Singularity analysis of a 3-RPS parallel manipulator using geometric algebra

Singular configurations must be avoided in path planning and control of a parallel manipulator. However, most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms. Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator. Twist and wrench in screw theory are represented in geometric algebra. Linear dependency of twists and wrenches are described by outer product in geometric algebra. Reciprocity between twists and constraint wrenches are reflected by duality. To compute the positions of the three spherical joints of the 3-RPS parallel manipulator, Tilt-and-Torsion angles are used to describe the orientation of the moving platform. The outer product of twists and constraint wrenches is used as an index for closeness to singularity(ICS) of the 3-RPS parallel manipulator. An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed, which is helpful to design, trajectory planning and control of this kind of parallel manipulator.     

一种用于无人驾驶汽车运动模拟的3自由度并联机构动力学建模

针对无人驾驶汽车半物理仿真试验对运动模拟系统精度要求高的特点,给出一种以3-RPS并联机构为基础的改进型3自由度并联机构.与3-RPS并联机构相比,由于该改进型并联机构中的被动约束承受了3-RPS并联机构中驱动器所承受的沿其转轴方向的力,因而改善了驱动器的力学特性.根据该并联机构的结构,建立运动学方程.基于Newton-Euler方法建立动平台的动力学方程.根据力矩平衡原理分别计算出同时垂直于驱动器及其转轴的分力以及同时垂直于被动约束上部及其转轴的分力.依照功率守恒原理计算出沿被动约束上部的力.驱动器的驱动力以及被动约束沿转轴的力即可求出.此计算方法对少自由度并联机构的动力学求解有借鉴意义.     

3(3-RPS)并-串联机构及其运动学分析研究

针对并联机构运动学和动力学性能方面存在的问题,提出了一种新结构-3(3-RPS)并-串联机构,对3(3-RPS)并-串联机构进行了运动学方面的研究,对3(3-RPS)并-串联机构的结构特点进行了介绍,利用螺旋理论及修正的Kutzbach–Grüble公式对3(3-RPS)并-串联机构进行了自由度计算,利用机构影响系数法和螺旋理论对3(3-RPS)并-串联机构的速度和加速度进行了建模,得到了3(3-RPS)并-串联机构速度和加速度的理论模型,利用工程分析软件ADAMS和Abaqus对3(3-RPS)并-串联机构进行了运动学仿真及结构受力分析,得到了上平台在空间中的速度和加速度曲线变化图与机构的结构受力变形图。研究结果表明:3(3-RPS)并-串联机构的自由度数为9,速度和加速度值等于各层之和;本研究分析3(3-RPS)并-串联机构运动学的方法也适合其他并-串联机构。     

求解3-RPS并联机构刚度的新方法

对于少自由度机构来说,由于结构约束的存在,机构中出现了约束反力,约束反力会在机构中产生变形,影响整个机构的精度,在机构分析中必须加以考虑。基于此,以传统的3-RPS并联机构为例,给出考虑约束反力产生变形的刚度模型的建立方法。首先,用观察法分析该机构中存在的约束反力。其次,建立该机构的6×6形式雅可比矩阵,并运用虚功原理建立该机构的静力学模型。最后,分析机构在驱动力和约束力共同作用下产生的弹性变形。在约束反力产生的变形方向上虚设P副,将3-RPS机构的变形和刚度分析转化为一个等效的无约束反力的6自由度并联机构3-RPPS的变形和刚度分析。这种方法给少自由度机构的研究提供了一些新观点。     

基于CAD变量几何法的并联机构静力学分析

以虚功原理为基础,利用CAD变量几何法,求解空间并联机构各分支的驱动力和约束力。以3-RPS并联机构为例,首先构造含有欧拉角的该机构的模拟机构,在此基础上进一步构造F/T(力/力矩)模拟机构,得到其驱动力和约束力解。当改变驱动参数时,F/T(力/力矩)模拟机构随之变化,驱动力和约束力自动求解和动态显示。结果表明,CAD变量几何法不仅快速直观,而且准确可靠。     

采用三点定位原理的反射镜支撑结构设计

在选择空间反射镜的支撑形式时,大口径反射镜一般采用柔性支撑结构加背板的支撑结构;小尺寸反射镜采用周边支撑的结构,但支撑结构质量都较大。为了降低反射镜支撑结构质量,通过对三点定位原理的自由度分析,设计了3个柔性铰链结构,通过柔性铰链的结构参数分析及有限元分析计算,设计出参数为R=1mm,t=2.5mm的三点柔性铰链,实现400mm口径反射镜的周边支撑,并使支撑反射镜的三个铰链直接与相机机身连接,省略了常规反射镜支撑的背板及边框,大大降低支撑结构质量;且该支撑结构具有较好的动态刚度和力、热环境适应能力。     

Fast forward kinematics algorithm for real-time and high-precision control of the 3-RPS parallel mechanism

A new forward kinematics algorithm for the mechanism of 3-RPS (R: Revolute; P: Prismatic; S: Spherical) parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10^–6. In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.     

