Geometric Design of Pure Rolling Rack and Pinion Mechanisms

The study of different types of pure rolling rack and pinion mechanisms is presented. They are designed based on the active design of the meshing line to provide pure rolling for the whole cycle of meshing. Parametric equations for contact curves on the rack and pinion are determined by coordinate transformation of the meshing line equations. Moreover, parametric equations for the tooth surfaces of the rack and pinion of three types of meshing, including the convex-to-concave meshing, convex-to-plane meshing, and convex-to-convex meshing are derived according to the motion of generatrices along the calculated contact curves. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. The contact ratio of rack and pinion mechanisms can be designed to be higher than one, which satisfies the condition for the continuous transmission of gears. At last, a numerical simulation is conducted to validate the kinematic performance. This paper lays the foundation for further research of pure rolling rack and pinion mechanisms, their manufacture technology and strength design criterion.