The relative motion between the gear teeth of harmonic drive belongs to the spatial conjugate motion under the spatial elastic deformation condition of the flexspline shell, and its spatial conjugate theory is the core factor that determines its motion and force transmission and comprehensive performance. For this purpose, a spatial conjugate motion model for harmonic drive is proposed based on adjoint approach. By means of the semi-moment theory of the shell and the kinematics between the components, the ruled surface motion equation of the neutral layer generatrix of the shell is established. According to the quasi-fixed line condition and the ruled surface motion of neutral layer generatrix, the axode equation of the gear teeth in harmonic drive is derived. The internal relationship between the axodes and the conjugate tooth surfaces is studied by the adjoint approach. Taking the axodes as the original surfaces and the tooth surfaces of the circular spline / flexspline as the concomitant surfaces, the conjugate condition formula of the spatial concomitant motion of the rigid tooth surface is derived, and the conjugate model of the space concomitant motion is formed. The relative motion between the meshing points is transformed into the spiral motion around the instantaneous axis, and the relationship between the instantaneous axis and the normal vector of the meshing point is analyzed. The spatial conjugate motion is degenerated into the planar conjugate motion, and the constraint properties of the spatial conjugate and planar conjugate are analyzed. The plane of action is constrained as a quasi-fixed surface, and the spatial conjugate motion characteristics under the condition of quasi-fixed surface are analyzed. Finally, through the simulation analysis of an example, it can be seen that the plane motion of the rigid gear teeth of harmonic drive is a special motion after the degradation of spatial motion, and the spatial motion after the degradation of harmonic drive is consistent with the plane motion, which verifies the correctness of the spatial conjugate model and motion characteristics described in this paper.