A corner smoothing approach for CNC machines based on $\eta^{3D}$-splines

Abstract

The efficiency of Computer Numerical Control (CNC) machines and the quality level of their products can be improved if GCode paths are properly smoothed through the use of junction primitives, so as to achieve a high-level of geometric continuity. In this work, a planning primitive named <tex>$\eta^{3D}$</tex>-splines is used for the generation of composite paths characterized by the third order geometric continuity. The tolerance between the original and the smoothed path can be imposed during the planning process. The strength of the proposed strategy is represented by its straightforward implementation: the <tex>$\eta^{3D}$</tex>-splines coefficients are directly and efficiently computed, through closed form expressions, from the assigned interpolating conditions. Additionally, smooth junctions can be easily created even when the original path includes circular segments. The low computational burden of the proposed strategy makes it suited for the real-time generation of smooth composite paths. Comparisons are proposed in the paper with an analogous technique based on the 3D general clothoids.