Path synthesis of planar four-bar linkages for closed and open curves using elliptical Fourier descriptors

Many researchers have widely applied shape descriptors to perform dimensional synthesis of mechanisms. This work investigates the path synthesis of planar four-bar linkages for closed and open curves using elliptical Fourier descriptors (EFDs). EFD is also a Fourier-based analysis method. Its Fourier coefficients of a coupler curve are obtained through separate Fourier expansion of the x and y components of the coupler curve rather than on a function. Elliptical Fourier descriptors are effective at describing complex curves with high curvature. A process has been developed for approximating non-periodic paths using EFD. By combining the process with the traditional EFD, a general method is established for the synthesis of four-bar linkages for open and closed curves in a single-step optimization process. The proposed approach offers an effective and efficient procedure in the path synthesis of four-bar linkages, providing a foundation for future research in the broader application of EFD in the dimensional synthesis of linkages.