Ball Screw Recirculation Groove for Smooth Ball Return

The patent transitions from conventional two-dimensional trajectory design (axial horizontal plane and axial cross-section) to three-dimensional trajectory design by introducing the radial direction as a third dimension. The recirculation trajectory is defined by coordinate values in three directions: axial direction (X), radial direction (R), and circumferential direction (θ), enabling continuous tangential connection between recirculation and helical trajectories for smooth ball movement

The patent changes the design parameters from conventional two-dimensional curves to three-dimensional coordinate values (X, R, θ) that define the recirculation trajectory in space. By specifying coordinate values at multiple points along the trajectory and connecting them smoothly, the patent achieves continuous tangential directions while maintaining design simplicity through systematic parameter definition

The patent divides the recirculation trajectory into multiple segments defined by discrete coordinate values at different points (e.g., start point, intermediate points, end point). Each segment is calculated independently using the three-dimensional coordinate system, and then connected to form the complete trajectory. This segmentation approach ensures tangential continuity while making the calculation process systematic and manageable

The patent performs preliminary calculation and definition of the three-dimensional recirculation trajectory before manufacturing. By pre-calculating the coordinate values (X, R, θ) that ensure tangential continuity with the helical trajectory, the patent eliminates the need for complex real-time adjustments during operation, thereby ensuring reliable and smooth ball recirculation