Abstract: The analytical solution of robot inverse kinematics can't be obtained by traditional methods of kinematical modeling when the robot configuration doesn't conform to the “Pieper criterion”. For this problem, a new method of exchanging the establishment order of adjacent joint axes is presented based on invariance property of the forward kinematics results after exchanging the establishment order. The robot configuration conditions for applying the proposed method are given. A minimally invasive surgery robot which doesn't conform to the “Pieper criterion” is taken as an example, the precise analytical solution is obtained by the proposed method, and the correctness of the proposed method is verified through Matlab Simulink.