Abstract: Usually it is thought that three rotational movements for a robot wrist are needed to give an arbitrary orientation of the end-effector.In fact,an arbitrary orientationcan be given by a single rotation about an adequately chosen lotational axis.In thispaper,the orthogonal orientations are defined;the transformation between two orthogonal orientations are classified,rotation axes and angles are given;and some ideal sketches of practical mechanisms are shown.Single rotation mechanism when used in repetitive production,is quite simple condconvenient.