一种2T2R自由度并联机构的运动学设计

发布时间：2018-07-12 10:17

本文选题：2-PSS(2-PRR)R机构 + 运动学分析　；参考：《天津大学》2012年硕士论文

【摘要】：本论文密切结合国家装备制造业对五坐标混联构型装备的迫切需求,深入研究了一种新型两平两转(2T2R)自由度并联机构2-PSS(2-PRR)R的设计方法,主要内容涉及结构学、逆运动学、位置正解、工作空间、奇异性及尺度综合等方面。本文取得以下研究成果: (1)结构学分析。建造了2-PSS(2-PRR)R机构实体模型,详细介绍了其结构组成原理,绘制了机构的结构简图,并借助螺旋理论揭示其末端的自由度数目与类型,实现了结构学分析。 (2)运动学分析。基于闭环矢量法,构建了2-PSS(2-PRR)R机构的逆运动学分析模型,获得了操作空间与关节空间之间的位置、速度及加速度映射关系,为机构运动学设计(尺度综合)奠定了基础。此外,借助Mathematica数学工具软件获得了该机构的全部位置正解。 (3)工作空间和奇异性分析。针对2-PSS(2-PRR)R机构的具体结构组成,定义了两种工作空间;计及驱动范围、运动副转角范围等工程约束,分别利用不同搜索算法获得了该机构的两种工作空间,并侧重研究了关键设计参数对机构工作空间的影响。通过对约束方程求导建立了雅可比矩阵,并深入研究了该并联机构的奇异问题。 (4)尺度综合。建立了2-PSS(2-PRR)R机构的无量纲雅可比矩阵(速度映射算子矩阵),并以其代数特征为基础,构造了恰当的运动学性能评价指标;借助单调性分析,揭示了关键设计参数对机构运动学性能的影响;在(2)、(3)基础上,根据给定的工作空间,并计及相关的几何、工程约束,通过MATLAB求解一类多变量含约束的非线性优化问题,实现了机构的运动学设计。
[Abstract]:In this paper, a new design method of 2-PSS (2-PRR) R of two parallel mechanisms with two flat and two rotation (2T2R) degrees of freedom is studied in close consideration of the urgent needs of the national equipment manufacturing industry for the five-coordinate hybrid configuration. The main contents of this paper are related to structural and inverse kinematics. Positive position solution, workspace, singularity and scale synthesis. The main results are as follows: (1) structural analysis. The solid model of 2-PSS (2-PRR) R mechanism is constructed, the principle of its structure is introduced in detail, the structure diagram of the mechanism is drawn, and the number and type of degrees of freedom at the end of the mechanism are revealed with the help of helical theory, and the structural analysis is realized. (2) Kinematics analysis. Based on the closed-loop vector method, the inverse kinematics analysis model of 2-PSS (2-PRR) R mechanism is constructed. The mapping relations of position, velocity and acceleration between the operating space and the joint space are obtained, which lays a foundation for the kinematics design (scale synthesis) of the mechanism. In addition, the positive solutions of all positions of the mechanism are obtained by means of Mathematica software. (3) Workspace and singularity analysis. According to the specific structure of 2-PSS (2-PRR) R mechanism, two kinds of workspace are defined, and the engineering constraints such as driving range and angle range of motion pair are taken into account, and two kinds of workspace of the mechanism are obtained by using different search algorithms. The influence of key design parameters on mechanism workspace is also studied. The Jacobian matrix is established by the derivation of the constraint equation, and the singularity problem of the parallel mechanism is studied in depth. (4) scale synthesis. The dimensionless Jacobian matrix (velocity mapping operator matrix) of 2-PSS (2-PRR) R mechanism is established. Based on its algebraic characteristics, an appropriate kinematic performance evaluation index is constructed. The influence of key design parameters on the kinematics performance of the mechanism is revealed. Based on (2), (3), a class of nonlinear optimization problems with multivariable constraints are solved based on the given workspace and taking into account the relevant geometric and engineering constraints. The kinematics design of the mechanism is realized.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH112

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