According to comparable study and application on new and old
formulas for calculating DOFs of mechanisms and structures,the new formula was proved to be correct, as well as Kutzbach Qrubler Formula. These two formulas work for all the DOF calculation in plain and space mechanisms,and reveal the basic law of kinetic
mechanisms and structures.With the new formula, the structures and number of DOFs was checked correctly in non-circular gear hydraulic motor, in AUDI 01V auto transmission planet row, hexagon 6-SPS and triangle 6-RUS spatial parallel mechanism and problem sets for plane and space structural mechanics.