非对称球面五杆机构的奇异轨迹与灵巧度分析

针对非对称球面五杆机构,研究了机构的奇异轨迹曲线和灵巧度.首先建立了球面五杆机构的运动学正、反解模型,并导出了机构的速度方程和雅可比矩阵.基于机构的雅可比矩阵,对机构的奇异位形和灵活度进行了计算分析,绘制了机构的奇异轨迹和灵巧度分布曲线,并讨论了球面五杆机构的结构参数对机构全条件指标的影响.     

3PSS-S型并联机构的奇异轨迹研究

针对一种3PSS-S球面并联机构,建立了该并联机构的位置反解数学模型,推导了并联机构速度方程和雅可比矩阵的解析表达式。基于机构的雅可比矩阵,应用等高线方法绘制了并联机构的奇异轨迹曲线,并讨论了固定平台结构参数对并联机构奇异轨迹的影响。     

新型并联机器人的奇异位形分析

奇异是并联机器人的固有性质,对机器人的工作性能有着种种影响,因此对于确定的机构,找出它的所有奇异位形具有重要的意义.从运动学角度分析,奇异位形有三类形式,每种形式都具有不同的物理意义.基于以上原因,研究一种新型6自由度3支链并联机器人3-UrPS的奇异位形,其中Ur为复合胡克铰,即2自由度球面并联机构,P为移动副,S为球副.根据机构自身的几何特点,非常方便地得出反解的唯一解析形式.对机构的反解方程进行求导,得出有规律的速度雅可比矩阵,然后通过求解雅可比矩阵的行列式,使奇异位形的解析形式很容易得出.讨论该并联机器人的第1类和第2类奇异位形,并得出3种特殊位置的奇异位形.奇异位形的分析对该并联机器人的轨迹规划和控制具有重要的意义.     

一种新型2R完全解耦并联机构的运动学和奇异性分析

提出了一种完全解耦的二维转动并联机构。基于自由度特征矩阵分析了机构运动类型,运用单开链法确定了机构的自由度和主动副,同时求解了机构的位置和速度,并根据正逆雅可比矩阵系统分析了机构的奇异位形。由于该机构的全局雅可比矩阵为三角阵,该机构的运动完全解耦,因此可以简化机器人轨迹规划和控制。     

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。     

基于球面并联机构的检测平台设计与性能研究

为提高光电产品自动视觉检测的准确性,研制了一种含冗余驱动支链的4SPS/S球面并联调姿平台样机。含冗余驱动支链的4SPS/S并联机构为调姿平台机构本体,具有绕动平台中心点的3个转动自由度,可以实现待检零件任意角度图像信息的获取。建立了该并联机构的运动学模型,导出了机构位置逆解方程和雅可比矩阵;基于雅可比矩阵的秩讨论了机构的奇异性,并验证了冗余驱动支链能消除机构内部奇异;基于雅可比矩阵的非冗余分解,提出了一种评价冗余驱动并联机构力传递性能的指标。分析机构动定平台球铰安装方式对机构运动学性能的影响,得到了机构姿态空间体积大、灵巧度好的动定平台球铰安装方式;设计制作了球面并联检测平台样机,分析并绘制了样机姿态空间以及灵巧度、力传递性能在姿态空间内的分布。结果表明,样机转动空间大,无内部奇异,灵巧度和力传递性能高且分布均匀,能满足光电产品瑕疵检测的工艺要求。     

平面冗余与非冗余并联机构的奇异性比较研究

基于运动变换的雅可比矩阵，分别研究了平面二自由度冗余并联机构和平面二自由度非冗余并联机构的三类奇异性。推导了奇异曲线方程，绘出了基于量纲一结构参数的奇异曲线簇。通过对奇异曲线簇的对比分析，说明了机构冗余性对消除奇异性的有效作用。研究结果为两种机构避免奇异性的路径规划提供了有益的参考。     

基于逆向运动学的6自由度并联机构尺度综合

对用于飞行器半实物仿真试验的6自由度并联机构逆向运动学性能进行尺度综合研究.提出逆向速度椭球的概念,当逆向速度椭球的长半轴长度越短时,对于给定的机构动平台运动学要求,所需的连杆驱动速度越低.由于逆向速度椭球的长半轴长度在数值上与雅可比矩阵的最大奇异值等价,因此以雅可比矩阵最大奇异值全工作空间最小为尺度综合的目标函数,在工作空间的约束下,利用穷举法对6自由度并联机构进行尺度综合.结果表明,机构在满足动平台运动学要求的同时,能够保证所需的连杆最大驱动速度最低,并且还具有很高的灵活度.     

一种二自由度并联机器人机构灵活度研究

研究一种命名为Diamond的新型二自由度平动并联机器人机构的灵活度指标,对常用的三种性能评价指标雅可比矩阵条件数、最小奇异值和可操作性指标进行推导得到其解析模型,分析它们在机构作业空间内的分布趋势,研究表明该机构具有良好的灵巧性.     

