Theoretical analyses of the kinematics of a single-nut double-cycle ball screw operating at heavy axial loads are undertaken in the present study. An adjustment in the preload can be achieved by generating an offset λ on the center pitch of two ball tracks. The critical load, which is very slightly higher than the preload, becomes the border of two axial load subregions. The contact kinematics for the axial load applied in each of these two load subregions are analyzed for these two ball tracks. Several parameters pertinent to the frictional forces and positions of pure rolling points formed at the ball-nut contact areas, and the mechanical efficiency of a ball screw can thus be derived for these two axial load subregions. The theoretical frictional forces and thus the resulting mechanical efficiencies obtained by considering the oil lubrication were obtained, and the mechanical efficiency was confirmed with experimental data. The frictional behavior formed at the left ball-nut contact point is quite different from that formed at the right ball-nut contact point. As to the left ball-nut contact point, the friction coefficient is elevated to the peak value as the axial load reaches the critical load. As for the right ball-nut contact point, the friction coefficient is always lowered by increasing the axial load. The mean oil thickness and contact deformation were considered into the calculation of pure rolling points established a well analytical model. The positions of pure rolling points existing at each contact regions show the sliding-rolling situations of contacting components of a ball screw and are varying with the normal load, and the rotational speed.