Kinematics of the Ball Screw Mechanism

This paper studies the kinematics of the Ball Screw Mechanism (BSM) with the aim of developing a foundation for understanding the motion of the balls and their contact patterns with the contacting elements. It is shown that there is always slip between the balls and the nut or screw, and therefore, the no slip condition assumed in the BSM literature is not attainable. The effect of contact deformation on the motion of the balls is also studied and is used to develop the pattern of the constant sliding lines of contacts between the ball and the screw or the nut. The results have applications in efficiency analysis, design, wear analysis and finite element modeling of the BSM.