6自由度机器人奇异形位分析及仿真

通过对6R机器人奇异形位形成条件的分析，把机器人奇异形位分为结构边界奇异、边界奇异、内部奇异和腕部奇异四种情况。在对边界奇异进行了详细分析的基础上，对每一情况给出了计算机仿真结果，获得了直观的边界奇异表达。     

3-RTT并联机器人奇异位形空间分析

采用基于机构瞬时运动分析的方法，建立了3—RTT并联机器人的奇异位形判别阵。分析了3—RTT机器人处于奇异位形时机构所满足的几何条件。编制了基于三维搜索算法的奇异位形空间分析程序，时实例进行搜索计算和分析，给出了3-RTT机器人的奇异位形空间的图形，并对其分布规律进行了分析。     

Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: Mobility,kinematics, and singularity

This study introduces a high-speed parallel robot with Schönflies motion. This robot exhibits a promising prospect in realizing high-speed pick-andplace manipulation for packaging production lines. The robot has four identical limbs and a single platform. Its compact structure and single-platform concept provides this robot with good dynamic response potential. A line graph method based on Grassmann line geometry is used to investigate the mobility characteristics of the proposed robot. A generalized Blanding rule is also introduced into this procedure to realize mutual conversion between the line graphs for motions and constraints. Subsequently, the inverse kinematics is derived, and the singularity issue of the robot is investigated using both qualitative and quantitative approaches. Input and output transmission singularity indices are defined based on the reciprocal product in screw theory and the virtual coefficient by considering motion/force transmission performance. Thereafter, the singular loci of the proposed robot with specific geometric parameters are derived. The mobility analysis, inverse kinematics modeling, and singularity analysis conducted in this study are helpful in developing the robot.     

Geometric condition of 3UPS-S parallel mechanism in singular configuration

The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.     

6-UPS并联机器人奇异姿态空间分析

对并联机器人的工作空间和奇异位形进行分析。采用分支杆许用驱动力作为并联机构奇异空间边界的判断依据,提出临界奇异和奇异空间的概念。在给出一种姿态空间描述方法的基础上,提出了一种姿态工作空间和奇异姿态空间的求解算法。通过计算机仿真,得到了6-UPS并联机器人的姿态工作空间和奇异姿态空间的可视化图形描述。     

基于矢量积法的六自由度工业机器人雅可比矩阵求解及奇异位形的分析

论述六自由度工业机器人奇异位置奇异和姿态奇异的问题。由于雅克比矩阵反映操作臂笛卡尔空间速度与关节空间速度之间的映射关系,因此,利用矢量积法求得雅克比矩阵,并将其分块,得雅克比行列式为零时对应的关于关节角表达式,利用关节角表达式得其臂部内部奇异和腕部内部奇异,由关节角的极限范围得边界奇异。最后仿真得出奇异位姿所对应的关节转角及其关系式,为示教、轨迹规划及其动力学分析提供了可靠的依据。     

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。     

一种求解复杂平面机构奇异位置的分析图解法

提出了复杂多环路平面机的奇异位置分析的一种简明的分析图解方法,即先将机的分解为基本运动链,再导出基本运动链的奇异性条件,后由其相应的奇异几何图形,解出其机构的奇异位置。揭示了机构奇异分析的三个重要结论。还给出了任意复杂多环路平面机构可能产生奇异位置的上限计算公式。最后举例说明了一个双环复杂机构的奇异位置求解过程,此外提出的方法可推广至空间机构的奇异性分析。     

基于微分几何的过驱动并联机器人驱动奇异性分析

运用微分几何方法对过驱动并联机器人驱动奇异性进行了分析。应用位形流形和环境流形上黎曼度量的投影关系,分析其驱动奇异性产生原因,进一步依据嵌入映射定义,提出用位形流形切空间的任一标架来代替雅可比矩阵分析驱动奇异性的方法,并利用矩阵秩的有关特性,给出分析驱动奇异性的简洁等价形式以避免矩阵乘积运算。与应用隐函数微分法相比,该方法避免多次求解逆矩阵,从而降低了计算的复杂性。最后,以平面2-DOF 过驱动并联机器人为例,说明上述理论是可行且有效的。     

一类非完整机械手的链式变换特性及其运动规划方法

针对一类非完整三关节机械手提出了规避链式逆变换奇异位形的运动规划方法。根据非完整机械手的结构特点分离出广义坐标向量中的自由变量,将其边界值作为控制输入中的待定系数进行求解。对于非完整机械手在链式逆变换过程中出现的奇异性问题,提出令链式空间中一条轨迹向关节空间映射有解的不等式约束条件,利用增加附加位形约束的方法来规避非完整机械手的链式逆变换奇异位形。仿真与实验结果证明了运动规划算法的可行性与有效性。     

6-PUS并联机器人的奇异性分析

本文对6-PUS并联机器人的奇异位形进行了分析。在运动学分析的基础上得出了该类并联机器人的运动学方程。将并联机器人的奇异条件表示为矢量的混合积形式,然后根据矢量混合积与并联机器人腿在空间的几何关系,给出了6-PUS并联机器人几种出现奇异位形的腿的几何条件。     