METHOD USED IN SINGULARITY RESEARCH BASED ON KINEMATICS AND ITS EXAMPLE IN APPLICATION

First the kinematic principle of singularity is proved, that is the intersecting point of three normal planes of three velocities at three non-collinear points in a rigid body lying in the plane determined by the three corresponding points. It is a sufficient and necessary condition that the velocities of three non-collinear points in a rigid body can determine a screw motion of the body. Based on this principle, a simple and direct new method to distinguish the singularity of the parallel manipulator is derived. With this new kinematic method, the 3-RPS parallel manipulator is studied. Its singularity loci are obtained for some orientations for the fast time and verified with Grassmann line geometary and screw theory and the force Jacobian matrix.     

METH0D USED IN SINGULARITY RESEARCH BASED 0N KINEMATICS AND ITS EXAMPLE IN APPLICATION

First the kinematic principle of singularity is proved, that is the intersecting point of threenormal planes of three velocities at three non-collinear points in a rigid body lying in the plane determined by the three corresponding points. It is a sufficient and necessary condition that the velocities ofthree non-collinear points in a rigid body can determine a screw motion of the body Based on thisprinciple, a simple and direct new method to distinguish the singularity of the parallel manipulator islered. Wth this new kinematic method, the 3-RPS parallel manipulator is studied. Its singularity lociare obtained for some orietations for the first time and verified with Grassmann line geometry andscrew theory and the force Jacobian matrix.     

基于APDL的3-RPS并联机构参数化建模

在3-RPS并联机构位置反解模型的基础上,运用APDL语言完成该机构的整体三维建模设计,在ANSYS中实现了有限元建模和分析的参数化。将参数化设计引入到有限元分析中,实现结构参数快速调整,自动生成分析模型,增强了有限元分析的准确性。该方法对并联机构的研发有一定的指导意义。     

Kinematic calibration for a hybrid 5DOF manipulator based on 3-RPS in-actuated parallel manipulator

The measurement method is a decisive step for any calibration method. This paper studies the practical performance of a 5DOF manipulator based on a 3-RPS parallel mechanism. By comparing the controlling data that resides in parallel part and serial part at different orientations, a calibration method has been put forward and proved to be applicable. The precision of the calibrated model mainly depends on the number of measurements carried out. The distribution of measurement points also affects the precision and the measurement number could be significantly reduced if uniform distribution were ensured.     

气动人工肌肉并联机器人平台

提出一种基于气动人工肌肉的新型3自由度并联机器人平台,该机器人平台结构简单,具有3转动自由度。在对该新型3自由度并联机器人平台运动学和动力学特性理论分析的基础上,采用模糊变结构控制策略设计了新型3自由度并联机器人平台的两层滑模模糊变结构控制器,并建立了试验系统,开展了新型3自由度并联机器人平台的试验研究,其最大位置跟踪误差0．3 mm,当气源压力改变后,最大跟踪误差仍小于0．6 mm。试验结果表明,采用气动人工肌肉作为驱动装置设计的3自由度并联机器人平台是可行的,两层滑模模糊变结构控制策略对于该系统是适合的。     

Mathematical model for the study and design of a solar dish collector with cavity receiver for its application in Stirling engines

This paper presents a mathematical model that allows representing the optical behavior of a solar parabolic dish concentrator and the thermal performance of a cavity receiver. A procedure and a graphical method for the design of dish/cavity systems are proposed. A parametric study of the main geometric variables is performed and the influence of climate variables on the thermal behavior of the system coupled to a Stirling engine is analyzed. The model considers errors of solar collector, intercept factor, reflected and emitted radiation, conduction, and convection heat losses. For the validation of the model, the results obtained were compared with theoretical and experimental results reported in the literature. The calculation of the radiation losses, emitted and reflected from the receiver presented errors of up to 14%, and the average error for the rest of the thermal losses, interception factor and the absorber??s temperature, was less than 3%. These results show that the proposed model can be used with sufficient certainty to design and optimize solar dish collectors with cavity receivers.     

Reachable workspace determination for a spatial hyper-redundant manipulator formed by several parallel manipulators

Solving the reachable workspaces of spatial hyper-redundant manipulators (SHRMs) formed by serially connected parallel manipulators is an important and challenging work. This study addresses the issue on reachable workspaces and establishes a novel CAD-VBbased workspace determination system for determining the reachable workspaces of SHRMs. The reachable workspace determination of a novel (3-RPS)+(3-SPR)+(3-RPS) SHRM, a triple delta-type SHRM, and a novel (3-RRS)+(3-SPR)+(3-RRS) SHRM shows the generality and effectiveness of the proposed approach. The system proposed in this study can contribute to reachable workspace analysis for SHRMs.

