Kinematics and optimization of 2-DOF parallel manipulator with revolute actuators and a passive leg

In this paper, a 2-DOF planar parallel manipulator with two revolute actuators and one passive constraining leg. The kinematic analysis of the mechanism is analytically performed: the inverse and forward kinematics problems are solved in closed forms, the workspace is derived systematically, and the three kinds of singular configurations are found. The optimal design to determine the geometric parameters and the operating limits of the actuated legs is performed considering the kinematic manipulability and workspace size. These results of the paper show the effectiveness of the presented manipulator.     

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。     

Motion capability analysis of a quadruped robot as a parallel manipulator

This paper presents the forward and inverse displacement analysis of a quadruped robot MANA as a parallel manipulator in quadruple stance phase, which is used to obtain the workspace and control the motion of the body. The robot MANA designed on the basis of the structure of quadruped mammal is able to not only walk and turn in the uneven terrain, but also accomplish various manipulating tasks as a parallel manipulator in quadruple stance phase. The latter will be the focus of this paper, however. For this purpose, the leg kinematics is primarily analyzed, which lays the foundation on the gait planning in terms of locomotion and body kinematics analysis as a parallel manipulator. When all four feet of the robot contact on the ground, by assuming there is no slipping at the feet, each contacting point is treated as a passive spherical joint and the kinematic model of parallel manipulator is established. The method for choosing six non-redundant actuated joints for the parallel manipulator from all twelve optional joints is elaborated. The inverse and forward displacement analysis of the parallel manipulator is carried out using the method of coordinate transformation. Finally, based on the inverse and forward kinematic model, two issues on obtaining the reachable workspace of parallel manipulator and planning the motion of the body are implemented and verified by ADAMS simulation.     

Atlas Based Kinematic Optimum Design of the Stewart Parallel Manipulator

Optimum design is a key approach to make full use of potential advantages of a parallel manipulator. The optimum design of multi-parameter parallel manipulators(more than three design parameters), such as Stewart manipulator, relies on analysis based and algorithm based optimum design methods, which fall to be accurate or intuitive. To solve this problem and achieve both accurate and intuition, atlas based optimum design of a general Stewart parallel manipulator is established, with rational selection of design parameters. Based on the defined spherical usable workspace(SUW), primary kinematic performance indices of the Stewart manipulator, involving workspace and condition number are introduced and analyzed. Then, corresponding performance atlases are drawn with the established non-dimensional design space, and impact of joint distribution angles on the manipulator performance is analyzed and illustrated. At last, an example on atlas based optimum design of the Stewart manipulator is accomplished to illustrate the optimum design process, considering the end-effector posture. Deduced atlases can be flexibly applied to both quantitative and qualitative analysis to get the desired optimal design for the Stewart manipulator with respect to related performance requirements. Besides, the established optimum design method can be further applied to other multi-parameter parallel manipulators.     

Evolutionary bi-criteria optimum design of robots based on task specifications

The optimum robot structure design problem based on task specifications is an important one, since it has greater influence on manipulator workspace design, vibrations of the manipulator during operation, manipulator efficiency in the work environment and power consumption. In this paper, an optimization robot structure problem is formulated with the objective of determining the optimal geometric dimensions of the robot manipulators considering the task specifications (pick and place operation). The aim is to minimize torque required for motion and maximize manipulability measure of the robot subject to dynamic, kinematic, deflection and structural constraints with link physical characteristics (length and cross-sectional area parameters) as design variables. In this work, five different cross-sections (hollow circle, hollow square, hollow rectangle, C-channel and I-channel) have been experimented for the link. Three evolutionary optimization algorithms namely multi-objective genetic algorithm (MOGA), elitist nondominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) are used for the optimum structural design of 2-link and 3-link planar robots. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best optimal solution. Two multiobjective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the Pareto optimal fronts. Two more multiobjective performance measures namely optimiser overhead and algorithm effort, are used to find computational effort of optimization algorithm. The results obtained from various techniques are compared and analyzed.     

