Following the development of micro-computer, the analytical method of mechanism with matrix equation has become an effective tool for the analysis space motion of mechanism. In this paper, a mathematical description of spindle motion either in rotative sensitive direction, or in fixed sensitive direction employing displacement matrix and coordinate change matrix as a tool is given. Finally a new way to evaluate error motion of spindle is proposed and some examples calculated by microcomputer are introduced. Some related problems being argued presently both at home and abroad are also dealt with.