Rotary Fourier transform spectrometers have many advantages such as high reliability, high spectral resolution and fast test speed etc. But when it scans optical path difference by uniform rotation, there is a nonlinear problem for the optical path. The nonlinear optical path difference scanning of a transmission Fourier spectrometer is analyzed. A mathematical model of nonlinear optical path difference is proposed. The optical path difference equation is established and the MATLAB simulation is carried out. When a rotating mirror is controlled to rotate at a constant speed by a speed feedback motor, the inhomogeneity of time can be obtained according to the established nonlinear equation. So the non-uniform sampling of time can be realized and accurate spectra can be obtained. Instead of using a stabilized He-Ne laser to trigger sampling, it can save cost and reduce the volume and weight of the spectrometer.