Synthesis of coupler curves of linkage mechanism through Fourier series method

The article presents a unified approach for path synthesis of linkage mechanism. The geometric meaning of mechanism for Fourier series was put forward. The relationship between the harmonic component of the coupler curves and the basic dimensional types of linkage mechanism is discovered. Based on this relationship, the method of establishment of numerical atlas database is given. The derivation process of formula, which can compute the position for coupler point, real size and installing dimensions of the linkage mechanism, is presented. The problem of path synthesis of linkage mechanism is solved by the numerical atlas database and the formula. This paper takes the spherical four-bar mechanism as example to illustrate the analysis process and application of this method.