Abstract: In this paper,collision-free paths planning for three dimensional object with rotation is described.According to the concepts of state space,rotation map graph (RMG) discussed in〔1〕,〔2〕,a new method for investigating the connectivity of RMG(or topologic structure of RMG) is presented by using topologic technique.Based on this approach the problem of finding collision-free paths for an object translating and rotating among obstacles is thus transformed to that of finding connected paths in a finite network.