三自由度空间柔性并联机器人动力学研究
摘要
柔性机器人、并联机器人是机器人领域中的两个前沿课题。由于柔性串联机器人满足了现代工业在轻质、高精度和高加速度运动等方面的要求,近三十多年来得到了快速发展。并联机器人具有运动惯量小、刚度大、运动精度高等优点,与串联机器人在结构和性能方面形成互补关系,从而扩大了机器人的应用范围。随着对机器人在高精度、高效率等方面要求的不断提高,同时具有柔性机器人和并联机器人两方面特点的柔性并联机器人将成为机器人领域的一个新方向。因此,进行这方面的研究具有重要的理论意义和实用价值。
本文将并联机器人与柔性机器人有机地结合起来,以具有柔性构件的三自由度空间并联机器人为分析对象,全面研究诸如动力学建模与分析、虚拟样机仿真、动态特性和优化设计、运动规划和动力规划等空间柔性并联机器人动力学分析和综合方面的问题。
首先,进行了具有柔性构件的空间并联机器人的动力学建模和求解。建立了一种空间柔性梁单元模型,推导了柔性梁单元的动力学方程和并联机器人支链的动力学方程。利用系统运动学约束和动力学约束,装配支链的动力学方程得到柔性并联机器人的系统动力学方程。讨论了柔性并联机器人动力学方程的求解,并通过数值算例分析了动平台的动力学响应。
其次,进行了柔性并联机器人的虚拟样机仿真。以SAMCEF软件为平台,分别建立了3-RRS、3-RSR和3-RRC柔性并联机器人的虚拟样机。分析了这些柔性并联机器人的位移误差、速度、加速度和动应力等的变化情况。通过数值计算结果和SAMCEF软件仿真结果的对比,验证了本文所建动力学模型的有效性和正确性。
再次,开展了柔性并联机器人的动态特性分析和机构优化设计的研究。分析了柔性并联机构系统的固有频率与设计参数的关系。由此,提出了基于系统固有频率的机构优化设计模型,以运动误差、动应力等为约束条件,进行了构件参数的结构优化设计。
最后,分别进行了柔性并联机器人系统的输入运动规划和动力规划。通过柔性并联机器人的初始位形选择和输入运动规划,达到了降低系统运动误差的目的;通过柔性并联机器人系统的动力规划,降低了系统驱动力矩的波动。
The study of flexible robots and parallel manipulators are two important components and advanced topics of robotics. Over the past three decades, the flexible serial robot has developed rapidly due to its light weight, high accuracy and high-acceleration motion, which met the requirements of the development of modern industry. The parallel manipulators provide a new way to improve the performance of robots in terms of lower inertia, higher stiffness and accuracy. Due to the complement to the serial robots in structure and performance, as a result, the application of robot is extended. With the increasing requirements of high precision and high efficiency, the flexible parallel manipulator characterized by both the flexible robot and the parallel manipulator will be a new hot topic in robotics research. Therefore, the research on the flexible parallel manipulator is of great theoretical significance and practical value.
In this dissertation, the parallel manipulators and the flexible robots were combined, and the 3-DOF (Degree Of Freedom) spatial parallel manipulators with flexible links were investigated. The dynamic analysis and synthesis of the flexible parallel manipulators, such as dynamic modeling and analysis, virtual prototype simulation, dynamic characteristic and optimal design, and kinematic/dynamic planning etc, were studied and discussed in a comprehensive manner.
Firstly, the dynamic modeling and solution of the spatial parallel manipulators with flexible links were studied. A model of spatial flexible beam element was proposed, and the dynamic equations of elements and branches of the parallel manipulator were derived. Using the kinematic and dynamic constraint equations of the parallel manipulator, the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches. The dynamic responses of the moving platform were analyzed through numerical simulation.
Secondly, the virtual prototype simulation of spatial flexible parallel manipulator was derived. The virtual prototypes of 3-RRS, 3-RSR and 3-RRC flexible parallel manipulator were established on the basis of the SAMCEF software, respectively. The displacement error, velocity, acceleration and dynamic stress of these flexible parallel manipulators were analyzed. The comparison results of the numerical simulation and SAMCEF software showed that the effectiveness and correctness of the dynamic models proposed in this dissertation.
Thirdly, the dynamic characteristics of the flexible parallel manipulator and design optimization of the parallel mechanism were furtherly investigated. The relationship of the natural frequency and design parameters of the parallel mechanism were studied. Then, the optimal design model of the flexible parallel manipulator based on natural frequency of the system was derived. The motion errors and dynamic stresses are regarded as constraints, and the optimal design of the links parameters was carried out to obtain the parallel mechanism with optimal comprehensive performance.
