The geometric design, meshing simul

The geometric design, meshing simulation, and stress analysis of pure rolling rack andpinion mechanisms are presented. Both the pinion and the rack are based on the activedesign of the meshing line to provide pure rolling for the whole cycle of meshing. The parametricequations of the contact curves on the rack and pinion tooth surfaces are determinedby coordinate transformation of the meshing line equations. Three types of meshing arederived according to the motion of the generatrices along the calculated contact curves:convex-to-concave meshing, convex-to-plane meshing, and convex-to-convex meshing.Then, the basic design parameters are analyzed and formulas for calculation of the geometricsize are given. Four different cases of design are considered to compare the meshingperformance and mechanical behavior of the proposed gear mechanisms. The resultsinclude contact patterns, the unloaded function of transmission errors, and the evaluationof stresses along two cycles of meshing. The analysis of the results shows that the proposedmethod of design of pure rolling meshing reduces the relative sliding between tooth surfaces,whereas it decreases the contact strength of the tooth surfaces. However, if thedesign parameters are properly evaluated as a result of simulation and applied as proposedhere, the mechanical behavior of the proposed rack and pinion mechanisms can be morefavorable than that of the standard geometry of involute rack and pinion sets.