空间柔性机械臂的动力学建模和分析
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哈尔滨工业大学工学硕士学位论文
摘 要
随着航天技术和机器人技术的迅速发展，柔性机械臂由于其质量轻、速度 快、耗能低等优点，在航空航天领域中获得了广泛的应用。但是机械臂在运行 过程中，关节柔性和柔性臂杆弹性变形的耦合，给机器人柔性臂的振动控制带 来了困难。建立准确、实用的动力学模型对于柔性机械臂的轨迹跟踪和主动振 动控制的研究具有重要意义。为此，本文针对全柔性机器人的动力学问题展开 了研究，主要内容如下： 1、简要的介绍了多柔体系统的运动学和动力学模型的建模方法。分别以假 设模态法与 Lagrange 方程相结合和全局模态法与 Hamilton 原理相结合建立柔性 机械臂动力学方程。 2、以典型柔性关节 /柔性臂杆系统为研究对象，分析整个柔性机械单臂系 统的复杂边界条件，建立柔性机械单臂系统的动力学模型，提出了柔性机械单 臂全局模态的概念。首先，基于 Hamilton 原理导出单臂机器人的柔性臂杆和柔 性关节的耦合运动微分方程。利用系统的边界条件和连接部件的匹配条件，导 出了求解系统固有特性的特征方程，据此可以用数值方法求出系统的固有频率 和全局模态。在求解全局模态的基础上，进一步证明了全局模态的正交性，采 用 Galerkin 截断对系统进行离散，得到用常微分方程描述的柔性机械臂的动力 学方程。将所得结果与采用假设模态法给出的频率和模态进行对比，据此说明 这里提出的全局模态概念准确地反映了系统的固有特性，其求解方法借用了传 统的模态求解方法的思路，但其适用范围更广。最后对所建立的柔性单臂模型 进行了响应时程仿真，分析关节的变形和臂杆末端的弹性振动位移。 3、采用全局模态法与 Hamilton 原理相结合的方法对具有柔性关节的双连 杆柔性机械臂进行动力学建模。首先，分析整个柔性机械臂系统的复杂边界条 件，基于 Hamilton 原理导出双臂机器人的柔性臂杆和柔性关节的耦合运动微分 方程。利用系统的边界条件和连接部件的匹配条件，导出含有参数（肩部关节 的角度变化）的系统特征方程，同时也可以容易地求出系统的固有频率和表征 机械臂运动的刚体运动、 柔性关节振动以及柔性臂杆弹性振动在内的全局模态。 通过求解系统的特征方程，研究系统构型的变化对柔性机械臂系统的固有频率 的影响，据此可以预测系统固有频率的变化趋势和变化范围。 关键词 ：柔性机械臂；柔性关节；固有频率；全局模态；
-I-
哈尔滨工业大学工学硕士学位论文
Abstract
With the rapid development of space technology and robot technology, the flexible manipulator are widely used in the field of aerospace,due to its light quality, high speed, and low energy consumption.However, it is difficulty to control the vibration of flexible manipulator owing to the joint flexiblity and flexible -link elastic deformation coupling.It is great significance that establish accurate and practical dynamic model for the trajectory tracking and active vibration control of flexible manipulator. To solve thisproblem,in this paper , the dynamic problems of flexible manipulator is atudied, the main content is as follows: 1、 The kinematics and dynamics modeling of flexible multibody chain system is briefly introduced. By assumption modal method combined with though Lagrange equations and global modal method combined with Hamilton principle, dynamics equation of flexible manipulator are establish. 2 、 Based on the analysis of the flexible manipulator that consists of flexible-link and flexible-joint, the global mode shapes of the flexible manipulator is presented. The coupling movement differential equation of flexible-link and flexible-joint are derived by using the Hamilton principle. Through their force boundary and matching conditions, the undamped natural frequencies and mode shapes of the linearized model of the flexible manipulator are determined, and orthogonality relations of the mode shapes are established. The undamped global mode shapes are used to discretize the coupling movement differential equation of flexible-link and flexible-joint. The simulation results show that the joint flexibility and the elastic deformation of flexible-link can have a significant effect on the system frequencies. A comparison between the results obtained by the proposed method and those from assume mode method is given to illustrate the validity of our approach. According to the global modal,it can reflect the inherent characteristics of the system.And its solving method is more used,which borrowed from the traditional mode. Finally,response history simulation is taken to study,and the deformation of joints and the end of link elastic vibration displacement is analyzed. 3、Dynamic model of two-link flexible manipulator with flexible joints is established by using global modal method combined with Hamilton principle. First of all, the complex boundary conditions are analyzed. The partial differential equations of motion for a two-link flexible manipulator are derived, along with their boundary conditions by using the Hamilton principle. Combining the governing equations of flexible link and flexible joint, the undamped natural frequencies a nd mode shapes of the linearized model of the two-link flexible manipulator are
