An Optimal Parametrization Scheme for Path Generation Using Fourier Descriptors for Four-Bar Mechanism Synthesis

Abstract

Fourier descriptor (FD)-based path synthesis algorithms for generation of planar four-bar mechanisms require assigning time parameter values to the given points along the path. An improper selection of time parameters leads to poor fitting of the given path and suboptimal four-bar mechanisms while also ignoring a host of mechanisms that could be potentially generated otherwise. A common approach taken is to use uniform time parameter values, which does not take into account the unique harmonic properties of the coupler path. In this paper, we are presenting a nonuniform parametrization scheme in conjunction with an objective function that provides a better fit, leverages the harmonics of the four-bar coupler, and allows imposing additional user-specified constraints.