三自由度平面全柔顺并联机构运动学分析

针对传统方法求解全柔顺并联机构Jacobian矩阵存在奇异性的缺陷,基于三自由度平面全柔顺并联机构的伪刚体模型,提出一种微位移法来求解机构的Jacobian矩阵。先建立机构的伪刚体模型,并采用传统方法和微位移法得到机构的输入输出Jacobian矩阵;通过HyperMesh软件仿真和实验测试分别得到机构动平台中心点位移的仿真值和实验值。最后,将两种方法得到的理论值分别与仿真值、实验值进行对比。对比结果表明:与传统法相比,微位移法的计算精度较高,误差较小,且验证了Jacobian矩阵的有效性,为全柔顺并联机构的运动特性分析提供了参考。

Kinematic Analysis of 3-DOF Planar Compliant Parallel Mechanism

The traditional method for solving Jacobian matrix of fully compliant parallel mechanism has the defects of singularity. A micro-displacement method was proposed to solve the Jacobian matrix of the mechanism based on the pseudo rigid body model of a 3-DOF planar fully compliant parallel manipulator. The pseudo rigid body model of the mechanism was established, and the Jacobian matrix of the mechanism was obtained by the micro displacement method and traditional method. The simulation results and the experimental values of the moving platform’s displacement of the center point were respectively obtained by HyperMesh software simulation and experimental tests. The theoretical values obtained by the two methods were respectively compared with the simulation values and the experimental values. The results show that compared with the traditional method, the precision of the micro-displacement method is higher and the error is smaller. The validity of the Jacobian matrix is verified. It provides reference for the kinematic analysis of the fully compliant parallel mechanism.