Singularity analysis of a novel 4-dof parallel manipulator H4

Recently, it has been shown that a novel parallel manipulator called H4 can be employed to perform high speed motion for semiconductor applications. In this new family of parallel manipulator, singularities are associated with either loss or gain of degrees of freedom (DOF). This paper deals with singularity analysis of H4 utilizing line geometry tools and screw theory. Firstly, the static equilibrium condition of the end effector is derived to obtain the full 6×6 matrix, which is set of governing lines of the manipulator. Based on linear dependency of these lines, the singular configurations of the manipulator can be identified. Moreover, in order to deal with singularities associated with loss of DOFs (serial singularity), the static equilibrium of the actuators is also defined. Secondly, architecture and constraint singularities associated with gain of DOFs (parallel singularity) are defined and analyzed using linear complex approximation algorithm (LCAA), which is employed to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines. The linear complex axis and pitch provide additional information and a better physical understanding of the manipulator’s self-motion when in or closed to a singular configuration. Lastly, various singularities of an example H4 manipulator are presented and analyzed using the proposed methods.     

含弹性杆件的并联机器人刚度分析

通过分析包含弹性杆件的并联机器人的刚度系数的性质,计算了机器人在各方向上的刚度,绘制了最小刚度系数的变化曲线,研究了刚度与奇异位形、机器人的固有频率及弹性振动振幅的关系.计算实例表明,刚度系数和奇异位形、机器人的固有频率有密切的联系,可用于预测含弹性杆件的并联机器人的弹性动力学特性和响应,不需要进行弹性动力学计算,计算时间节省94%.     

基于位姿反馈的三臂空间机器人抓捕轨迹规划

以三臂空间机器人为研究对象,针对经历奇异位形时出现的位姿误差问题,提出一种基于位姿误差反馈的轨迹规划算法。根据系统一般运动学方程并结合动量守恒方程建立系统运动学模型,利用位姿期望指令得到误差运动方程。以关节角速度为控制量,设计了基于位姿误差反馈的控制率,使闭环系统的跟踪误差按指数速度收敛。该方法能够减小机器人奇异点邻域内的位姿跟踪误差,且在离开奇异区域后能完全消除误差。仿真结果证明了该方法的有效性。     

基于螺旋理论的5R三自由度并联机器人奇异形位分析

并联机器人每个支链由5个转动副组成,通过对支链结构采用坐标变换方法,从而使每个支链等效为一个串联机械手的形式,从而在分析过程中使得原来所要分析的参数由5个减少至4个,降低了分析的难度,这一方法对于今后并联机器人的结构分析方面做出了重要的贡献。为今后的动力学、运动学分析中避免奇异形位做出了理论探索。     

Asymptotic reduced-dimensional steering strategies for CMG singularity-free control

The geometric singularity problem is one of principal difficulty when using single-gimbal control moment gyros as spacecraft attitude control devices. To overcome singularity, new steering logics are suggested in this paper which results in a reduction in the difficulty of generating gimbal rates around a singular state. One of the suggested steering laws presented is the reduced dimensional singular value decomposition steering law, which adopts the singular value decomposition in reduced dimensional forms. Two other steering laws make use of the least square method in reduced dimensional forms. All of the suggested steering laws have been generated for the compensation of the torque insufficiency. These logics are verified mathematically and simulations at a singular condition and non-singular condition are performed to see how well they work.     

任意复杂多回路平面机构及操作手奇异分析的模块法

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。即一个复杂机械可看作是由输入一个或多个零自由度的基本运动键组成,对这些数量有限的基本运动链进行奇异分析,然后将灾看作是复杂机构和操作手奇异分析的基本模块;仅当一个基于运动键达到奇异位置时,复杂机构即处于奇异位置。还得到了任意复杂多回咱平面机构产生奇异位置的奇异性条件总数的计算公式。因此,该方法可求解所有复杂的多回路平面机构及操作手的     

On the forward and inverse displacement of spatial parallel manipulators

In engineering applications, the singularity, and the forward and inverse displacement of spatial parallel manipulators have received a great deal of attention. This paper presents a new simple but effective methodology to investigate these problems based on the analysis of the degree of freedom (DoF) of the spatial parallel manipulator. Through numerical method, the singularity and the forward displacement problems can be cracked simultaneously. With a numerical example, we point out that the Newton-GMRES algorithm is quite a good redeeming method to solve the forward displacement of spatial parallel manipulators, in which cases the differential coefficient matrix of the Newton?Raphson method is nearly singular.     

Stress field near transverse cracks under extension or in-plane shear in cross-ply composite laminates

Based upon the method of eigenfunction expansion and Leknitskii’s complex-variable potentials for the generalized plane deformation, the singular stress field near transverse cracks is examined for cross-ply composite laminates under two types of deformation, extension and in-plane shear. The stress singularity for each deformation is obtained from the eigenvalue equation resulting from appropriate near field conditions. It is found that the stress singularity for in-plane shear deformation is much stronger than for extension. To compute the stress intensity, use is made of the asymptotic representation for the stress and displacement field in conjunction with the singular hybrid finite element method. The numerical results are confirmed through comparison to those from other numerical techniques such as the boundary collocation method.