一种两自由度并联机床平台机构及其运动学分析

提出了一种新型的两杆两自由度并联机床机构 ,介绍了其机构的组成 ,推导了运动学正反解计算公式 ,并给出了雅可比矩阵及其工作空间的分析。为两自由度的平面加工设备提供了设计和控制的理论依据。     

用遗传算法解具有给定工作空间的并联机构综合问题

提出一种利用遗传算法求解6自由度空间并联机器人机构综合问题的新方法。该机构的工作空间必须包含预先给定的且具有一定姿态能力的工作空间。为了描述具有一定姿态能力的工作空间，给出了一种简单有效和搜索算法。该法考虑了连杆长度限制、铰链转角限制和连杆干涉。算例表明结构参数可得到有效地优化，从而获得紧凑的机器人机构。     

一种6-6UHU并联机器人的设计和实验研究

研制了一种新型结构的大工作空间 6 6UHU并联机器人。通过对虎克铰摆角极限对机器人工作空间的影响研究 ,在机构设计上解决了杆间干涉和下关节极限问题 ,简化了干涉检测算法 ,降低了运动控制算法的复杂性 ,并且增大了工作空间。研制出基于DSP的多轴控制器PMAC卡的交流伺服电机控制系统和实验系统 ,并进行了实验。给出了不同姿态下该机器人的工作空间分析。仿真数据和实验结果表明 ,所研制的新型 6 6UHU并联机器人 ,结构精巧 ,工作空间大 ,动平台的倾斜角达到 4 5° ;同时具有高刚度、高精度、操作性能好等特点。干涉防护系统能保证机器人在大工作空间机动运行情况下的安全     

Obtaining configuration space and singularity maps for parallel manipulators

The aim of this paper is to describe a general methodology to obtain the entire set of positions that a parallel manipulator can reach and the workspace regions where the robot is controllable. The workspace is computed using a hybrid analytical-discrete procedure. Next the singularity maps are traced by carrying out a kinematic analysis of the positions obtained. To perform the latter a systematic method has been introduced to obtain the corresponding Jacobian matrices. The result of the whole process is the computation of singularity-free workspace regions, associated with certain working and assembly modes. After that, strategies to enlarge the accessible space are easier to plan and implement. This methodology is based on disassembling the manipulator into a mobile platform and a set of kinematic chains.     

基于三分支非均匀分布球面并联机构的腰关节设计

通过分析球面三转动副并联机构中三个分支的布局对工作空间大小的影响，把一般球面并联机构的三个分支由均匀分布改为非均匀分布，提出了基于三分支非均匀分布球面并联机构的拟人腰关节，选取了一组合理的几何参数，给出了完整的设计方案。该拟人腰关节前弯后弯角度大，基本能满足人体腰关节对工作空间的要求。     

3SPS-3PRS并联机构构型分岔特性

作为轴对称矢量喷管转向控制驱动机构的Gough-Stewart类并联机构,主要工作在奇异位置状态.在该位置,驱动平台能够获得一个绕其法线的自由转动,导致转向控制驱动机构的运动具有不确定性.为此,采用少自由度3SPS-3PRS并联机构限制该自由转动,通过对少自由度3SPS-3PRS并联机构的分岔特性研究发现,该并联机构存在尺度极限奇异位置,且输入参数的取值对由尺度极限奇异位置决定的并联机构的工作空间影响较大.对于给定的矢量状态要求,3SPS-3PRS并联机构的输入参数变化范围有可能超出由尺度极限奇异位置确定的工作空间,导致3PRS运动链产生较大的约束内应力,同时并联机构的工作空间跨越奇异位置使得动平台在通过奇异位置后的构型具有不确定性,因此该并联机构的运动奇异性问题依然存在.     

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.     

