Abstract: The calculation of degrees of freedom of mechanism has attacted many scholars' attention all over the vv orld. This paper has put forth a theory concerning the analysis of the motion of the end member which is assumed to be cut off from the frame temporarily according to the closed loop characteristic of mechanical system, and immediately welded to the origiinal frame of the mechanism back again to reform the original mechanical system, and the theory is applied to calculating the degrees of freedom of mechanical system (inclding mechanisms and structures) . This paper elucidates the internal relationship between the degrees of statical indeterminacy and the degrees of freedom in mechanical system. It creates a necessary criterion for determining whether the finite displacement occurs in the mechanical system, and a sufficient criterion for determining whether the mechanical system can serve as a structure. It also reveals the physical concept of statical indeteerminateness and degrees of freedom, and finally proves exactly that the previous theory to classify the mechanism into six families is wrong, and that the classification of mechanism into families makes no practical sense at all.