基于运动误差约束的平面定位平台拓扑优化设计

Planar Positioning Stage Designed by Topology Optimization Based on Motion Error Constraints

针对传统平面定位平台拓扑优化设计过程中无法预先了解输入输出位移映射矩阵的问题,基于固体各向同性材料惩罚法,采用遗传算法优化得到具有最大运动空间时的平面并联机构雅克比矩阵作为平面定位平台输入输出期望位移映射矩阵,在相同输入条件下,建立以机构实际运动与期望运动间误差最小为目标函数和以机构体积为约束函数的平面定位平台拓扑优化模型并求解。通过3D打印方式得到实验样品,实验与仿真分析表明:采用运动误差约束的平面定位平台拓扑优化设计方法,在一定偏差范围能够得到输入输出位移映射矩阵与给定期望映射矩阵相一致的平面定位平台,表明该方法对平面定位平台设计具备有效性,为其后续研究提供基础。

In the design process of the planar positioning stage,the traditional topology optimization method can not know the input and output displacement mapping matrix of the planar positioning stage in advance.In view of this problem,based on the solid isotropic material with penalization(SIMP)topological description method,take the planar parallel mechanism Jacobian matrix with the largest motion space optimal by genetic algorithm as the input and output expected displacement mapping matrix,take the minimize motion error by actual motion and expect motion under the same input as object function,the volume of the mechanism as the constraint function to established the topology optimization model of the planar positioning stage and solved.Obtain experimental samples by 3D printing and analyzed.The experimental and simulation analysis results show that the planar positioning stage topology optimization design method based on motion error constraint can obtain the positioning stage whose input-output displacement mapping matrix is consistent with the given expectation mapping matrix in a certain deviation range,which indicates that the method is effective in planar positioning stage and provides a basis for its follow-up research.