To prevent the rocking of a spindle in the radial direction and repeatedly position a center and a chuck in the radial direction with high precision by providing a split wedge section for supporting the spindle on a sleeve arranged between a cylinder and the spindle.

A center 2 is advanced by the exciting force of a spring 52 via a spindle 4, and a work W is held between the center on the spindle stock side and a chuck. A sleeve 3 is also advanced, a front split wedge section 31 is inserted between the tapered face 41 of the spindle 4 and a cylinder 1, and the spindle 4 is firmly supported along the cylinder 1. The front section of the spindle 4 can be supported on the cylinder 1 via the split wedge section 31 of the sleeve 3, the rocking of the front section of the spindle 4 in the radial direction is prevented, and the center 2 can be positioned in the radial direction with high precision.