On the application of the curve curvature in path synthesis

This paper presents an analysis of the applicability of the curve curvature in optimal synthesis of mechanisms. The concept of utilizing the normalized Fourier coefficients of the curvature as a curve description is known, but so far it was not applied to curves for which the continuity of the first or second derivatives cannot be assumed. An additional discussion aims at pointing out that the method can be applied in synthesis of all the varieties of the coupler curves. Special attention is put on the curves of C0 class. The numerical experiments follow the analysis of how the distribution of points on the curve affects the Fourier coefficients. By means of the Fourier coefficients a distance norm between two curves is introduced to measure their similarity. The effect of the curve shape on convergence of the norm is investigated on the examples of the curves generated by four-bar linkages using “Mathematica” software. The curve description is used to formulate a goal function to synthesize the coupler curve using the genetic algorithm.