关键词: 环数, 平面机构, 球面机构, 约束数, 运动副, 自由度

Abstract: Based on the theory that the four-bar mechanism has flexibility and three-connecting rod structure has stability, the calculating formula of degree of freedom of mechanism has been researched.The results of research indicate that the new calculating formula is more simple and clearer than the formula which was builded at 1896 by B. Blwe, who was a academician of the Russian Academy of Sciences.The formula has advantages of rapid computing speed .The new formula is suitable not only for single ring, multiple ring，open chain，closed chain，mixed chain，higher pair，turnover wheel and planet row of car，but also for calculating the degree of freedom of statically determinate mechanism and super statically determinate.The easy and correct theoretical calculating formula is provided for calculating degree of freedom of planar and spherical mechanism.

Key words: Number of rings, Degree of freedom, Kinematic pair, Number of restrictions Planar mechanism, Spherical mechanism