A new involute-helix gear drive, which is point contact with convex and concave circular-arc tooth profiles, is proposed in this article. The basic principle characterized by the advantages of involute and circular-arc gears is put forward. Based on the theory of conjugates curves, generation and mathematical model of this new transmission are presented. The separability of center distance on involute-helix gear is discussed and meshing characteristic of point contact is also analyzed. Finally, the three-dimensional solid model of a gear pair is developed to demonstrate the properties of this new transmission.

A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.

The generation principle and meshing characteristics of conjugate-curve circular arc gears, which is proposed based on the theory of conjugate curves, are studied in this paper. The generation principle and mathematical model of this gear drive are introduced according to the given spatial screw curve. Tubular meshing surfaces contacting in the orientation of designated contact angle are provided to build up circular arc tooth profiles, which inherit all properties of conjugate curves. Geometrical three-dimensional models are established based on a numerical example and the results of motion simulation show that the generated gear drive meets general meshing and motion conditions. The comparisons between this designed gear drive and conventional circular arc gearing for the generation method and meshing characteristics are carried out. And the transmission efficiency of gear pair manufactured by hobbing cutter tools is also test. Through the analysis, it shows not only the general corresponding relationship between two gears, but also the conjugate meshing essence of circular arc gears. Theoretical and experimental results demonstrate the feasibility and correctness of proposed conjugate curves theory and the application to new types of gear drive with high performance will be carried out.

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Conjugate curves have been put forward previously by authors for gear transmission. Compared with traditional conjugate surfaces, the conjugate curves have more flexibility and diversity in aspects of gear design and generation. To further extend its application in power transmission, the geometric and meshing properties of conjugate curves are discussed in this paper. Firstly, general principle descriptions of conjugate curves for arbitrary axial position are introduced. Secondly, geometric analysis of conjugate curves is carried out based on differential geometry including tangent and normal in arbitrary contact direction, characteristic point, and curvature relationships. Then, meshing properties of conjugate curves are further revealed. According to a given plane or spatial curve, the uniqueness of conjugated curve under different contact angle conditions is discussed. Meshing commonality of conjugate curves is also demonstrated in terms of a class of spiral curves contacting in the given direction for various gear axes. Finally, a conclusive summary of this study is given.