Dexterity analysis for omni-directional wheeled mobile manipulator based on double quaternion

The unified analysis of omni-directional wheeled mobile manipulator(OWMM) through the dimensionally nonhomogeneous Jacobian matrix may lead to unreliable results. The existing researches focus on the integrated performance evaluation of OWMM, without taking the influence of velocity difference into consideration. This paper presents a new approach to formulate the dimensionally homogeneous Jacobian matrix and a new index for OWMM. First, the universal transformational matrix of the link coordinate frame is derived based on double quaternion. The degree of locomotion of a mobile platform and the degrees of manipulation of a manipulator are treated equally as the joints of a redundant composite robot. Then the integrated modeling of OWMM is established, and the non-dimensional Jacobian matrix is obtained from the above matrix. Next, by examining the concept of directional manipulability, a new index is proposed to evaluate the directional manipulability of OWMM along the specified task direction. Furthermore, for the same task and the time of simulation, the kinematic performance of the fixed base operation of the manipulator and the operation of OWMM are analyzed by numerical simulation. The results suggest that the proposed approach is equivalent to the method of traditional kinematic modeling, with the error of numerical solution being 10-7 , and the varying frequency of DMTR is higher than that of the condition number. This indicates that DMTR is more effective to reflect the variation of the task direction. The proposed method can be used to analyze the manipulating capability of OWMM, and has a simple structure and generality in the unified analysis of OWMM.     

基于雅克比矩阵的并联机器人运动学性能分析

基于雅克比矩阵的机构运动特分析对于并联机构的设计具有重要指导意义。本文主要介绍3-UPS/RRR并联机构的运动特性,首先建立机构的雅克比矩阵,利用雅克比矩阵建立机构的可操作度指标,其次借助可操作度指标对在不同姿态下的机构可操作度进行评估。通过MATLAB仿真结果表明,该机构具有良好的可操作性能。     

Dimensional Synthesis of a 3-DOF Parallel Manipulator with Full Circle Rotation

Parallel robots are widely used in the academic and industrial fields. In spite of the numerous achievements in the design and dimensional synthesis of the low-mobility parallel robots, few research ef...     

Optimum design of 6-DOF parallel manipulator with translational/rotational workspaces for haptic device application

This paper proposes an optimum design method that satisfies the desired orientation workspace at the boundary of the translation workspace while maximizing the mechanism isotropy for parallel manipulators. A simple genetic algorithm is used to obtain the optimal linkage parameters of a six-degree-of-freedom parallel manipulator that can be used as a haptic device. The objective function is composed of a desired spherical shape translation workspace and a desired orientation workspace located on the boundaries of the desired translation workspace, along with a global conditioning index based on a homogeneous Jacobian matrix. The objective function was optimized to satisfy the desired orientation workspace at the boundary positions as translated from a neutral position of the increased-entropy mechanism. An optimization result with desired translation and orientation workspaces for a haptic device was obtained to show the effectiveness of the suggested scheme, and the kinematic performances of the proposed model were compared with those of a preexisting base model.     

Force transmission analyses with dimensionally homogeneous Jacobian matrices for parallel manipulators

To avoid the unit inconsistency problem in the conventional Jacobian matrix, new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points was presented (Kim and Ryu, 2003). This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived unit consistent Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.     

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.     

3-UPS/S并联机构运动学分析及机构优化设计

对3-UPS/S并联机构进行了运动学分析和静力学分析,得到了该机构的运动雅可比矩阵和静力学雅可比矩阵;采用离散的方法对该机构的工作空间进行了分析;对该机构进行了基于给定工作空间的尺寸参数优化,在优化的过程中考虑了机构的奇异性、关节约束和机构几何尺寸约束等条件.     

