of a double parallel manipulator

Singularity analysis is an important issue in the design of parallel manipulators, since they become uncontrollable at singular configurations due to the rank deficiency of the Jacobian. This paper analyzes the singularity of a double parallel manipulator with respect to its workspace. The workspace is decoupled into a positional workspace generated by the first parallel mechanism, and an orientational workspace by the second mechanism. The singularities occurring outside each workspace are analytically found by a Jacobian matrix derived for the velocity transformation from the end-effecfor to the linear actuators. The singularity loci are presented and their geometric properties are examined to prove that the double parallel manipulator is free from the singularity problem.     

Singularity kinematics principle and position-singularity analyses of the 6-3 Stewart-Gough parallel manipulators

This paper presents a new principle and method of kinematics to analyze the singularity of Stewart-Gough parallel manipulators and addresses the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulators for special orientations. Based on the kinematic relationship of a rigid body, a necessary and sufficient condition that three velocities of three non-collinear points in a moving rigid body can determine a screw motion is addressed and some typical singular configurations of the 6-3 Stewart-Gough parallel manipulators are also addressed in detail. With the above-mentioned condition, a symbolic analytical polynomial expression of degree three in the moving platform position parameters, representing the position-singularity locus of the 6-3 Stewart-Gough manipulators for special orientations, is derived; and the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulator for these special orientations is investigated at length. It is shown that position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations will be a plane and a hyperbolic paraboloid, even three intersecting planes.     

Property Identification of the Singularity Loci of the 6/6-Stewart Manipulator

This paper addressed the problem of identifying the property of the singularity loci of the 6/6-Stewart manipulators. The singularity locus equation of the manipulator can be obtained by setting the determinant of the Jacobian matrix be zero. The singularity loci for different orientations are illustrated with examples. The singularity locus equation of the manipulator with respect to the oblique plane is derived either which is a polynomial expression of two degree. It shows that the singularity loci of the manipulator in the parallel oblique planes are hyperbolas accompanied with four pairs of intersecting straight lines and a parabola. Their geometric interpretations and the properties of the singularity loci are further analyzed.     

Eighteen fully symmetrical 5-DoF 3R2T parallel manipulators with better actuating modes

Different to currently existing serial manipulators, the actuators for some parallel manipulators can be assembled directly for base pairs or prismatic pairs near the base platform. Such a base-mounted actuator or near-base actuator structure will reduce the extra load, thinner links and promote the speed of the device, which will, consequently, promote the production efficiency for a manipulator. Recently, researchers have paid more and more attention to lower-mobility parallel manipulators. However, 5-DoF 3R2T (three rotational, two translational) parallel manipulators with fully symmetrical structures have not yet received enough attention, although they have a wide application background. This study identified 11 5-DoF 3R2T parallel manipulators from a group of about 70 existing structures and proposed seven novel ones. Fifteen of them adopt a base-mounted actuator structure. The other three adopt a near-base actuator structure. All of them have fully symmetrical structures. Moreover, a simple method for all 18 manipulators to avoid assembly singularity is also illustrated in this study.     

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.     

避免设计位形下发生平台奇异的三自由度转动并联机器人设计方法

设计一种基于反螺旋理论的系统方法,给出了具有三个转动自由度的并联机器人的设计要求。分析了产生平台奇异时三条支链所提供的反螺旋的线性关系,利用三条支链对平台所提供的特殊约束,避免设计位形下发生平台奇异现象。给出了设计该类结构的运动副组成类型和空间放置原则。     

Design procedure for cuspidal parallel manipulators

In the design of parallel manipulators, a major problem is their reduced operational workspace. This is mainly due to the existence of a complex singularity locus within the workspace. The singularity-free workspace therefore corresponds to only a fraction of the potential workspace, and dimensioning the manipulator is intended to optimize such singularity-free workspace. The singularity locus often divides the workspace into isolated volumes according to assembly modes and working modes. As a result, it is common to restrict the operational space to a simple geometric shape inside a singularity-free workspace. However, it is well known that appropriate motion planning can make the most of a more complex workspace by means of transitions between working mode and/or assembly mode. In this paper, the authors obtain the locus of cusp points in the joint space entity, which will permit non-singular assembly mode changing in cuspidal manipulators. Making use of such entity, the optimum dimensional parameters are obtained which increase the possibility of non-singular transitions while obtaining a maximal, regular-shaped workspace.     

Different manipulation mode analysis of a radial symmetrical hexapod robot with leg–arm integration

With the widespread application of legged robot in various fields, the demand for a robot with high locomotion and manipulation ability is increasing. Adding an extra arm is a useful but general method for a legged robot to obtain manipulation ability. Hence, this paper proposes a novel hexapod robot with two integrated leg–arm limbs that obtain dexterous manipulation functions besides locomotion ability without adding an extra arm. The manipulation modes can be divided into coordinated manipulation condition and single-limb manipulation condition. The former condition mainly includes fixed coordinated clamping case and fixed coordinated shearing case. For the fixed coordinated clamping case, the degrees of freedom (DOFs) analysis of equivalent parallel mechanism by using screw theory and the constraint equation of two integrated limbs are established. For the fixed coordinated shearing case, the coordinated working space is determined, and an ideal coordinated manipulation ball is presented to guide the coordinated shearing task. In addition, the constraint analysis of two adjacent integrated limbs is performed. Then, mobile manipulation with one integrated leg–arm limb while using pentapod gait is discussed as the single-limb manipulation condition, including gait switching analysis between hexapod gait and pentapod gait, different pentapod gaits analysis, and a complex six-DOF manipulation while walking. Corresponding experiments are implemented, including clamping tasks with two integrated limbs, coordinated shearing task by using two integrated limbs, and mobile manipulation with pentapod gait. This robot provides a new approach to building a multifunctional locomotion platform.     

