Abstract: A kinematic reliability analysis method based on envelope method is proposed for the research on the kinematic reliability of end-effector of 7 degree-of-freedom redundant robots subjected to the link length，link offset and joint angle. The deduced kinematic error functions of the robot are linearized by the first-order Taylor formula. A failure model of position and pose of end-effector is obtained by the probabilistic method. The time-varying kinematic reliability problem can be transformed into time-invariant kinematic reliability problem by the envelope method. The point of the greatest failure probability in the trajectory is found，and the internal relationship between the maximum failure point and the end point is analyzed by introducing covariance matrix. The kinematic reliability of the robot is calculated by multidimensional normal integration. Finally，a simulation case is conducted to verify the proposed method. The results show that the results obtained by the envelope method agree with those obtained by the Monte Carlo method，but the efficiency of the solution is greatly improved. Compared with the equivalent extremum method，the envelope method has higher accuracy and better robustness.

Key words: redundantrobot, kinematicreliability, envelopemethod, probabilisticmethod