3-RRR平面并联机构刚度分析

刚度是并联机构重要性能指标,为了评价并联机构刚度,提出了一种刚度评价方法.基于3-RRR机构的逆运动学模型,推导出其雅可比矩阵.在力雅可比矩阵的基础上,给出了刚度评价指标,该指标不仅适用于3-RRR并联机构,而且可以应用于其它并联机构.将提出的刚度指标应用于3-RRR并联机构,数值仿真结果表明3-RRR机构在工作空间中具有对称的刚性.     

Tricept机器人的尺度综合方法研究

Tricept机器人是目前商业上最为成功的并联机器人之一。提出一种Tricept机器人中三自由度并联机构的最优尺度综合方法。该方法首先导出尺度参数间的关系,其次构造一种均衡条件数全域均值及其极差间矛盾的综合操作性能指标,进而将尺度综合问题归结为一类双参数优化问题。该方法对掌握这类及其他并联机构的运动学设计理论有一定指导意义。     

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.     

一种新型大刚度高灵敏度的并联六维力传感器设计研究

腕力传感器是一类重要的机器人传感器,腕力传感器的结构设计好坏直接影响到传感器的各项指标。在分析了并联力传感器的力变换原理,利用并联传感器的空间力传递关系,直接推导出感测力的六维雅可比矩阵,并将六维力雅可比矩阵用具体的结构参数解析表达,在此基础上设计了一种新的并联六维力传感器,新设计的附加弹性体的采用,使该传感器具有很大的刚度,同时具有很高的检测灵敏度,从而很好地解决了传感器的刚度与灵敏度之间的矛盾,探索了传感器设计的新方法和途径。     

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.     

4自由度非全对称并联机构的完整雅可比矩阵

少自由度并联机构完整雅可比矩阵为6x6矩阵,包括运动子矩阵和约束子矩阵两部分,由于前者的代数特征不能反映出机构的约束特性,在对此类机构进行运动学分析和几何参数优化设计时,必须建立完整的6x6雅可比矩阵.鉴于此,基于对偶螺旋理论,以4自由度机构2RPS-2UPS为例,给出非全对称少自由度并联机构完整雅可比矩阵的推导方法.首先,根据螺旋理论推导约束支链中的运动螺旋系和反螺旋系,并利用互易积获得约束子矩阵.其次,锁定每个支链中的主动关节,根据螺旋理论计算约束支链和全运动支链中新增反螺旋系,并利用互易积建立运动子矩阵.将约束子矩阵和运动子矩阵联立建立机构完整雅可比矩阵.最后,分析雅可比矩阵的秩,得到2RPS-2UPS并联机构产生奇异位形的条件.     

类人机器人腕用六维加速度传感器的理论研究

类人机器人灵巧手抓取过程中的惯性力会影响到抓取的鲁棒性,为了消除惯性力的影响,需要检测出加在手上的空间加速度反馈给控制系统,以确保抓取的平稳性和快速性.采用并联机构作为弹性元件研究了一种六维加速度传感器,建立了静态数学模型,推导了加速度和灵敏度雅可比矩阵,并对传感器的静态特性进行了研究.根据定义的静态性能指标采用空间模型理论的图谱寻优法,优化设计了传感器的理论模型参数.为了验证设计参数的可靠性,给出了1种类人机器人腕用六维加速度传感器的算例,仿真实验获得的各弹性连接杆上应变的实验值与理论值的最大误差为1.617％.最后标定实验结果证明研究的理论和方法是有效和可靠的.     

新型碟式太阳能聚光器跟踪机构优化设计

提出了一种通用3-RPS并联机构,其动平台、定平台为相似的任意三角形,且转动副轴线垂直于定平台中心与顶点的连线,基于该机构设计了一种新型碟式太阳能聚光器。采用封闭矢量法求得机构的运动学位置逆解,并以此为基础,运用螺旋理论分析机构输入与输出的速度映射关系,建立了机构的雅可比矩阵。以全域灵巧度、全域刚度性能及全域承载能力为优化指标,利用遗传算法对机构的结构参数进行优化设计,确定了定平台半径,借助性能图谱法定量地对比分析了优化前后各性能指标在可达工作空间内的分布情况,并采用ANSYS软件对优化前后机构进行静力学验证分析,结果表明：新型碟式太阳能跟踪装置的定平台半径为860 mm时,其灵巧度、刚度及承载能力等均有不同程度的提高。     

