Generation Principle and Mathematical Models of Involute-circular Gear

A new tooth profile gear,involute-circular gear,is proposed by integrating involute gear's advantageous edges with circular tooth gear's advantages in this research.The concept of involute-circular gear is also defined,namely that choosing two single-valued curves which are corresponding engaged from the involute profiles between driving and driven wheels respectively,and replacing involute profile with the convex and concave circular arc separately to form new tooth profile at any point of these curves.According to differential geometry,the equation of tooth surface is established based on method of coordinates transformation.Insensitivity to central distance variation on involute-circular gear is discussed.The analyzed results indicate that the transformation ratio remains still unchanged as long as the gear pair can keep meshing drive,even if central distance generates change.An example of this gearing was presented and calculated,and 3D models of a pair of gears are established.The results offer theoretical supports for further studies on the involute-circular gear and reference value for the design and machining of gear.