3P-Delta并联机构的参数优化与轨迹规划

发布时间：2018-02-20 07:35

本文关键词： 并联机构运动学分析工作空间参数优化轨迹规划　出处：《中北大学》2017年硕士论文　论文类型：学位论文

【摘要】：并联机构由于其运动学和动力学性能良好,已广泛应用于航空航天、医疗康复及排险救灾等各个领域。3P-Delta并联机构为空间三自由度平动并联机构,具有结构简单、易于控制等优点,可应用于分拣、搬运、封装等自动化生产线中。本文以3P-Delta并联机构为研究对象,对3P-Delta并联机构的运动学、参数优化、运动仿真及轨迹规划等方面进行研究。首先,对3P-Delta并联机构进行了自由度计算,确定了机构具有三维平移的运动形式。利用闭环矢量法建立机构的运动学方程,求解得到机构的位置正、逆解。对机构的运动学方程进行一阶泰勒展开,得出机构的雅可比矩阵表达式,利用雅可比矩阵求出了机构的奇异位形。其次,基于机构的位置逆解,采用数值搜索法对3P-Delta并联机构的工作空间进行求解,用Matlab软件对求解过程进行编程,得到了机构的工作空间三维图。用Solid Works软件建立机构的三维模型,对机构进行了运动仿真,得出机构的工作空间边界曲线。与Matlab软件求得的工作空间比较,两种方法得到的工作空间大小和形状基本相同,验证了所求工作空间的正确性。基于微分思想,将3P-Delta并联的工作空间分割成许多微小子空间,以此求得机构工作空间体积。根据3P-Delta并联机构的雅可比矩阵,对机构的雅可比条件数进行分析,得出工作空间内各处雅可比条件数的值,并求得3P-Delta并联机构的全局雅可比条件数。用遗传算法对3P-Delta并联机构进行了结构参数优化,分析了机构的各结构参数对工作空间体积和全局雅可比条件数的影响。分别以工作空间体积最大化和全局雅可比条件数最小化为优化目标,选择合适的优化参数,对机构进行了优化。然后,利用ADAMS软件建立3P-Delta并联机构的虚拟样机模型,对3P-Delta并联机构进行了位置正逆解、速度和加速度的运动仿真,得到机构的运动规律曲线。将得到的曲线与对3P-Delta并联机构理论求解得到的曲线相对比,两种方法得到的曲线基本重合,验证了机构运动学理论分析的正确性。最后,对3P-Delta并联机构分别进行五次多项式插值规划和梯形速度曲线规划,搭建了3P-Delta并联机构的实验样机平台,选择梯形速度曲线对实验样机进行轨迹规划、测试。通过轨迹规划,使得动平台能以良好的运动学性能通过给定的路径,并通过实验验证轨迹规划的可行性。
[Abstract]:Because of its good kinematics and dynamic performance, the parallel mechanism has been widely used in aerospace, medical rehabilitation, disaster relief and other fields. The 3P-Delta parallel mechanism is a 3-DOF parallel mechanism with a simple structure. It is easy to control and can be used in automatic production lines such as sorting, handling and packaging. In this paper, the kinematics and parameter optimization of 3P-Delta parallel mechanism is studied. The kinematics simulation and trajectory planning are studied. Firstly, the degree of freedom of the 3P-Delta parallel mechanism is calculated, and the kinematic equation of the mechanism is established by using the closed-loop vector method. The position forward and inverse solutions of the mechanism are obtained. The first order Taylor expansion of the kinematics equation of the mechanism is carried out. The Jacobian matrix expression of the mechanism is obtained. The singular configuration of the mechanism is obtained by using the Jacobian matrix. Secondly, based on the position inverse solution of the mechanism, The workspace of 3P-Delta parallel mechanism is solved by numerical search method, the solution process is programmed by Matlab software, and the three-dimensional graph of the mechanism workspace is obtained. The three-dimensional model of the mechanism is established by Solid Works software, and the kinematic simulation of the mechanism is carried out. The workspace boundary curve of the mechanism is obtained. Compared with the workspace obtained by Matlab software, the size and shape of the workspace obtained by the two methods are basically the same, which verifies the correctness of the workspace. The workspace of 3P-Delta parallel mechanism is divided into many micro-small spaces, and the workspace volume of the mechanism is obtained. According to the Jacobian matrix of 3P-Delta parallel mechanism, the Jacobian condition number of the mechanism is analyzed. The values of Jacobian conditions are obtained and the global Jacobian conditions of 3P-Delta parallel mechanisms are obtained. The structural parameters of 3P-Delta parallel mechanisms are optimized by genetic algorithm. The effects of structural parameters on the workspace volume and the number of global Jacobian conditions are analyzed. The optimum parameters are chosen to maximize the volume of the workspace and minimize the number of global Jacobian conditions, respectively. Then, the virtual prototype model of 3P-Delta parallel mechanism is established by using ADAMS software, and the position inverse solution, velocity and acceleration of the 3P-Delta parallel mechanism are simulated. The kinematic curve of the mechanism is obtained. Compared with the curve obtained by the theoretical solution of 3P-Delta parallel mechanism, the curves obtained by the two methods basically coincide with each other, which verifies the correctness of the kinematics theory analysis of the mechanism. The fifth polynomial interpolation planning and trapezoidal velocity curve planning of 3P-Delta parallel mechanism are carried out respectively. The experimental prototype platform of 3P-Delta parallel mechanism is built. The trapezoidal velocity curve is selected to plan and test the trajectory of the experimental prototype. The platform can pass through a given path with good kinematic performance, and the feasibility of trajectory planning is verified by experiments.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH112

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