6-PRRS并联机器人正逆奇异性研究

Study on Forward and Inverse Singularity of a 6-PRRS Parallel Robot

基于雅可比矩阵研究了一种6-PRRS并联机器人的奇异性问题.对于正奇异,推导出一种基于速度投影的雅可比矩阵求解方法,提出了空间瞬时轴这一新的概念,并给出奇异产生时并联机构正奇异的表现形式.对于逆奇异,将并联机构拆分成多个串联机构,由指数积方法求得其雅可比矩阵,并证明了机构逆奇异产生时的雅可比矩阵为奇异.基于正、逆奇异,又提出了一种更为特殊的复合奇异现象,即在某个特定的空间位姿下,正、逆奇异同时发生,并给出了可能的存在形式.所提雅可比矩阵的求解过程及其奇异性的证明,以及对机构奇异的表现形式的描述,为研究并联机构的奇异性提供了新的、直观的方法.

The singularity of a 6-PRRS parallel robot is studied based on Jacobins matrix. For forward singularity, the Jacobins matrix is obtained based on velocity projection, a new notion of spatial instantaneous axis is introduced, and the expressive form of the parallel mechanism singularity is given when it is generated. For inverse singularity, the parallel robot is divided into several series mechanisms, and the Jacobins matrix of these series mechanisms is solved by the exponential product equation and proved to be singular when the series mechanisms are singular. Based on forward or inverse singularity, a more special composite singular phenomena is proposed, which is generated when the forward and inverse singularities occur simultaneously under a certain spatial pose, and its possible existent form is given. The solving process of Jacobins matrix, the proving of matrix singularity and the description of the mechanism singularity provide a new and intuitional method for studying the singularity of parallel mechanism.