Evaluation of Clothoids in Manufacturing Context

Polynomial based curves are the de facto standard methods used in numerical control systems for curvature continuous corner blending, i.e. smoothing path transitions with different tangent vectors. Disadvantages of polynomial based curves are mostly the non-linearity of the curvature profile over the arc length and the approximation of the arc length. A curve which does not suffer from these disadvantages is Clothoids. In this paper, an algorithmic concept to use Clothoid as blending curves is addressed. The algorithms consider the corner-based and the intermediate point-based blending. Based on theoretical foundations, these two blending types are analyzed. Further, Clothoids and Pythagorean hodograph curve are compared to outline the benefit of applying Clothoids as a blending curve.