Parametrization-Independent Non-Uniform Fourier Approach to Path Synthesis of Four-Bar Mechanism

This paper deals with the classical problem of dimensional synthesis of planar four-bar linkages for path generation. Using Fourier descriptors, a given path is represented by harmonic series. Extensive research has been done on this approach in mechanism synthesis with the assumption that the path is assigned a prescribed parametrization or timing beforehand, and the input link of mechanisms rotates with constant angular velocity. However, little research efforts have been put into pure path synthesis independent of parametrization. In this paper, we present an exact method that can efficiently and accurately carry out the pure path matching using arc length parametrization. Meanwhile, curve normalization combined with artificial neural network is used to decouple the design space, which leads naturally to a fast synthesis approach.