Use of shape invariants in optimal synthesis of geared five-bar linkage

Two functions describing a closed curve are proposed and applied to synthesis of 1-DOF planar geared five-bar mechanism as a path generator. The functions are the distance of the curve from its centroid and mutual distribution of the curve points. The former is well-known as a tool of pattern recognition in computer image processing and the latter one is proposed by the author. The functions are represented by normalized coefficients of their expansions into Fourier series. A construction of a curve description without referring to the harmonic analysis is also presented. Distance norms in the sense of the affinity of shapes are introduced. The norms are used as objective functions in optimal synthesis of 1-DOF geared five-bar linkage and minimized using the evolutionary algorithm. The introduced methods are confronted with the curvature-based approach. Results of numerical search for the mechanisms generating a wide variety of shapes prove that the descriptions can be effectively used in optimal synthesis.