A novel method for the design of discretionary N-lobed pitch curve and intermittent N-lobed pitch curve is presented. And a general formulation for classification identification model of the pitch curve with nondifferentiable points for N-lobed noncircular gear (N-LNG) is proposed. The formulation is based on the differentiable principle. In particular, the steepest rotation modification model and method of the pitch curve with discontinuous points for any type of N-LNG are established by resorting to fundamentals of the calculus of variations. The modification model can be calculated via the Euler–Lagrange equation, and its conjugate pitch curves which contain outer contact and inner contact can be obtained in general by using the principle of noncircular gear meshing. This identification and modification model and method are implemented in several numerical examples, and simulation results demonstrate that the pitch curve with nondifferentiable points for N-LNG can be effectively identified and modified.