When robot is at singular configuration, the limited hand velocity wouldrequire some joints with infeasible speeds so as to lead unsafely of the system. A method of solvingthe approximate velocity of joint near singular configuration point by adding damped vector isproposed and a modified algorithm is provided. With the analysis of J^(-1) the singularconfigurations of 6R robot are divided into structure boundary singularity , boundary singularity ,inner singularity and wrist singularity. The conditions of singularities of the robot have beenascertained. The computer simulations of the singularities of the robot are developed, which havemany advantages over previous description methods of the singular configurations of robot. With thehelp of boundary singularity analysis, a application in welding trajectory planning checking of therobot has been carried out and the simulation result proved visualized and useful.