- II -
哈尔滨工业大学工学硕士学位论文
determined. Through the frequency equation presented in this article, a study on the variation of natural frequencies with the time-varying elbow angles is performed using a two-link flexible manipulator with a set of typical geometrical parameters and material constants. Thus we can predict the tendency and range of the system natural frequency. Keywords: flexible manipulator, flexible-joint, natural frequencies , global mode shapes
Dissertation for the Master Degree in Engineering
DYNAMIC MODELING AND ANALYSIS OF SPACE FLEXIBLE MANIPULATOR
Candidate： Supervisor： Academic Degree Applied for ： Speciality： Affiliation： Date of Defence ：
Wei Jin Senior Engineer. Liang Tingwei Master of Engineering General and Fundamental Mechanics School of Astronautics July, 2013
Degree-Conferring-Institution： Harbin Institute of Technology
硕士学位论文
空间柔性机械臂的动力学建模和分析
DYNAMIC MODELING AND ANALYSIS OF SPACE FLEXIBLE MANIPULATOR
魏进
哈尔滨工业大学 2013 年 7 月
国内图书分类号： O326，V11 国际图书分类号： 531.3, 534.1
学校代码： 10213 密级：公开
- III -
哈尔滨工业大学工学硕士学位论文
目
摘
录
要 ..........................................................................................................................I 论 ........................................................................................................... 1
工学硕士学位论文
空间柔性机械臂的动力学建模和分析
硕 士 研 究 生： 魏 导
进
师： 梁廷伟 高工
申 请 学 位 ： 工学硕士 学 科： 一般力学与力学基础
所 在 单 位： 航天学院 答 辩 日 期： 2013 年 7 月 授予学位单位 ： 哈尔滨工业大学
Classified Index: O326，V11 U.D.C: 531.3, 534.1
哈尔滨工业大学工学硕士学位论文
摘 要
随着航天技术和机器人技术的迅速发展，柔性机械臂由于其质量轻、速度 快、耗能低等优点，在航空航天领域中获得了广泛的应用。但是机械臂在运行 过程中，关节柔性和柔性臂杆弹性变形的耦合，给机器人柔性臂的振动控制带 来了困难。建立准确、实用的动力学模型对于柔性机械臂的轨迹跟踪和主动振 动控制的研究具有重要意义。为此，本文针对全柔性机器人的动力学问题展开 了研究，主要内容如下： 1、简要的介绍了多柔体系统的运动学和动力学模型的建模方法。分别以假 设模态法与 Lagrange 方程相结合和全局模态法与 Hamilton 原理相结合建立柔性 机械臂动力学方程。 2、以典型柔性关节 /柔性臂杆系统为研究对象，分析整个柔性机械单臂系 统的复杂边界条件，建立柔性机械单臂系统的动力学模型，提出了柔性机械单 臂全局模态的概念。首先，基于 Hamilton 原理导出单臂机器人的柔性臂杆和柔 性关节的耦合运动微分方程。利用系统的边界条件和连接部件的匹配条件，导 出了求解系统固有特性的特征方程，据此可以用数值方法求出系统的固有频率 和全局模态。在求解全局模态的基础上，进一步证明了全局模态的正交性，采 用 Galerkin 截断对系统进行离散，得到用常微分方程描述的柔性机械臂的动力 学方程。将所得结果与采用假设模态法给出的频率和模态进行对比，据此说明 这里提出的全局模态概念准确地反映了系统的固有特性，其求解方法借用了传 统的模态求解方法的思路，但其适用范围更广。最后对所建立的柔性单臂模型 进行了响应时程仿真，分析关节的变形和臂杆末端的弹性振动位移。 3、采用全局模态法与 Hamilton 原理相结合的方法对具有柔性关节的双连 杆柔性机械臂进行动力学建模。首先，分析整个柔性机械臂系统的复杂边界条 件，基于 Hamilton 原理导出双臂机器人的柔性臂杆和柔性关节的耦合运动微分 方程。利用系统的边界条件和连接部件的匹配条件，导出含有参数（肩部关节 的角度变化）的系统特征方程，同时也可以容易地求出系统的固有频率和表征 机械臂运动的刚体运动、 柔性关节振动以及柔性臂杆弹性振动在内的全局模态。 通过求解系统的特征方程，研究系统构型的变化对柔性机械臂系统的固有频率 的影响，据此可以预测系统固有频率的变化趋势和变化范围。 关键词 ：柔性机械臂；柔性关节；固有频率；全局模态；
-I-
哈尔滨工业大学工学硕士学位论文
Abstract
With the rapid development of space technology and robot technology, the flexible manipulator are widely used in the field of aerospace,due to its light quality, high speed, and low energy consumption.However, it is difficulty to control the vibration of flexible manipulator owing to the joint flexiblity and flexible -link elastic deformation coupling.It is great significance that establish accurate and practical dynamic model for the trajectory tracking and active vibration control of flexible manipulator. To solve thisproblem,in this paper , the dynamic problems of flexible manipulator is atudied, the main content is as follows: 1、 The kinematics and dynamics modeling of flexible multibody chain system is briefly introduced. By assumption modal method combined with though Lagrange equations and global modal method combined with Hamilton principle, dynamics equation of flexible manipulator are establish. 