一种直线电机驱动的六棱锥式并联机器人研究
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摘要
并联机器人因其具有承载能力强、积累误差小、动态响应快等优点,逐渐成为目前国内外研究的热点之一。本文提出一种由直线电机驱动,导轨呈六棱锥式倾斜布置的新型并联机器人结构,运用仿真分析与实验验证相结合的方法对并联机器人机构学、运动学和动力学等关键理论进行了深入研究,旨在深化并联机器人相关理论和扩大工程化应用范围。本文主要展开了以下几个方面的理论和实验研究：
(1)提出了一种直线电机驱动的六棱锥式并联机器人总体方案。从驱动方式、铰链组成和导轨布置三方面对比分析了Stewart和Hexaglide两种典型结构并联机器人的特点。以机构的最大转角和最高运动频率为基本性能指标,确定了由课题组自行研制的直线电机驱动、导轨呈六棱锥式倾斜布置的并联机器人结构,通过分析认为其具有速度精度高、运动惯量小和转动角度大等特点。
(2)建立了六棱锥式并联机器人运动学和动力学通用模型。采用几何法和求导法根据运动连杆长度不变的几何约束条件建立了负载平台位姿与直线电机动子位移、速度和加速度之间的映射关系,并获得了机构的雅克比矩阵;提出质点系法结合拉格朗日法,将运动连杆视为质点系计算其动能,保证运算速度的同时提高了模型的精度,获得了负载平台位姿与直线电机驱动力的映射关系。所建立的数学模型为后续更深入的理论研究和工程应用奠定理论基础。
(3)确定了六棱锥式并联机器人的主要结构参数。以结构紧凑、无奇异和无机械干涉为原则,讨论运动连杆长度、负载平台半径和导轨倾斜角度变化对机构平动和转动性能的影响；分析了机构运动频率与驱动力、导轨倾斜角度与能耗的关系。完成了机构零部件和基于dSPACE硬／软件的工程设计,成功研制出样机及其控制系统,并进行了运动学和动力学的验证实验,实验结果表明所建立的数学模型是正确的、可行的。
(4)对六棱锥式并联机器人奇异性和工作空间这一关键理论进行了深入研究。基于雅克比矩阵行列式讨论六棱锥式并联机器人发生奇异的条件,并引入可操作度表征任务轨迹远离奇异位形的程度。分析了机构工作空间的约束条件,采用圆柱坐标搜索法获得了定姿态工作空间和定位置转动工作空间,为轨迹规划提供理论依据。进行了样机的性能测试实验,实验结果表明样机性能与仿真结果吻合并且能够满足总体方案的性能指标要求。
(5)对六棱锥式并联机器人冗余任务下驱动力优化这一关键理论进行了深入研究。以瞬时动能最小为优化目标,分别采用极值法和遗传算法对单自由度和三自由度冗余驱动力分配进行优化和验证实验。研究结果表明,与冗余自由度上变化规律为零的情况对比,优化后的机构能耗有大幅度降低,说明优化方法是正确的、可行的。
(6)为将基础研究向工程化应用发展,对六棱锥式并联机器人在车辆工程领域应用方案的可行性进行了探讨。通过对样机特点和不同应用场合的需求分析,提出机构作为车载零部件振动试验台的应用方案设想。采用谐波叠加法通过Matlab编程获得了国家级公路的路谱,并建立了简化的车辆模型,获得了车载零部件六个自由度上的振动情况。进行了振动实验,实验结果表明六棱锥式并联机器人能够较好再现车载零部件振动情况。
Parallel robot has strong bearing capacity, small accumulated error, fast dynamic response and other advantages, so it gradually becomes one of the research focus. This dissertation presents a novel parallel robot driven by linear actuator which rail was tilted as a six pyramid. Combined the method of simulation analysis and experimental verification, mechanism、kinematics and dynamics theory of parallel robot has conducted in-depth research to deepen the parallel robot theory and expand engineering application. This dissertation mainly includes the following several aspects of the theory and experiment research:
(1) The general structure scheme of the six pyramid parallel robot driven by linear actuator is presented. The structural characteristics of typical Stewart and Hexaglide are analyzed from drive source, hinge and rail structure. Set the maximum angle and maximum frequency as basic performance index, determined the overall program consist of linear actuator and six pyramid rail, through the analysis it has the advantages of high speed and precision, small moment of inertia and large rotation angle.
