The new calculation methods for the maximum radial deviation of sun pinion in operating and the minimal length of a toothed coupling are given. And the maximum radial deviation of sun pinion in operating are consisted of four parts: the total radial composite deviation of sun pinion plus the total radial composite deviation of planetary gear,the half of the maximum radial clearance of planetary gear bearings,the maximum deviation of the center distance for planetary gear with the sun pinion,and the deviation under loads. It is recommended,that a reasonable limit for angular misalignment in a single articulated coupling is 0. 001 radians. It is confirmed,that these methods and the recommended value are right,reasonable and reality in a various of practical applications.