Abstract: This paper presents a matrix form of the positional and orientational errors of a robot linkage.By thematrix theory,the paper reaches a conclusion that if the positional and orientational errors in its workspaceis minimum,the aberrations of structure parameters and the kinematic errors in joints must be theeigenvector corresponding to the least eigenvalue of the coefficient matrix of positional and orientationalerrors.The method for choosing the optimum tolerances of structure parameters is also presented in the pa-per,and the optimum kinematic errors in joints is given.A numerical exampte of a six DOF robot linkage ispresented.