Singularity analysis of parallel manipulators using constraint plane method

One of the most challenging problems in dealing with parallel manipulators is identifying their forward singular configurations. In such configurations these mechanisms become uncontrollable and cannot tolerate any external force. In this article a geometrical method, namely Constraint Plane Method (CPM), is introduced with the use of which one can easily obtain the singular configurations in many parallel manipulators. CPM is a methodical technique based on the famous Ceva plane geometry theorem. It is interesting to note that CPM involves no calculations and yields te result quickly. In addition, some of the previous geometrical methods led to many separate singular configurations; however, CPM yields the answer in just one phrase. In this article we have obtained singular configurations of some parallel manipulators. Moreover, a comparison is made between CPM and the previous methods to show the advantages of CPM.     

基于粒子群算法的并联机器人运动学正解研究

并联机器人运动学正解问题由于涉及到求解非线性方程组问题而不易解决。在对粒子群算法研究的基础上,对其进行改进,以提高全局搜索能力。同时结合外点罚函数法,对并联机器人运动学正解问题重新进行建模,以便于使用粒子群算法进行求解。结合二者形成新的正解求解方法。最后使用该方法,以一台并联机器人为对象进行研究,获得了其运动学正解。     

A methodology for actuator failure recovery in parallel manipulators

In this paper, the failure of parallel manipulators is examined considering the failure modes of manipulators. A methodology for investigating the effect of actuator/joint failures on the force/moment capabilities of manipulators is presented, and the criteria for full and partial recovery from these failures are established. The proposed methodology is valid for both planar and spatial parallel manipulators; in the case study and simulation, the planar manipulators are used as an example.     

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.     

并联机构动力学建模及控制研究

为了系统地研究并联机构动力学特性,分析了4种基本建模方法（牛顿-欧拉方法、直接拉格朗日方法、拉格朗日-达朗贝尔方法和虚功原理方法）,总结了各种方法的优缺点。在此基础上,对动力学的3种控制算法（经典PD控制、机器人控制中常用的计算力矩控制以及数控加工中的先进轮廓控制）在并联机构上的应用进行了分析研究。针对开发的三自由度（3-DoF）纯平动并联机构Orthopod,采用拉格朗日-达朗贝尔方法进行了动力学建模,并对其进行了控制仿真。研究结果显示,轮廓控制在轮廓误差控制方面具有更好的性能,适合于雕刻机的控制应用。     

Workflow balancing strategies in parallel machine scheduling

Workflow balancing on a shop floor helps to remove bottlenecks present in the manufacturing system. Workflow refers to the total time during which the work centres are busy. Idle time is not taken into account when calculating workflow. Earlier researchers have not specified the method for jobs to be executed in parallel in order to balance the workflow to each machine. In many manufacturing environments, multiple processing stations are used in parallel to obtain adequate capacity. In parallel machine scheduling there are m machines to which n jobs are to be assigned based on different priority strategies. The procedure is based on the idea of workload balancing and on balancing the workload among machines. In this paper, workflow and workload are assumed to have the same meaning. A machine with the lowest workflow is selected for assignment of a new job from the list of unfinished jobs. Different priority strategies are followed for the selection of jobs. Three different strategies are considered, namely random (RANDOM), shortest processing time (SPT) and longest processing time (LPT) for the selection of jobs for workflow balancing. The relative percentage of imbalance (RPI) is adopted among the parallel machines to evaluate the performance of these strategies in a standard manufacturing environment. The LPT rule shows better performance for the combination of larger job sizes and higher number of work centres or machines. A computer program was coded for validation in a standard manufacturing environment on an IBM/PC compatible system in the C++ language.     

Singularity analysis of planar parallel manipulators based on forward kinematic solutions

An efficient approach for determining the force-unconstrained poses (singularity loci) of planar parallel manipulators (PPMs) is presented. The approach is implemented for the 3-RPR, 3-PRR, and 3-RRR PPMs, where the underline indicates the actuated joint. The force-unconstrained poses are identified based upon concepts of reciprocal screws, kinematics, and elimination methods. The use of screw quantities provides a clear insight as to how the forces are acting on the mechanism. This allows finding conditions of singular configurations that are related to displacements of passive joints. Based on these conditions, the force-unconstrained poses are obtained by solving the forward kinematic analysis of manipulators with the same architecture but different actuation layouts. It is demonstrated that the singularity loci of the 3-RPR, 3-PRR, and 3-RRR PPMs can be described with single-variable polynomials of degrees 2, 2, and 6, respectively.     

A parallel and integrated system for structural dynamic response analysis

A new method, to parallel the dominating computing work of structural dynamic response analysis, is presented in this paper. Then, based on “ShenWei I” supercomputer, MSC.NASTRAN and PATRAN, a parallel and integrated system is implemented. The system tightly couples advantages of the FEA code and high performance of the supercomputer. The system can improve the structural scale and velocity of dynamic response analysis greatly. Finally two examples are presented to demonstrate the validity and efficiency of the system.     

并联机器人奇异性判定方法研究

奇异性是机器人设计中不可避免要考虑的问题。由于机器人奇异的定义的可操作性不是很强,在实际应用中难以处理。在上述定义的基础上给出了两种使用的并联机器人奇异判定方法,从数值计算的角度对原有的理论进行了新的阐述,并讨论了这些方法在并联机器人设计中的应用。     

Kinematic analysis and optimal design of 3-PPR planar parallel manipulator

This paper proposes a 3-PPR planar parallel manipulator, which consists of three active prismatic joints, three passive prismatic joints, and three passive rotational joints. The analysis of the kinematics and the optimal design of the manipulator are also discussed. The proposed manipulator has the advantages of the closed type of direct kinematics and a void-free workspace with a convex type of borderline. For the kinematic analysis of the proposed manipulator, the direct kinematics, the inverse kinematics, and the inverse Jacobian of the manipulator are derived. After the rotational limits and the workspaces of the manipulator are investigated, the workspace of the manipulator is simulated. In addition, for the optimal design of the manipulator, the performance indices of the manipulator are investigated, and then an optimal design procedure is carried out using Min-Max theory. Finally, one example using the optimal design is presented.     