一种新型并联机器人的奇异性与工作空间研究

针对一种六棱锥式新型并联机器人的轨迹规划问题,基于具有反解选取准则的机构逆运动学方程,对奇异性和工作空间进行深入研究。由雅可比矩阵提出机构奇异判别方程,并引入可操作度性能指标进行奇异性分析。考虑运动副范围以及连杆干涉等约束条件,采用三维边界搜索法,给出机构在定姿态下工作空间的三维可视化描述。进行边界采样实验,实验结果表明了仿真的正确性。研究结果可为无奇异轨迹规划提供理论依据。     

混合输入五杆机构速度空间的连续性研究

讨论了并联机构存在奇异性的几种情况,运用混合输入五杆机构输入输出速度的矩阵关系表达式,在整个铰链空间分析Jacobian矩阵中各项的连续性,推导出输出端速度空间连续性的判定准则。给出算例并进行仿真计算,验证了研究的正确性。     

新型并联机床工件坐标系定位的研究

建立了5-UPS/PRPU并联机床机构的雅可比矩阵。在此基础上,得到了3个影响机床机构灵巧度的指标,即条件数、最小奇异值、可操作性。通过对这3个并联机床灵巧度评价指标进行分析,定义了两个灵巧度的综合评价指标——综合灵巧度系数和综合灵巧度。把5-UPS/PRPU并联机床工件坐标系的定位问题归结为在满足工作空间前提下,对刀位文件综合灵巧度的优化,对这个非线性优化问题进行了求解,得到定位矢量,并结合一个曲面定位的具体实例,给出了算法验证。     

Design and forward kinematics of the compliant micro-manipulator with lever mechanisms

This paper presents the forward kinematics of a five-bar compliant micro-manipulator. To overcome the limited displacement of such a flexure-based mechanism driven by piezoelectric actuators, lever mechanisms are utilized to enlarge the working range. The mechanical design of the micro-manipulator is firstly described. Mathematical formulations for the five-bar mechanism are described and the solutions are developed to decide the end-effector position in Cartesian space. The amplification factor of the lever mechanism is also derived based on the analytical solution of the four-bar linkages. The velocity of the end-effector is obtained by differentiating the forward position kinematic equation, and the local mobility index of the five-bar compliant mechanism is determined and analysed. Based on linearization of trigonometric functions and constant Jacobian matrix, numerical simulations are carried out to investigate the performance of the five-bar compliant manipulator and to determine the optimal geometric parameters for the configuration. The comparisons between the exact solution and simplified methodologies are conducted. Experiments are carried out to validate the established model and the performance of the developed micro-manipulator.     

Cusp points and assembly changing motions in the PRR-PR-PRR planar parallel manipulator

Most parallel manipulators have multiple solutions to the direct kinematic problem. The ability to perform assembly changing motions has received the attention of a few researchers. Cusp points play an important role in the kinematic behavior. This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator. The direct kinematic problem of the manipulator yields a quartic polynomial equation. Each root in the equation determines the assembly configuration, and four solutions are obtained for a given set of actuated joint coordinates. By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates, the direct kinematic singularity loci in the joint space are determined by the implicit function. Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve. Two assembly changing motions by encircling different cusp points are highlighted, for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.     

Formulating Jacobian matrices for the dexterity analysis of parallel manipulators

The condition number of the Jacobian matrix has been commonly used in determining the dexterous regions of a manipulator workspace. This has been successful when applied to manipulators having either solely spherical or solely Cartesian degrees of freedom. However, for manipulators having a mix of both rotational and translational degrees of freedom, i.e., complex degree of freedom manipulators, the condition number of the Jacobian matrix may not be used due to dimensional inconsistencies with its elements. This paper furthers earlier work introduced in obtaining a Jacobian matrix which may be used to determine the dexterity of parallel mechanisms regardless of the number and type of degrees of freedom of the mechanism. The result of the method introduced in this paper is a dimensionally homogeneous Jacobian matrix mapping m actuator velocities to n independent end effector velocities. In the typical case where m = n, the Jacobian matrix is also square. As opposed to earlier works, the singular values of the Jacobian matrix obtained here have an evident physical significance. Furthermore, the ratio of the maximum and minimum singular values, i.e., the condition number may be used to measure the dexterity of the manipulator at a given pose. To illustrate the concepts introduced in this paper, the 3-PRS manipulator is analyzed.     

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.     

基于螺旋理论对3-RPS并联机器人运动学分析及仿真

3-RPS型并联机构具有3个结构对称的支链形式,每个支链由一个转动副连接基座,一个球面副与动平台相连接,转动副与球面副由移动副所连接。采用螺旋理论对3-RPS型并联机器人自由度分析,采用反螺旋的方法建立约束雅可比矩阵、运动雅可比矩阵和完整雅可比矩阵,导出了动平台的速度到驱动关节速度之间的映射,从而计算出末端执行器的速度、加速度并进行奇异性分析。基于Matlab SimMechanics软件建立3-RPS型并联机器人仿真模型,进行运动学仿真对比研究,结果表明:动平台的实际输出变化与给定的参考值变化基本相符,验证了该建模方法的正确性。     

平面并联机器人的速度控制精度分析

对各种衡量机器人灵活性的指标进行了比较,分析了平面并联机器人的基于雅可比矩阵的速度控制精度,并模拟计算了速度控制精度的分布情况。