Abstract: A novel analytical approach is presented to solve path synthesis problems for planar five-bar linkages with timing. Firstly, the planar five-bar linkage is decomposed into two dyads for the purpose of decoupling the design parameters of the linkage. The relationship between the design parameters of the linkage and the harmonic parameters of the path is obtained, based on which, the new synthesis equations with different transmission ration for planar five-bar linkages are established. A quartic equation is obtained by dialytic elimination. As a result, a general formula is derived for calculation of the design parameters of a planar five-bar linkage. The design parameters of two dyads are obtained with the general formula respectively. At last, all design parameters of the planar five-bar linkage are obtained. Two numerical examples are provided to verify the effectiveness of the proposed algorithm.

Key words: five-bar linkages, path synthesis, Fourier series, analytical approach