Based on topological principles of general parallel mechanisms

the decoupling steps of parallel mechanisms are concluded. Also the kinematic analysis of the un-symmetrical parallel mechanism of 3-RRRP（4R） with three translational degrees of freedom is carried out. On the basis of better topological decoupling

the mechanism is simple in structure with fewer solutions for position analyses by choosing appropriate input-joints

and its unexpected outputs are constants. Because of simple mechanism

a few direct and inverse solutions

better real-time ability

the parallel mechanism simplified greatly the questions of real control and path planning. The mechanism provides a new typed practical model for mini un-symmetrical parallel robot.