PURPOSE: To apply cylindrical grinding concentrically accurately to the internal and external diameters of an optical connector part by holding a workpiece in the vicinity of its diameter with disks and rotating the workpiece.

CONSTITUTION: Since rotation of a spindle 20 is stopped, all the parts in a spindle surface plate 19 are placed in a stationary condition. Under this condition, because a main unit 6 is pulled by a tensile spring 16 toward a balancer 8, when disks 1-a, 1-b are sufficiently mounted to a spindle center 22 so that a workpiece 21 can be easily inserted, the workpiece is held by a tail center paired with both the centers. Then the spindle 20 is started to perform throwup- rotation in the counterclockwise direction. Next, when the rotation reaches a certain rotary speed, the main unit 6 is moved by its own centrifugal force toward the periphery against force of the tensile spring 16, and following this action, the disks 1-a, 1-b hold the workpiece 21 rotated in the counterclockwise direction. Next a grindstone approaches from the right to grind the workpiece 21 in the predetermined dimension.