Design of Non-Circular Gears Using a Generalized Parametric Algorithm and Verification via Additive Manufacturing

Although non-circular gears offer significant advantages in mechanical systems that require variable transmission ratios, they are not widely used due to the limited availability of design methods that can be generalized to different geometries and the complexity of manufacturing processes. In this study, a generalized parametric algorithm is presented that enables the design of non-circular gears with different numbers of lobes. The proposed approach is based on a parametric definition of the step curve and enables the derivation of elliptical and polygonal geometries within a single mathematical framework. The developed algorithm automatically generates mating tooth profiles based on user-defined parameters such as module, number of teeth, number of lobes, and eccentricity. In addition, the problem that the classical parametric model produces a constant speed ratio in symmetric cases has been identified, and an improved kinematic model incorporating a harmonic term has been proposed to address this issue. The resulting gear geometries have been modeled in a computer-aided design (CAD) environment and manufactured using a Fused Deposition Modeling (FDM)-based additive manufacturing process. Tests conducted on the prototypes confirmed that the gear pairs operated without interference and that the periodic speed variation predicted by the proposed model can be observed experimentally. The results demonstrate that the proposed approach can be generalized to different geometries, is feasible, and is applicable to engineering applications requiring variable-speed transmission.