The nonlinear performance of a single-nut, preloaded ball screw actuator is analyzed in this paper. The study identifies the source of nonlinear torque in the ball screw and subsequently maps that torque into the nonlinear displacement response due to windup in the shaft. The study is complemented with an experimental verification using a small angle rotation fixture (ARC) to input very small amplitude angular displacements to the screw while measuring induced torque and displacements. The experimental results are obtained from a Precision Linear Optimization Testbed (PLOT) which was developed to study the ability of different actuator systems to provide long range motion with nanometer accuracy. The analysis is conducted for the case of no axial loading. The study shows that the nonlinearities in the ball screw originate in the rolling friction between the balls and the races which induces torque in the nut and subsequently windup in the shaft. It also shows that the torque can be deduced from a relationship of the torque between a ball spinning in a race.