Abstract: The geometric meaning of mechanism for the Fourier series is put forward. A brief uniform mathematical description of the coupler curves is established. The harmonic component of the mathematical expression is analyzed by using the Fourier series theory. 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 given. A unified approach for path synthesis of linkage mechanism is presented. The spatial linkages are taken as examples to illustrate the analysis process and application of this method.

Key words: Fourier series, Linkage mechanism, Numerical atlas, Path synthesis