基于并行计算的平面可调七杆机构动力学解析模型研究

基于运动学分析、凯恩动力学方程及数字-符号法,提出采用并行计算建立平面可调七杆机构动力学解析模型的方法,并研究了构件杆长及惯性参数变化对驱动力/力矩的影响.利用封闭矢量法对平面可调七杆机构进行运动学分析,得到各构件的速度和加速度表达式;将独立广义坐标、杆长及惯性参数作为符号量,其余参数处理为数值量,导出动力学解析模型的数字-符号表达式,并构造了解析模型的并行算法.由于动力学模型及实时代码优化是离线建立的,并且采用并行计算结构,减少了在线计算时间,从而为实时控制打下了基础.给出的仿真实例证明了此方法的有效性.     

基于并行计算的可调节型6-SPS并联机器人运动学和动力学分析

利用一种矩阵的广义标量积,导出6-SPS并联机器人动平台和驱动腿的速度及加速度显式表达式,并运用虚功原理和达朗伯原理建立了动力学模型。根据其计算特点,构造动力学并行算法,减少在线计算量和时间,为机构的实时控制提供有利条件。还对其作为可调节型机构,研究了平台半径和构件质量对驱动力的影响。给出的仿真实例证明此方法的有效性。     

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.     

3-RPS型并联机器人的运动学及动力学分析

并联机器人的运动学分析及动力分析是一个非常复杂的计算过程,自编程序的通用性和正确性需要大量的验证.ADAMS软件是一个大型的仿真软件.以ADAMS软件为基础,针对并联机器人建立了分析用模型,给出一种基于ADAMS的的运动学及动力学分析方法.这种方法不需大量的数学计算和计算机语言编程工作,非常快捷、方便、准确.从分析结果可以看出这种分析方法所得到的解完全可以用到实际中.     

整体弹性关节平面并联微动机器人ANSYS有限元分析

对整体弹性关节平面并联机器人建立刚性模型,采用闭环线型原理建立理论运动学线性模型(Jacobian矩阵),然后用ANSYS软件对其进行有限元分析,得到有限元运动学模型(Jacobian矩阵值),最后讨论两者关系,发现有限元模型比理论模型要精确.     

A new screw theory method for the estimation of position accuracy in spatial parallel manipulators with revolute joint clearances

This paper presents a novel method based on screw theory for the analysis of position accuracy in spatial parallel manipulators with revolute joint clearances. The method is general, and can tackle with an arbitrary pose error function, expressed as a quadratic function of the end-effector displacement.The method performs a maximization of the pose error function, based on a 2-step computational procedure. The first computational step is analytical and leads to a sub-optimal estimate of the maximum pose error. This analytical solution represents the exact maximum pose error for the calculus of the angular accuracy in the special case of fully translational parallel mechanisms. The second computational step is numerical, and starting from the previous solution, can converge to the exact maximum pose error in a limited number of iterations.The relevance of the method is demonstrated through some application examples, where the worst-case angular and linear position accuracy in translating fully parallel manipulators is determined. As a further contribution, this paper shows how the position accuracy due to joint clearances in parallel manipulators is strictly dependent of the mechanism pose and its association to kinematic isotropy.     

基于遗传算法的平面并联机构运动学设计

针对平面并联五杆机构提出了基于总体灵活度的运动学设计方法。该方法将运动学设计问题归结为全局运动性能指标最大为目标的单目标有约束优化设计问题，并采用遗传算法搜索到一个最优解，将其与采用随机方向法所得到的解进行比较，结果表明遗传算法具有明显的优点。     

Optimum selection of mechanism type for heavy manipulators based on particle swarm optimization method

The mechanism type plays a decisive role in the mechanical performance of robotic manipulators. Feasible mechanism types can be obtained by applying appropriate type synthesis theory, but there is still a lack of effective and efficient methods for the optimum selection among different types of mechanism candidates. This paper presents a new strategy for the purpose of optimum mechanism type selection based on the modified particle swarm optimization method. The concept of sub-swarm is introduced to represent the different mechanisms generated by the type synthesis, and a competitive mechanism is employed between the sub-swarms to reassign their population size according to the relative performances of the mechanism candidates to implement the optimization. Combining with a modular modeling approach for fast calculation of the performance index of the potential candidates, the proposed method is applied to determine the optimum mechanism type among the potential candidates for the desired manipulator. The effectiveness and efficiency of the proposed method is demonstrated through a case study on the optimum selection of mechanism type of a heavy manipulator where six feasible candidates are considered with force capability as the specific performance index. The optimization result shows that the fitness of the optimum mechanism type for the considered heavy manipulator can be up to 0.578 5. This research provides the instruction in optimum selection of mechanism types for robotic manipulators.     

基于并行计算的平面可调五杆机构动力学解析模型与仿真

基于凯恩动力学方程、数字-符号方法和并行计算建立了杆长和惯性参数可变平面可调五杆机构的动力学解析模型,并对驱动构件质量和杆长对驱动力/力矩的影响进行了仿真分析。将动力学模型的推导问题转化为特定条件下运用运动学和动力学计算公式求解机构驱动力矩的问题,并将广义坐标以及驱动构件杆长和惯性参数作为符号量,导出了模型矩阵元素数字-符号表达式。     

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.