Fourier series representation of the coupler curves of spatial linkages

In this paper, the three-dimensional Fourier series which can describe the coupler curves of spatial linkages are derived. Based on the geometric properties of one-dimensional and two-dimensional Fourier series, a geometric constraint conditions are proposed to establish the three-dimensional Fourier series. The geometric meaning of mechanism for the three-dimensional Fourier series is put forward. Finally, an example is given to show the feasibility and the validity of this approach.