Linear Motor Curved Track with Variable Radius Geometry

The patent applies parameter changes by transitioning from a constant radius of curvature to a variable radius of curvature that changes continuously along the track. Specifically, the radius of curvature is designed to vary as a function of position, creating a clothoid-like geometry where the curvature transitions smoothly from straight to curved sections. This eliminates abrupt changes in higher-order derivatives (jerk and snap) while maintaining modular manufacturability through precise geometric design of each track section.

The patent replaces the need for complex electronic control signals with a mechanically optimized track geometry. Instead of using control algorithms to compensate for abrupt transitions and manage higher-order derivatives, the solution embeds the dynamic optimization directly into the physical shape of the track. The variable radius of curvature naturally provides smooth transitions, eliminating the need for complex real-time control interventions and reducing control system complexity.

The patent applies local quality by designing each modular track section with a specific variable radius of curvature profile optimized for its local function. Straight sections have infinite radius, transition sections have progressively changing radius to provide smooth clothoid-like transitions, and curved sections have controlled variable radius to maintain appropriate curvature while enabling smooth entry and exit. This localized optimization of geometry at each section level achieves superior dynamics without requiring excessive geometric complexity throughout the entire track system.