PURPOSE: To quickly/reliably index a cutting tool to be polished by arranging an indexing means elastically supported to hold a release state of a spindle when deciding an angular position of the spindle, and arranging a second actuating means to lock the spindle to actuate this indexing means.

CONSTITUTION: A first actuating means B1 moves a roller 16 against a spring 43, holds the roller 16 in a state of being tightly pressed to a spindle 14, and releases the actuation by shaft directional displacement of the spindle 14. While an indexing means 53 to adjust an angular position of the spindle 14 holds the spindle 14 in a release state, the spindle 14 can be locked by this indexing means 53 by actuation of a manually releasable second actuating means B2.