The authors attempted to apply traction drive to a constant-speed servomechanism for Numerically Controlled (NC) machines. High-precision servomechanisms require high-resolution encoders to detect rotary position, whereas conventional high-resolution encoders cannot rotate at high speed. Therefore, the authors attempted to solve the problem of resolution and maximum rotary speed using a nonsinusoidal-wave quadrature Phase-Locked Loop (PLL). Using this nonsinusoidal-wave quadrature PLL for interpolating the tracking error, a very high-resolution detection of rotary angle at high-speed rotation was achieved even when using inexpensive encoders whose output is nonsinusoidal wave. Traction drive damps the high-frequency torque ripple, but transmits torque ripple of low frequency. Most of the torque ripple of low frequency is due to the eccentricity of rollers. As the rotary speed of rollers becomes high, the torque ripple has a frequency at which it cannot be eliminated either by traction drive or feedback control. Because the mechanism of torque ripple is very complicated, it is difficult to compensate by detecting roller eccentricity. Therefore, the authors used repetitive control to reduce the position error associated with roller rotation, and obtained high-accuracy rotation in the experiments. In this paper, the interpolation method of tracking error using a nonsinusoidal-wave quadrature PLL and the reduction method of tracking error using repetitive control are presented.