By adopting the geometric method for analysing the relative position of rigid bodies

the authors analyze and discusse.the definition

the measure methods and the adjustment methods of the shaft alignment error of a coupling

and points out that the shaft alignment error of a coupling can exist in the form of elastic deformation of the system and the four independent parameters of the shaft alignment error can be measured approximately here

and on this base the adjustment process for the shaft alignment error can be conducted.So the characteristics of the shaft alignment error of a coupling are demonstrated clearly and thoroughly form theory and practice.It forms a base for setting up the tolerance standard and the uniform measure methods and the uniform adjustment methods of the shaft alignment error of a coupling.