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A hyperboloid is created when a straight line rotates around an axis that is not in the same plane. This geometric shape can be visualized as a surface formed by the movement of a straight line, which is similar to how a shaft rotates inside a hole. When comparing one of these lines to the outer edge of the shaft, their contact forms a straight line. In theory, this type of contact is similar to a clearance fit between a hole and a shaft, where the line remains in contact throughout the motion. This ensures smooth gear meshing and allows for automatic adjustment, while maintaining the full contact length between the shaft and the hole.
The concept of "hyperbolic holes" was introduced in the design of planetary gear systems. In some foreign designs, the inner hole of the planetary gear takes on a drum-like shape. Instead of being cylindrical, the inner surface has a curved profile with a radius R, allowing the planetary gear to automatically adjust the meshing gap when it engages with the side gear on its shaft. However, this design often results in only the central part of the hole making contact with the shaft, leading to increased wear over time. To address this issue, a double-curved hole design has been developed, which improves contact distribution and reduces wear, enhancing the overall durability and performance of the system.