Finally, the input motion programming and dynamic planning of the flexible parallel manipulators were discussed, respectively. The input motion programming and initial configuration selection were applied to decrease the motion error of the moving platform. The dynamic planning was applied to decrease the fluctuation of driving torques.
本文将并联机器人与柔性机器人有机地结合起来,以具有柔性构件的三自由度空间并联机器人为分析对象,全面研究诸如动力学建模与分析、虚拟样机仿真、动态特性和优化设计、运动规划和动力规划等空间柔性并联机器人动力学分析和综合方面的问题。
首先,进行了具有柔性构件的空间并联机器人的动力学建模和求解。建立了一种空间柔性梁单元模型,推导了柔性梁单元的动力学方程和并联机器人支链的动力学方程。利用系统运动学约束和动力学约束,装配支链的动力学方程得到柔性并联机器人的系统动力学方程。讨论了柔性并联机器人动力学方程的求解,并通过数值算例分析了动平台的动力学响应。
其次,进行了柔性并联机器人的虚拟样机仿真。以SAMCEF软件为平台,分别建立了3-RRS、3-RSR和3-RRC柔性并联机器人的虚拟样机。分析了这些柔性并联机器人的位移误差、速度、加速度和动应力等的变化情况。通过数值计算结果和SAMCEF软件仿真结果的对比,验证了本文所建动力学模型的有效性和正确性。
再次,开展了柔性并联机器人的动态特性分析和机构优化设计的研究。分析了柔性并联机构系统的固有频率与设计参数的关系。由此,提出了基于系统固有频率的机构优化设计模型,以运动误差、动应力等为约束条件,进行了构件参数的结构优化设计。
最后,分别进行了柔性并联机器人系统的输入运动规划和动力规划。通过柔性并联机器人的初始位形选择和输入运动规划,达到了降低系统运动误差的目的;通过柔性并联机器人系统的动力规划,降低了系统驱动力矩的波动。
The study of flexible robots and parallel manipulators are two important components and advanced topics of robotics. Over the past three decades, the flexible serial robot has developed rapidly due to its light weight, high accuracy and high-acceleration motion, which met the requirements of the development of modern industry. The parallel manipulators provide a new way to improve the performance of robots in terms of lower inertia, higher stiffness and accuracy. Due to the complement to the serial robots in structure and performance, as a result, the application of robot is extended. With the increasing requirements of high precision and high efficiency, the flexible parallel manipulator characterized by both the flexible robot and the parallel manipulator will be a new hot topic in robotics research. Therefore, the research on the flexible parallel manipulator is of great theoretical significance and practical value.
In this dissertation, the parallel manipulators and the flexible robots were combined, and the 3-DOF (Degree Of Freedom) spatial parallel manipulators with flexible links were investigated. The dynamic analysis and synthesis of the flexible parallel manipulators, such as dynamic modeling and analysis, virtual prototype simulation, dynamic characteristic and optimal design, and kinematic/dynamic planning etc, were studied and discussed in a comprehensive manner.
Firstly, the dynamic modeling and solution of the spatial parallel manipulators with flexible links were studied. A model of spatial flexible beam element was proposed, and the dynamic equations of elements and branches of the parallel manipulator were derived. Using the kinematic and dynamic constraint equations of the parallel manipulator, the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches. The dynamic responses of the moving platform were analyzed through numerical simulation.
Secondly, the virtual prototype simulation of spatial flexible parallel manipulator was derived. The virtual prototypes of 3-RRS, 3-RSR and 3-RRC flexible parallel manipulator were established on the basis of the SAMCEF software, respectively. The displacement error, velocity, acceleration and dynamic stress of these flexible parallel manipulators were analyzed. The comparison results of the numerical simulation and SAMCEF software showed that the effectiveness and correctness of the dynamic models proposed in this dissertation.
Thirdly, the dynamic characteristics of the flexible parallel manipulator and design optimization of the parallel mechanism were furtherly investigated. The relationship of the natural frequency and design parameters of the parallel mechanism were studied. Then, the optimal design model of the flexible parallel manipulator based on natural frequency of the system was derived. The motion errors and dynamic stresses are regarded as constraints, and the optimal design of the links parameters was carried out to obtain the parallel mechanism with optimal comprehensive performance.
Finally, the input motion programming and dynamic planning of the flexible parallel manipulators were discussed, respectively. The input motion programming and initial configuration selection were applied to decrease the motion error of the moving platform. The dynamic planning was applied to decrease the fluctuation of driving torques.
引文
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