Development of a Theoretical Model for 2D Tool Trajectories in Robotic Polishing Using a Space-Filling Curves Approach

In the realm of advanced manufacturing, robotic polishing has emerged as a pivotal process that demands high precision and uniformity, particularly for complex 2D metallic workpieces. This paper presents a novel theoretical model for robotic polishing trajectory planning using Space-Filling Curves (SFCs), specifically Hilbert, Moore, and Peano curves. These curves promise comprehensive coverage without overlap, which is a critical factor for achieving uniform material removal during polishing. The goal of this study was to leverage the unique properties of SFCs to optimize coverage and ensure uniformity in polishing intricate geometries. This research delves into the kinematic properties of the polishing tool's trajectory, such as speed, acceleration, and exerted forces, which are crucial for attaining the desired surface quality. Employing Finite Element Analysis (FEA), this study investigates the contact dynamics between the tool and workpiece, underscoring the importance of a consistent contact force in achieving high-quality polishing. The proposed theoretical model serves as a foundation for future practical applications, aiming to bridge the gap between theoretical research and industrial practice and paves the way for empirical validation and software development for industry-wide adoption.