基于几何代数的平面3-RRR并联机构性能评估与优化设计

Performance Evaluation and Optimal Design of Planar 3-RRR Parallel Manipulator Based on Geometric Algebra

摘要:

为使平面3-RRR并联机构满足多样的工作环境，本文基于几何代数对该机构进行性能评估和优化设计。基于闭环矢量法建立平面3-RRR并联机构运动学模型。以几何代数为数学工具，分析平面3-RRR并联机构局部和全局运动/力传递性能；考虑分支杆件柔性，结合应变能方法对平面3-RRR并联机构进行弹性静刚度建模，通过ANSYS软件进行验证，并基于刚度矩阵确定局部和全局虚功刚度指标。基于参数无量纲优化方法，以全局运动/力传递性能指标、刚度指标和可达工作空间为目标，对机构进行尺度优化设计，并分析关键尺度参数对机构性能的影响，从而获得平面3-RRR并联机构在不同工作环境下的最优结构尺度与性能图谱。研究结果可为并联机构样机设计提供参考。

Abstract:

Aiming to enable the planar 3-RRR parallel manipulator (PM) to meet various working environments, the performance evaluation and optimal design of the 3-RRR PM was conducted based on geometric algebra, where R denoted revolute joint. Firstly, the inverse kinematic model of the planar 3-RRR PM was established by using the closed-loop vector method. Secondly, utilizing geometric algebra as a mathematical tool, the motion/force transmission performance of the 3-RRR PM was analyzed in combination with local and global indices. And the transmission performance maps of the 3-RRR PM were plotted at different positions and postures. Nextly, considering the compliances of limbs, a systemic elastostatic stiffness modeling of the planar 3-RRR PM was presented based on the strain energy, which was verified by commercial ANSYS software in two cases. The local and global virtual-work stiffness indices were acquired at different external wrenches and positions. Based on the parameter-finiteness normalization method, the dimensional parameters of the 3-RRR PM were optimized with the objectives of global motion/force transmission performance, stiffness performance and reachable workspace. Based on the above results, the influence of the key dimensional parameters on the manipulator performance was discussed, from which the optimal structures and performance chart of the planar 3-RRR PM in different working environments can be obtained. The research results were of great significance for the prototype design of PMs.