Geometrical way for describing body motion and equations of relationships between geometrical and kinematical parameters

The geometrical/conjugate surfaces way for describing body motion by a pair of conjugate surfaces of point conjugation is detailed. The equations of relationships between the parameters of the geometrical/conjugate surfaces way (geometric parameters) and those of the traditional way (kinematical parameters) are derived by using concepts from the theory of conjugate surfaces. The conjugate surfaces of line conjugation are investigated as the degenerated case of the point conjugation cases, and are appropriated to describe body motion of one dof. The formula for determining the geodesic relative curvature of the instantaneous conjugation curve to guarantee line conjugation is derived and reported herein for first time. Both the line conjugation ruled surfaces and the axodes may be regarded as the special and singular case, respectively, of the general conjugate surfaces of line conjugation for describing body motion of one dof.