基于任务空间的 2P3RR 并联机构尺度综合

结合一种五坐标混联工作台的开发,对其少自由度并联机构部分进行了深入的研究。给出了该并联机构的运动学位置正、逆解,求解了雅可比矩阵,分析了工作空间,基于任务空间探讨了该并联机构主要结构参数之间的相互关系,采用雅可比矩阵条件数的倒数的全域均值作为该并联机构灵巧度评价指标,对其进行灵巧性分析,给出了混联工作台开发实例并进行了设计计算,为混联运动平台的设计开发奠定了理论基础。     

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.     

Microassembly of micropeg and -hole using uncalibrated visual servoing method

In order to achieve high performance visual servoing, substantial efforts must be made for the calibration of intrinsic parameters of the camera and the transformation matrix as well. In order to avoid the tedious and difficult calibration work, a Kalman filtering-based estimation algorithm is proposed to estimate the composite image Jacobian or the homogeneous transformation matrix on-line, which can reduce the influence of noise. Using the estimated Jacobian matrix, a PD visual controller is used to make features converge to desired values with satisfactory dynamic performance, without a priori knowledge of the kinematic structure and system parameters. The proportional and differential gains are tuned using a genetic algorithm to obtain optimal controller parameters. A series of experiments are performed on peg and hole assembly to investigate the feasibility and effectiveness of this method.     

Optimal design of 3-DOF PKM module for friction stir welding

Friction stir welding (FSW) has recently emerged as a solid-joining technology for high-strength aluminum alloys and light metal welding. The large axial force to be maintained between the welding tool and workpiece is the primary requirement of FSW process, which has also been a great obstacle to the design and application of FSW in manufacturing. Further complicating the issue is the need to perform FSW over three-dimensional contours, which requires a mechanism dexterous enough to set the stir pin used in welding to track a predefined trajectory with prescribed poses. Apart from the position specification, the design of a dexterous mechanism to pose the orientation of stir pin is a great challenge. This paper proposed the application of 3-PRS (P, R, and S standing for prismatic, revolute, and spherical joint, respectively) parallel mechanism as a welding tool head and employed it to form a five-axis welding machine tool for FSW. In order to accommodate the orientation capability requirements, the kinematic feature has been analyzed. With the dimensionless treatment of the Jacobian matrix of 3-PRS manipulator, a global condition index is proposed to estimate the kinematic dexterity in the whole orientation workspace. Finally, by means of an optimal design method and performance atlas, optimal designs of the 3-PRS parallel mechanism is carried out. A preferable set of optimized geometric parameters are obtained to achieve a compact and dexterous design, and the optimization results are used in development of a prototype machine for FSW.     

平面2自由度驱动冗余并联机器人的性能分析

以一种平面2自由度驱动冗余并联机器人为研究对象,对该机器人机构尺寸进行量纲一化,给出反映机构几何参数变化范围的空间模型,建立机构的运动学方程,得到位置反解和速度雅可比矩阵。定义并计算机器人的全域性能指标,探讨机器人的雅可比矩阵条件数、承载能力及刚度等全域性能指标与机构杆件尺寸之间的关系,并在空间模型内绘制相应的性能图谱;根据性能图谱,总结三种性能指标在空间模型内的分布规律,分别给出每种性能指标值较好的机构尺寸范围;最后对三种性能指标较好的尺寸范围进行了综合,得到同时考虑三种性能指标优化的最佳尺寸范围。这些图谱使机器人依据运动学性能指标进行优化设计成为可能,图谱分析为实现并联机器人机构设计的计算机辅助设计提供了一种简单、有效途径。