Synthesis of the steepest rotation pitch curve design for noncircular gear

A steepest rotation method for designing pitch curve with fixed boundaries of noncircular gear is proposed by resorting to calculus of variations. A general mathematical model is established to design the steepest rotation pitch curves with integral constraint for noncircular gear pair, including external and internal meshing gear pair. In particular, to achieve the design of pitch curve with epicyclic constraint for driven noncircular gear, the epicyclic constraint conditions are also established. In addition, the unified design algorithm of pitch curves of noncircular gear pair with this steepest rotation characteristic is given in this paper, the pitch curves of desired geometrical and transmission properties can be solved easily by using the proposed algorithm. Examples presented in this paper are implemented in MATLAB, and feasibility and validity of above algorithm are verified.