Optimization of parallel manipulator trajectory for obstacle and singularity avoidances based on neural network

This paper presents a novel method for singularity-free path planning and obstacle avoidance of parallel manipulators. A modified 3-4-5 interpolating polynomial is used to plan a trajectory for a planar 3-DOF parallel manipulator. The polynomial function which is smooth and continuous in displacement, velocity, and acceleration is used to find a smooth path avoiding the obstacles and singularities. An artificial neural network is implemented to solve forward kinematics of the manipulator to estimate the distance between gripper and singularity or obstacle. The simulating results demonstrate the efficiency of the proposed algorithm.     

基于反螺旋理论的3-RSR并联机器人雅可比矩阵研究

运用反螺旋理论对3-RSR三自由度并联机器人的雅可比矩阵进行了研究。采用简单的方法,找到支链关节螺旋的反螺旋,从而得到了约束雅可比矩阵、驱动雅可比矩阵和完全雅可比矩阵,不但导出动平台的运动速度到驱动关节速度之间的映射,而且易于进行全面的奇异位形分析;3-RSR并联机器人无约束奇异,当支链的驱动旋转副轴线、被动旋转副轴线和球铰共面时,产生结构奇异。该文方法亦可用于其他三自由度并联机器人的雅可比矩阵研究。     

A centro-based characterization of singularities in the workspace of planar closed-loop manipulators

The paper presents a centro-based characterization of singularities in planar multi-DOF mechanisms with arbitrary kinematic structure. A multi-DOF mechanism is treated as an assembly of several single DOF link sets and hence the terms like affected link set, active link set and active centro have been defined. Criteria for end-effector dependent and end-effector independent singularities of a closed-loop manipulator with given output link have been established in the paper in terms of centroes. Based on the relative disposition of the centroes, the singularities have been classified into five types and their physical implications have been explained. End-effector dependent singularities are shown to lie on the coupler curve of a larger single DOF mechanism. A simple linkage transformation has been proposed for the study of manipulators with physical limits on joint motion under the general framework of close-loop manipulators. Several examples have been worked out to demonstrate the centro-based method of singularity analysis.     

Analysis and Application of the Singularity Locus of the Stewart Platform

The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.     

三个复杂基本运动链奇异性条件的求解与识别

提出了求解任意复杂多回路平面连杆机构及操作手奇异位置分析的模块法。即对组成复杂机构的数量有限的基本运动链进行奇异分析 ,推导出这些复杂基本运动链产生奇异位置构型的奇异性条件 ,然后将之看作是复杂机构和操作手奇异分析的基本模块 ;只要一个基本运动链达到奇异位置时 ,该复杂机构即处于奇异位置。在此基础上本文又推导出三个复杂基本运动链产生奇异位置构型的奇异性条件 ,从而扩展了用该方法求解复杂多回路平面连杆机构及操作手奇异位置的应用范围。     

Transmission Index Research of Parallel Manipulators Based on Matrix Orthogonal Degree

Performance index is the standard of performance evaluation, and is the foundation of both performance analysis and optimal design for the parallel manipulator. Seeking the suitable kinematic indices is always an important and challenging issue for the parallel manipulator. So far, there are extensive studies in this field, but few existing indices can meet all the requirements, such as simple, intuitive, and universal. To solve this problem, the matrix orthogonal degree is adopted, and generalized transmission indices that can evaluate motion/force transmissibility of fully parallel manipulators are proposed. Transmission performance analysis of typical branches, end effectors, and parallel manipulators is given to illustrate proposed indices and analysis methodology. Simulation and analysis results reveal that proposed transmission indices possess significant advantages, such as normalized finite (ranging from 0 to 1), dimensionally homogeneous, frame-free, intuitive and easy to calculate. Besides, proposed indices well indicate the good transmission region and relativity to the singularity with better resolution than the traditional local conditioning index, and provide a novel tool for kinematic analysis and optimal design of fully parallel manipulators.     

6－UPS型并联机构的刚体动力学模型

建立了6－UPS型并联机构的动力学模型。为了能使动力学模型包含所有构件的重力和惯性力,以6－UPS并联机构的支链为研究对象,运用D－H方法建立了各构件的坐标系,推导了支链的运动学反解的解析方程,并给出了各个构件的速度、加速度与动平台的速度、加速度的映射关系。然后用牛顿－欧拉方法推导了6－UPS并联机构的动力学模型,为支链中各个构件支反力的求解和整个机构的动力学分析奠定了基础。最后以并联机床为例,运用动力学模型进行了实际计算并绘制了连杆驱动力的变化曲线。     

A study of workspace and singularity characteristics for design of 3-DOF planar parallel robots

A study of workspace and singularity characteristics is presented for two common types of 3-DOF planar parallel robot manipulators. The robots considered feature a kinematic structure with three in-parallel actuated, R-R-R, and R-P-R serial chain geometries. In this study, computer simulations aided with graphic visualization were used to characterize the complete pose workspace (for ranges of both position and orientation) and the singularity inherent to the systems. Parametric studies have also been performed to ascertain the way in which both characteristics vary with respect to various geometric parameters such as pivot locations, link lengths, and size of end-effector. Results are shown by way of a unique composite ratio of the available workspace to the density of singularity within that workspace, which can be used to optimize the geometry of the robots in design.