Stress-driven and user-guided Pythagorean-Hodograph print-paths for additive manufacturing

This paper presents a stress-driven and user-guided framework for generating Pythagorean–Hodograph (PH) print-paths in additive manufacturing (AM). PH curves are employed due to their unique properties, including polynomial representation, exact arc-length parametrization, and closed-form expressions for curvature. In this work, PH-based print-paths are introduced as a novel input representation for additive manufacturing. To execute these paths efficiently, a G-code interpolator tailored for PH curves is developed. Principal stress directions obtained from FEM analysis or user-defined constraints are used to construct smooth orthonormal vector fields, from which print-path points, tangents, and extruder orientations are derived. PH curves are then fitted to these points and tangents, representing the PH-based AM print-paths. The proposed method is validated using both an AM simulator and a physical machine.