Structural Design and Performance Analysis of a Planar 3-DOF Compliant Mechanism
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摘要: 采用并联原型机构微分雅克比矩阵与实体各向同性材料惩罚函数法（Solid isotropic material with penalization，SIMP）相结合的拓扑优化方法，以柔度最小和低阶模态频率最大为多设计目标，建立平面三自由度柔顺机构拓扑优化模型实现拓扑优化。以拓扑优化得到的模型边界为形状优化为设计变量，对拓扑优化模型应力与末端位移约束为优化目标进行二次优化。采用增材制造方法3D打印技术对平面三自由度柔顺机构拓扑构型进行加工，并采用雷尼绍双频激光干涉仪进行测量与数据采集。实验与有限元仿真对比结果表明：采用多目标拓扑优化和形状优化组合形成二次优化，运用二次优化方法设计得到的平面三自由度柔顺并联机构，在满足机构具有很好的整体刚度要求下，拥有很高的低阶模态频率实现振动拟制，而且能够实现微纳尺度位移运动特性。Abstract: A topological optimization method combines the differential Jacobian matrix of the parallel prototype mechanism with the solid isotropic material with penalization. Taking the minimum structural compliance and the maximum modal frequency as multi-objective, we establish the planar 3 degree-of-freedom (DOF) compliant mechanism's topological optimization model. Using the topological optimization model's boundary as the shape optimization design variable, the stress and moving platform displacement constraints were optimized twice. The twice optimization model was established with the 3D printing method, and the moving platform displacement data were measured and collected by using the Renishaw dual-frequency laser interferometer. Experimental results and finite element simulation results show that:the planar 3-DOF compliant mechanism designed by combining multi-objective topological optimization with shape optimization and using twice optimization has a low-order modal frequency to realize vibration fitting, thus satisfying the requirements of the planar compliant mechanism with good overall stiffness and realizing micro/nano-scale displacement movement.
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表 1 柔顺机构理论、实验、仿真分析位移
方向 理论计算 仿真分析 实验分析 X轴/μm -0.822 9 0.895 0.572 Y轴/μm -0.763 7 -1.74 1.193 Z轴/nrad 31.2 20.2 31.2 
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