新型6-PSS并联机器人工作空间分析

提出一种由Stewart平台演绎而来的正交6－PSS并联机器人新机型，介绍其结构布局特点，基于位置反解及其结构约束条件，绘制其工作空间的轮廓图，并定量分析该并联机器人RPY角和机构尺寸参数对其工作空间大小的影响，为该并联机器人的设计与实用化提供理论依据。     

基于弦方法的平面并联操作手工作空间分析

采用一种工作空间边界求解的新方法——弦方法对平面并联操作手工作空间的综合问题进行了研究。首先给出了弦方法的基本原理和求解步骤。在平面并联操作手运动学分析的基础上,利用弦方法易于加入约束条件的特点,以机构的灵巧性指标为约束,采用约束跳步优化搜索算法得到具有良好运动学特性的工作空间边界。最后给出了几个具体的设计算例。     

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...     

角度与运动约束下串联式机械臂工作空间求解与结构优化

深水作业机械臂通常采用串联式结构,机械臂每个关节的转动角度与长度会受到相应的限制,这些参数会直接影响到机械臂的运动轨迹规划和作业效率。机械臂的有效工作空间的求解是一个多目标多约束的优化问题。通过数学分析建立机械臂的运动学模型,分析影响有效工作空间的相关参数,利用图解法来分析机械臂工作空间的边界曲线,得到机械臂的有效工作空间的截面。针对机械臂有效工作空间的截面积建立数学解析模型,最后运用遗传算法求得满足约束条件下的机械臂有效工作空间最优解和能够实现高效作业的最优结构参数。仿真结果表明,该模型能够有效求解角度与运动约束下的串联式机械臂结构优化问题。     

Optimal design of the TriVariant robot to achieve a nearly axial symmetry of kinematic performance

This paper revisits the optimal kinematic design of a 3-DOF parallel mechanism that forms the main body of a 5-DOF reconfigurable hybrid robot named the TriVariant. The dimensional synthesis of the 3-DOF parallel mechanism is carried out by introducing a tilt structure angle that enables to achieve a nearly axial symmetry of kinematic performance with respect to the configuration when the properly constrained active limb is vertically or horizontally placed. The results are then compared with those of the Tricept robot via an example. It concludes that for the same task workspace the modified version of the TriVariant has a very similar kinematic performance to that of the Tricept provided that they both have similar dimensions.     

三维平动球平台机器人的位置与工作空间分析

提出一种新颖的三维平动球平台机器人并分析其位置与工作空间问题。该新型机器人是DELTA机器人的一种变异形式，结合其结构布局特点，建立了其位置正反解方程式，分析其工作空间及其影响因素，为其设计和实用化提供理论依据。该新型机器人运动平台无过约束，在三雏平动微动机器人、并联机床和振动环境模拟台等领域有广阔的应用前景。     

双支链六自由度并联机构尺度设计与性能分析

提出了一种新型六自由度并联机构,该机构由两条运动支链组成,每条支链各包含一个主动球副。与常规六自由度并联机构相比,支链数目的减少可有效增大机构工作空间。基于封闭矢量法求得所提机构的运动学位置逆解,在此基础上分析了机构输入与输出的速度映射关系,建立了机构雅可比矩阵。以工作空间和全域灵巧度为性能评价指标,借助性能图谱法完成了机构尺度设计,基于该尺度参数,对特定工作姿态下的工作空间、灵巧度、承载性能及刚度性能进行了全面研究。最后,搭建了3D打印样机,并对其典型应用场景进行了分析。     

2自由度高速高精度并联机器人的运动学优化设计

提出一种基于工作空间综合和灵巧度、速度和几何精度等性能指标分析的2自由度并联机器人运动学优化设计方法,构造一种由灵巧度、运动速度和运动分辨率等变量组合而成的工作空间全局评价指标。优化过程分为两步进行：首先以灵巧度、力传递特性和避免奇异位形的几何条件为约束,综合出具有良好特性的工作空间,在此基础上研究不同杆长比下实现目标工作空间所需的尺度参数;然后根据全局运动学性能评价指标从第一步的优化结果中遴选出最合适的杆长比,从而实现了对机构的几何尺度参数优化。并给出了算例以说明方法的有效性。