(2) The kinematics and dynamics model of six pyramid parallel robot are established. According to the geometric constraints that the length of the connecting rod is invariant, the displacement, velocity and acceleration mapping relationship between load platform and linear actuator are established using geometric method and derivation method, and obtained the Jacobian matrix of the robot. Particle system combined with Lagrange method to establish force relationship between load platform and linear actuator is proposed. The kinetic energy is calculated regarding the connecting rod as a particle system, which can guaranteeing the computing speed and improves the precision of the model. The mathematical model is the base of follow-up to more in-depth theoretical study and engineering application of the robot theory.
(3) Main structure parameters are determined. With compact structure, no singular and mechanical interference principle, the effects of parameter such as connecting rod length, load platform radius and angle of tilt rail change on translation and rotation performance are discussed, the relationship between frequency and force, angle of tilt rail and consumption are analyzed. Completion the engineering design of the robot and selection and configuration of hardware/software based on dSPACE are done successfully developed a prototype and control system, then the kinematics and dynamics of example verification experiment are done to show that the model is correct, feasible.
(4) Singularity and workspace of the six pyramid parallel robot has conducted in-depth research. Based on Jacobian matrix, singular condition of the six pyramid parallel robot is discussed, and introduce the operational characterization to show the degree of path away from the singularity; workspace constraints are analyzed, and three axis motion range and rotate range are obtained using the cylindrical coordinate search method, provide a theoretical basis for track planning. Experiment for the performance of prototype show that the performance of prototype and simulation results and can meet the design requirements of performance index.
(5) Optimization of driving forces under redundancy task of the six pyramid parallel robot has conducted in-depth research. Set instantaneous kinetic energy as the optimization target, optimization and validation experiment of single degree of freedom and3DOF redundant driving force distribution are done respectively using the extreme value method and genetic algorithm. The results show that, contrast with zero trajectory case on the redundant degree of freedom, optimized mechanism energy consumption is greatly reduced; the optimization method is correct and feasible.
(6) Applications of six pyramid parallel robot in the field of vehicle engineering were studied. Based on the prototype characteristics and the requirements of different application occasions, the application scheme of vehicle parts of the vibration test is presented. National A-class road spectrum is obtained using harmonic superposition method by programming with Matlab, and the vibration of vehicle parts on six degree of freedom are obtained by a simplified model. Vibration experiments done to show that the six pyramid type parallel robot can reproduce the vibration of vehicle parts.
(1)提出了一种直线电机驱动的六棱锥式并联机器人总体方案。从驱动方式、铰链组成和导轨布置三方面对比分析了Stewart和Hexaglide两种典型结构并联机器人的特点。以机构的最大转角和最高运动频率为基本性能指标,确定了由课题组自行研制的直线电机驱动、导轨呈六棱锥式倾斜布置的并联机器人结构,通过分析认为其具有速度精度高、运动惯量小和转动角度大等特点。
(2)建立了六棱锥式并联机器人运动学和动力学通用模型。采用几何法和求导法根据运动连杆长度不变的几何约束条件建立了负载平台位姿与直线电机动子位移、速度和加速度之间的映射关系,并获得了机构的雅克比矩阵;提出质点系法结合拉格朗日法,将运动连杆视为质点系计算其动能,保证运算速度的同时提高了模型的精度,获得了负载平台位姿与直线电机驱动力的映射关系。所建立的数学模型为后续更深入的理论研究和工程应用奠定理论基础。
(3)确定了六棱锥式并联机器人的主要结构参数。以结构紧凑、无奇异和无机械干涉为原则,讨论运动连杆长度、负载平台半径和导轨倾斜角度变化对机构平动和转动性能的影响；分析了机构运动频率与驱动力、导轨倾斜角度与能耗的关系。完成了机构零部件和基于dSPACE硬／软件的工程设计,成功研制出样机及其控制系统,并进行了运动学和动力学的验证实验,实验结果表明所建立的数学模型是正确的、可行的。
(4)对六棱锥式并联机器人奇异性和工作空间这一关键理论进行了深入研究。基于雅克比矩阵行列式讨论六棱锥式并联机器人发生奇异的条件,并引入可操作度表征任务轨迹远离奇异位形的程度。分析了机构工作空间的约束条件,采用圆柱坐标搜索法获得了定姿态工作空间和定位置转动工作空间,为轨迹规划提供理论依据。进行了样机的性能测试实验,实验结果表明样机性能与仿真结果吻合并且能够满足总体方案的性能指标要求。
(5)对六棱锥式并联机器人冗余任务下驱动力优化这一关键理论进行了深入研究。以瞬时动能最小为优化目标,分别采用极值法和遗传算法对单自由度和三自由度冗余驱动力分配进行优化和验证实验。研究结果表明,与冗余自由度上变化规律为零的情况对比,优化后的机构能耗有大幅度降低,说明优化方法是正确的、可行的。
(6)为将基础研究向工程化应用发展,对六棱锥式并联机器人在车辆工程领域应用方案的可行性进行了探讨。通过对样机特点和不同应用场合的需求分析,提出机构作为车载零部件振动试验台的应用方案设想。采用谐波叠加法通过Matlab编程获得了国家级公路的路谱,并建立了简化的车辆模型,获得了车载零部件六个自由度上的振动情况。进行了振动实验,实验结果表明六棱锥式并联机器人能够较好再现车载零部件振动情况。
