With mathematical theory of differential geometry

the curvature of involute curve is scientifically researched.It is indicated that the involute curvature radius has quantitative relation with polar radius and pressure angle

and the involute curvature center has corresponding connection with base circle.The pressure angle and curvature radius are quantitatively calculated

and their distribution along the involute tooth profile curve are given.Based on the analysis of involute curvature

the method of substituting lower pair for higher pair is used to analyze gear tooth mesh mechanism.The analysis of transmission ratio accord with traditional theory about gear transmission.It poves that the analysis of involute curvature is correct and practical.Furthermore

the analysis of involute curvature has theoretical guidance meaning for deep research of gear mesh

innovative design of gear tooth profile and development of tooth profile modification machining technology

and it is significant for innovative research and development of gear transmission.