基于单开链单元的并联机构动力学响应建模方法的研究
发布时间：2018-07-17 21:32
【摘要】：并联机构动力学响应是机器人动力学研究领域的一个重要方面,具有多变量、多参数耦合和形式复杂等特点,建模和求解效率直接影响机器人实时控制的灵敏度和精度。对此,本文基于序单开链法,结合虚功原理建立了平面和空间并联机构的动力学响应模型,该法将方程维数降至最低,具有形式简洁,求解效率高,通用性强,并与结构学、运动学分析高度统一的特点。具体内容包括以下几个方面： 一、按照机构分解路线的耦合度K算法,将并联机械系统分解为约束度大于零、等于零和小于零三种类型的单开链单元。通过对约束度大于零单开链单元的运动学参数进行虚拟赋值,并利用约束度小于零的单开链单元建立运动学相容性方程完成整个系统的运动学分析。以此建立常用单开链单元的运动学模型,为后续并联机器人机构的动力学响应分析奠定基础。 二、将序单开链法思想与虚功原理相结合,建立平面和空间并联机构动力学响应方程的一般通式,其中包含两种类型：1)不含运动副支反力动力学响应模型,通过速度和加速度分析,将各构件质心运动表达为关于广义速度和加速度的函数,并通过线性化处理与广义坐标特殊赋值的方法求得动力学响应方程系数矩阵中的各元素,避免对广义坐标进行复杂的偏导运算,从而提高建模效率；2)含运动副支反力动力学响应模型,通过解除单开链相关运动副约束和新增广义坐标的方法,并结合单开链的动态静力分析,得出系统在运行过程中各运动副的受力情况,能有效地降低动力学分析约束方程的个数,降低计算的复杂度。 三、以一个平面3自由度(3-RRR)和空间4自由度(2SPS-2RPS)并联机器人研究为例,详细介绍了运用序单开链法进行动力学响应建模的一般思路和步骤。并通过Matlab编程计算得出它们的动力学响应特性曲线,以此对机构运动的动力学性能做出了简要评估。 机构动力学分析是在结构学,运动学分析的基础上逐步建立起来的,序单开链法不仅使得动力学方程的维数降至最低,而且在运动学及动力学分析时都基于统一单开链单元模型,从而形成完整、统一的机构学理论。
[Abstract]:The dynamic response of parallel mechanism is an important aspect in the field of robot dynamics. It has the characteristics of multi-variable, multi-parameter coupling and complex form. Modeling and solving efficiency directly affect the sensitivity and precision of robot real-time control. In this paper, the dynamic response model of planar and spatial parallel mechanisms is established based on the order single open chain method and virtual work principle. The method reduces the dimension of the equation to the lowest, and has the advantages of simple form, high efficiency, strong generality, and structural analysis. The characteristics of a high degree of unity in kinematics analysis. The specific contents include the following aspects: firstly, according to the coupling degree K algorithm of the mechanism decomposition route, the parallel mechanical system is decomposed into three types of single open chain units with constraint degree greater than zero, equal to zero and less than zero. The kinematics parameters of single open chain unit with constraint degree greater than zero are given by virtual assignment. The kinematics compatibility equation of single open chain element with constraint degree less than zero is used to complete the kinematics analysis of the whole system. The kinematics model of single open chain element is established, which lays a foundation for the dynamic response analysis of the subsequent parallel robot mechanism. Secondly, by combining the idea of order single open chain method with the principle of virtual work, a general formula for the dynamic response equations of planar and spatial parallel mechanisms is established, which includes two types: 1) the dynamic response model of reaction force without the support of motion pair. Through velocity and acceleration analysis, the motion of mass center of each component is expressed as a function of generalized velocity and acceleration, and the elements in the coefficient matrix of dynamic response equation are obtained by linearization and special assignment of generalized coordinates. In order to avoid complex partial derivative operation of generalized coordinates and improve the efficiency of modeling, the dynamic response model of reaction force with motion pair support is improved, and the method of lifting the constraint of motion pair associated with single open chain and adding generalized coordinate is adopted. Combined with the dynamic static analysis of single open chain, the force of each pair of motion pairs in the running process of the system is obtained, which can effectively reduce the number of constraint equations in dynamic analysis and reduce the computational complexity. Thirdly, taking a planar 3-RRR and space 4-DOF (2SPS-2RPS) parallel robot as an example, the general idea and steps of dynamic response modeling by using order single open chain method are introduced in detail. The dynamic response curves are calculated by Matlab programming, and the dynamic performance of the mechanism is evaluated briefly. The mechanism dynamics analysis is based on the structural and kinematic analysis. The ordered open chain method not only reduces the dimension of the dynamic equation to the minimum. Moreover, the kinematics and dynamics analysis are based on the unified single open chain element model, thus forming a complete and unified mechanism theory.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH112
本文编号：2131002
[Abstract]:The dynamic response of parallel mechanism is an important aspect in the field of robot dynamics. It has the characteristics of multi-variable, multi-parameter coupling and complex form. Modeling and solving efficiency directly affect the sensitivity and precision of robot real-time control. In this paper, the dynamic response model of planar and spatial parallel mechanisms is established based on the order single open chain method and virtual work principle. The method reduces the dimension of the equation to the lowest, and has the advantages of simple form, high efficiency, strong generality, and structural analysis. The characteristics of a high degree of unity in kinematics analysis. The specific contents include the following aspects: firstly, according to the coupling degree K algorithm of the mechanism decomposition route, the parallel mechanical system is decomposed into three types of single open chain units with constraint degree greater than zero, equal to zero and less than zero. The kinematics parameters of single open chain unit with constraint degree greater than zero are given by virtual assignment. The kinematics compatibility equation of single open chain element with constraint degree less than zero is used to complete the kinematics analysis of the whole system. The kinematics model of single open chain element is established, which lays a foundation for the dynamic response analysis of the subsequent parallel robot mechanism. Secondly, by combining the idea of order single open chain method with the principle of virtual work, a general formula for the dynamic response equations of planar and spatial parallel mechanisms is established, which includes two types: 1) the dynamic response model of reaction force without the support of motion pair. Through velocity and acceleration analysis, the motion of mass center of each component is expressed as a function of generalized velocity and acceleration, and the elements in the coefficient matrix of dynamic response equation are obtained by linearization and special assignment of generalized coordinates. In order to avoid complex partial derivative operation of generalized coordinates and improve the efficiency of modeling, the dynamic response model of reaction force with motion pair support is improved, and the method of lifting the constraint of motion pair associated with single open chain and adding generalized coordinate is adopted. Combined with the dynamic static analysis of single open chain, the force of each pair of motion pairs in the running process of the system is obtained, which can effectively reduce the number of constraint equations in dynamic analysis and reduce the computational complexity. Thirdly, taking a planar 3-RRR and space 4-DOF (2SPS-2RPS) parallel robot as an example, the general idea and steps of dynamic response modeling by using order single open chain method are introduced in detail. The dynamic response curves are calculated by Matlab programming, and the dynamic performance of the mechanism is evaluated briefly. The mechanism dynamics analysis is based on the structural and kinematic analysis. The ordered open chain method not only reduces the dimension of the dynamic equation to the minimum. Moreover, the kinematics and dynamics analysis are based on the unified single open chain element model, thus forming a complete and unified mechanism theory.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH112
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