Parallel robot has strong bearing capacity, small accumulated error, fast dynamic response and other advantages, so it gradually becomes one of the research focus. This dissertation presents a novel parallel robot driven by linear actuator which rail was tilted as a six pyramid. Combined the method of simulation analysis and experimental verification, mechanism、kinematics and dynamics theory of parallel robot has conducted in-depth research to deepen the parallel robot theory and expand engineering application. This dissertation mainly includes the following several aspects of the theory and experiment research:
(1) The general structure scheme of the six pyramid parallel robot driven by linear actuator is presented. The structural characteristics of typical Stewart and Hexaglide are analyzed from drive source, hinge and rail structure. Set the maximum angle and maximum frequency as basic performance index, determined the overall program consist of linear actuator and six pyramid rail, through the analysis it has the advantages of high speed and precision, small moment of inertia and large rotation angle.
(2) The kinematics and dynamics model of six pyramid parallel robot are established. According to the geometric constraints that the length of the connecting rod is invariant, the displacement, velocity and acceleration mapping relationship between load platform and linear actuator are established using geometric method and derivation method, and obtained the Jacobian matrix of the robot. Particle system combined with Lagrange method to establish force relationship between load platform and linear actuator is proposed. The kinetic energy is calculated regarding the connecting rod as a particle system, which can guaranteeing the computing speed and improves the precision of the model. The mathematical model is the base of follow-up to more in-depth theoretical study and engineering application of the robot theory.
(3) Main structure parameters are determined. With compact structure, no singular and mechanical interference principle, the effects of parameter such as connecting rod length, load platform radius and angle of tilt rail change on translation and rotation performance are discussed, the relationship between frequency and force, angle of tilt rail and consumption are analyzed. Completion the engineering design of the robot and selection and configuration of hardware/software based on dSPACE are done successfully developed a prototype and control system, then the kinematics and dynamics of example verification experiment are done to show that the model is correct, feasible.
(4) Singularity and workspace of the six pyramid parallel robot has conducted in-depth research. Based on Jacobian matrix, singular condition of the six pyramid parallel robot is discussed, and introduce the operational characterization to show the degree of path away from the singularity; workspace constraints are analyzed, and three axis motion range and rotate range are obtained using the cylindrical coordinate search method, provide a theoretical basis for track planning. Experiment for the performance of prototype show that the performance of prototype and simulation results and can meet the design requirements of performance index.
(5) Optimization of driving forces under redundancy task of the six pyramid parallel robot has conducted in-depth research. Set instantaneous kinetic energy as the optimization target, optimization and validation experiment of single degree of freedom and3DOF redundant driving force distribution are done respectively using the extreme value method and genetic algorithm. The results show that, contrast with zero trajectory case on the redundant degree of freedom, optimized mechanism energy consumption is greatly reduced; the optimization method is correct and feasible.
(6) Applications of six pyramid parallel robot in the field of vehicle engineering were studied. Based on the prototype characteristics and the requirements of different application occasions, the application scheme of vehicle parts of the vibration test is presented. National A-class road spectrum is obtained using harmonic superposition method by programming with Matlab, and the vibration of vehicle parts on six degree of freedom are obtained by a simplified model. Vibration experiments done to show that the six pyramid type parallel robot can reproduce the vibration of vehicle parts.
引文
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