2-RPR+RRP球面混联机构的可达工作空间研究

Research of Reachable Workspace of 2-RPR+RRP Spherical Hybrid Mechanism

研究2-RPR+RRP球面混联机构的可达工作空间,首先,应用修正的Kutzbach-Grvbler公式对机构的自由度进行求解,得出了机构的自由度以及动平台的运动特性;其次,以机构的几何关系为约束条件,结合旋转矩阵建立了机构的运动学位置封闭正解数学模型;最后,根据运动学正解模型应用MATLAB软件绘制出动平台参考点在特定条件下的可达工作空间,并利用SolidWorks仿真软件对同条件下的可达工作空间进行了验证。证明了正解模型的正确性,为机构进一步分析与优化提供了理论基础。

The reachable workspace of 2 - RPR ＋ RRP spherical hybrid mechanism is researched. Firstly, the degree of freedom of the mechanism is solved by the modified Kutzbach - Grvbler formula, the degree of freedom of the mechanism and the motion characteristics of moving platform are obtained. Secondly, taking the geometric relation of mechanism as the constraint condition and combining with the rotation matrix, the mathe- matical model of the closed positive solution of the kinematics position of the mechanism is established. Finally, according to the positive kinematics solution model, the Matlab software is used to draw up the workspace of the reference point in the specific condition, and the reachable workspace of the same conditions is verified by using the SolidWorks. simulation software. The correctness of the positive solution model is proved, a theoretical basis for the further analysis and optimization of the mechanism is provided.