To improve the global stiffness and conveniently build a model of a compliant mechanism with spatial multiple degrees of freedom(DOF),the topology optimization method,combined with the isomorphic mapping matrix,is proposed in this paper for structure synthesis of a 6-DOF spatial compliant mechanism.By using the differential approximation method,the Jacobian matrix of the Stewart prototype platform is calculated as the isomorphic mapping matrix,and its eigenvalues and eigenvectors are considered.Combining the isomorphic mapping matrix with the solid isotropic material with the penalization topology optimization method,the topological model of the 6-DOF spatial compliant mechanism is constructed,and a topological structure of the 6-DOF spatial compliant mechanism is derived which has the same differential kinematic characteristics as the Gough-Stewart prototype platform.Piezoelectric actuators are mounted inside the topological structure during the three-dimensional printing manufacturing process,and its driver directions are in accordance with the driver configuration directions of the Gough-Stewart prototype platform.The effectiveness of the proposed method for topological structure synthesis of the 6-DOF spatial compliant mechanism is demonstrated through several numerical examples and experimental studies.
基于平面三自由度全柔顺并联机构与传统并联机构的微分运动学矢量连续映射关系,建立整体式平面三自由度全柔顺并联机构构型拓扑优化模型-固体各向同性材料插值(Solid isotropic material with penalization,SIMP)模型,运用优化准则(Optimization criterion,OC)算法对所建立模型求解,采用Heaviside过滤技术处理优化过程中棋盘格和网格依赖问题。基于曲线拟合方法对优化后整体构型轮廓进行拟合,在Solid Works软件中建立其三维模型,进而应用有限元软件进行静力学仿真分析与对比,结果表明:以微分运动学矢量连续映射关系为拓扑优化设计条件,所得出的平面三自由度全柔顺并联机构与传统并联机构具有相同的微分运动特性,定性验证了基于拓扑方法对平面全柔顺并联机构设计的有效性。
