Parametric 5-Axis CNC interpolation for spiral thread machining on spherical geometries

Spiral-threaded spherical components, though less commonly used than their cylindrical counterparts, play a vital role in high-performance engineering systems where sealing, spatial efficiency, and multi-axis articulation are paramount. These features are indispensable in specialized sectors such as sealed robotic joints, precision biomedical implants, and aerospace enclosures. Beyond their role as coupling elements, spherical threads may also serve as functional surface features, for example as channels for lubrication, sealing, or controlled fluid distribution. However, the generation of such threads remains a substantial challenge due to the lack of native support for spiral interpolation on curved geometries within conventional CAD/CAM environments. This paper introduces a parametric interpolation algorithm for directly computing spiral toolpaths on spherical surfaces, supporting user-defined parameters such as pitch, number of turns, and thread direction. Compatible with 5-axis CNC machines, the algorithm synchronizes linear motion (X, Y, Z) with rotational compensation (A, B), maintaining the tool orientation perpendicular to the local surface tangent and ensuring a uniform thread profile that cannot be achieved using. 3-axis machines. Applicable to both internal and external threads, the approach eliminates the need for multi-step CAD modeling and CAM programming by directly generating curvature-conforming toolpaths and CNC-ready G-code through an intuitive graphical interface, thereby reducing dependence on user expertise. The proposed framework provides a scalable solution for manufacturing compact, mechanically robust spherical threaded components, addressing an overlooked yet crucial capability in advanced machining practice.