     

Compound Impedance Control of a Hydraulic Driven Parallel 3UPS/S Manipulator

The hydraulic parallel manipulator combines the high-power density of the hydraulic system and high rigidity of the parallel mechanism with excellent load-carrying capacity. However, the high-precision trajectory tracking control of the hydraulic parallel manipulator is challenged by the coupling dynamics of the parallel mechanism and the high nonlinearities of the hydraulic system. In this study, the trajectory control of a 3-DOF symmetric spherical parallel 3 UPS/S manipulator is evaluated. Focusing on the highly coupling and nonlinear system dynamics, a compound impedance control method for a hydraulic driven parallel manipulator is proposed, which combines impedance control with the spatial motion characteristics of a parallel manipulator. The control strategy is divided into the inner and outer loops. The inner loop controls the impedance of the actuator in the joint space, and the outer loop controls the impedance of the entire platform in the task space to compensate the coupling of the actuators and improve the tracking accuracy of the moving platform. Compound impedance control does not require force or pressure sensors and is less dependent on modeling precision. The experimental results show that the compound impedance control e ectively improves the tracking accuracy of the moving platform. This research proposes a compound impedance control strategy for a 3-DOF hydraulic parallel manipulator, which has high tracking precision with a simple and cheap system configuration.     

气动肌肉并联关节的位姿轨迹跟踪控制

针对多输入多输出的气动肌肉并联关节,建立包含任务空间负载动态方程、容腔压力动态方程和高速开关阀平均流量方程的多阶动态系统数学模型。为保证气动肌肉并联关节系统良好动态特性的同时具有高精度的位姿轨迹跟踪,采用基于非连续投影算法的自适应鲁棒控制策略。该策略通过自适应参数估计来消除因气动肌肉并联关节系统动态数学模型的参数未知而引起的较大参数不确定,通过鲁棒反馈来消除因气动肌肉的伸缩力模型误差、摩擦力时变和关节系统的不可知干扰等引起的严重非线性不确定,且控制器基于反推设计,对多输入多输出的多阶耦合动态系统具有很好的适用性。试验结果表明：所研究的气动肌肉并联关节阶跃响应的静态误差小于0.09°,连续轨迹跟踪的标准误差小于0.15°,且具有较强的自适应性和鲁棒性。     

太阳能热发电技术进展及产业链分析

太阳能热发电主要包括槽式、塔式以及碟式发电。对太阳能热发电产业链进行了分析,针对三种类型电站的各个组件,包括吸收器、反射面、蓄热装置、支撑结构以及跟踪控制系统进行介绍,并介绍了这些部件的研究、应用现状以及设备生产厂商的情况。     

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。     

一种打磨机械臂的静刚度建模与实验

设计出一种采用(U+UPS)P+UPS并联机构的打磨3-DOF机械臂。运用子结构拆分和叠加思想,将机械臂手腕的位姿变形因素拆分为只考虑各支链拉/压变形、只考虑UP支链扭转变形、只考虑UP支链弯曲变形3个主要影响因素。通过基于矢量回路的虚功原理和结构矩阵建立3个主要影响因素的刚度模型,并根据各支链的结构特点定义了支链内各部件变形系数。通过叠加原理将各影响因素的刚度模型叠加整合为机械臂的整体刚度模型。研制出机械臂的实验样机本体,采用一套高精度机器人刚度实验系统对机械臂实验样机进行了刚度标定。实验结果表明：机械臂实验样机的位置变形实测值与理论值之间偏差均小于3μm,姿态变形实测值与理论值之间偏差均小于0.05°,机械臂实验样机的变形均在合理范围之内。     

DESIGN FEATURES OF A PARALLEL TESTING PLATFORM FOR SIMULATING KINEMATIC CHARACTERISTICS OF HIP JOINT

To simulate the movement of a human during daily activities, such as walking, running, squatting, and kneeling, a novel parallel hip joint simulator whose key movement component is a 3SPS + 1PS parallel manipulator with four degrees of freedom (DOF) was proposed. SPS denotes the spherical-prismatic-spherical leg, and PS denotes the prismatic-spherical leg where only the prismatic joint is actuated and hence underlined. Firstly, the formulae for solving the inverse kinematics of the 3SPS + 1PS parallel manipulator were derived based on the unit quaternion method. Then, the parallel hip joint simulator was designed and finally developed by means of constructing the mechanical module, control module, hydraulic loading module, and data transmission module. In addition, three linear actuators are driven by the scheduled inverse displacement trajectories to enable the moving platform to output rotations about the Z-, Y-, and X-axes for representing flexion/extension, abduction/adduction, and external/internal rotations of the human hip joint. Simultaneously, the hydraulic loading module represents the dynamic loading as described by ISO 14242 Part-1 acting on the hip joint during the kinematic experiment. The kinematic experiment and dynamic loading experiment show that the fitting curves of the experimental results are consistent with the designed movement and loading trajectories. All these illustrate that the developed 3SPS + 1PS parallel hip joint simulator with effective design of all modules can substantially represent the designed movement and loading trajectories. The developed hip joint simulator can provide more reliable tribology test data for artificial prosthesis of hip joint.