Abstract: An apparatus for preventing circumferential overspeeding of a grinding wheel is provided in which first and second rejection members, pivotably carried respectively on a motor base and a wheel head, are connected with each other through a transmitting mechanism. The mechanism is arranged to prevent, by the first rejection member, the attachment of a large diameter pulley to a motor on the motor base when a grinding wheel with a maximum useable diameter, or one having a diameter greater than a predetermined pulley exchange diameter, is on a wheel spindle of a wheel head, without interference with the second rejection member. A parallel motion mechanism is incorporated in the transmitting mechanism so that the same may transmit pivotal movement of the first rejection member to the second rejection member without being affected by movement of the motor base on the wheel head.