A Novel Analytical Method for Path Synthesis of Spherical Four-Bar Mechanism Based on Fourier Series

In this paper, a novel analytical approach for synthesizing a path-generation mechanism of spherical four-bar mechanism without any limitation on the number of precision points is presented. Compared with classical analytical methods, the novelty of the proposed method is that the synthesis equations were established based on the relationship between the design variables and the Fourier coefficients of the path instead of the displacement matrix. Based on the presented synthesis equations, the path generation problem of spherical four-bar linkages was reduced to solving two polynomial equations of low complexity. Moreover, a general formula was derived from the analytical solutions of the new synthesis equations, where the design variables could be directly calculated with the Fourier coefficients of the prescribed path. An example is provided to evaluate the efficiency and accuracy of the proposed method. The findings indicate that the proposed method is simple, efficient, and readily programmed.