2 、 Based on the analysis of the flexible manipulator that consists of flexible-link and flexible-joint, the global mode shapes of the flexible manipulator is presented. The coupling movement differential equation of flexible-link and flexible-joint are derived by using the Hamilton principle. Through their force boundary and matching conditions, the undamped natural frequencies and mode shapes of the linearized model of the flexible manipulator are determined, and orthogonality relations of the mode shapes are established. The undamped global mode shapes are used to discretize the coupling movement differential equation of flexible-link and flexible-joint. The simulation results show that the joint flexibility and the elastic deformation of flexible-link can have a significant effect on the system frequencies. A comparison between the results obtained by the proposed method and those from assume mode method is given to illustrate the validity of our approach. According to the global modal,it can reflect the inherent characteristics of the system.And its solving method is more used,which borrowed from the traditional mode. Finally,response history simulation is taken to study,and the deformation of joints and the end of link elastic vibration displacement is analyzed. 3、Dynamic model of two-link flexible manipulator with flexible joints is established by using global modal method combined with Hamilton principle. First of all, the complex boundary conditions are analyzed. The partial differential equations of motion for a two-link flexible manipulator are derived, along with their boundary conditions by using the Hamilton principle. Combining the governing equations of flexible link and flexible joint, the undamped natural frequencies a nd mode shapes of the linearized model of the two-link flexible manipulator are
- II -
哈尔滨工业大学工学硕士学位论文
determined. Through the frequency equation presented in this article, a study on the variation of natural frequencies with the time-varying elbow angles is performed using a two-link flexible manipulator with a set of typical geometrical parameters and material constants. Thus we can predict the tendency and range of the system natural frequency. Keywords: flexible manipulator, flexible-joint, natural frequencies , global mode shapes
Dissertation for the Master Degree in Engineering
DYNAMIC MODELING AND ANALYSIS OF SPACE FLEXIBLE MANIPULATOR
Candidate： Supervisor： Academic Degree Applied for ： Speciality： Affiliation： Date of Defence ：
Wei Jin Senior Engineer. Liang Tingwei Master of Engineering General and Fundamental Mechanics School of Astronautics July, 2013
Degree-Conferring-Institution： Harbin Institute of Technology
硕士学位论文
空间柔性机械臂的动力学建模和分析
DYNAMIC MODELING AND ANALYSIS OF SPACE FLEXIBLE MANIPULATOR
魏进
哈尔滨工业大学 2013 年 7 月
国内图书分类号： O326，V11 国际图书分类号： 531.3, 534.1
学校代码： 10213 密级：公开
- III -
哈尔滨工业大学工学硕士学位论文
目
摘
录
要 ..........................................................................................................................I 论 ........................................................................................................... 1
工学硕士学位论文
空间柔性机械臂的动力学建模和分析
硕 士 研 究 生： 魏 导
进
师： 梁廷伟 高工
申 请 学 位 ： 工学硕士 学 科： 一般力学与力学基础
所 在 单 位： 航天学院 答 辩 日 期： 2013 年 7 月 授予学位单位 ： 哈尔滨工业大学
Classified Index: O326，V11 U.D.C: 531.3, 534.1