大射电望远镜精调稳定平台奇异性分析

The singularity analysis of the fine tuning stable Stewart platform for the large radio telescope

阐述了Stewart型平台奇异性的分类 ,利用位置向量关系推导了其Jacobian矩阵 .在设计参数和运动速度给定的条件下 ,通过考查Jacobian矩阵所形成的关于时间t的方程的解是否在所要求的工作空间内 ,来判断基于Stewart平台的大射电望远镜精调稳定平台是否会发生奇异 ;如果时间t小于完成整个工作空间所要求的时间 ,则修改设计参数 ,重复上述过程 ,直到在所选定的设计参数条件下 ,不会发生奇异为止 .计算机仿真发现该方法既方便又可靠 .

The classification of the singularities of Stewart platform is first described, and the kinematics Jacobian matrix is then deduced with the position vector. Under the condition of given design parameters and required kinematical velocity, a methodology to judge whether there are some singularities in the whole workspace is developed by finding the roots about time t of the formulation of the determinant of the Jacobian matrix. We can modify the design parameters to avoid the singularity based on the species of the roots. The simulation results have shown that the proposed methodology is very reliable and convenient.