Apparatus for checking diametral dimensions of a pin, rotating about a geometrical axis, in the course of the machining in a numerical control grinding machine having a grinding-wheel slide carrying a grinding-wheel, with • a reference device adapted to cooperate with the pin to be checked, • a measuring device, movable with the reference device, • a support device for supporting the reference device and the measuring device, the support device comprising • a support element adapted to be fixed to the grinding-wheel slide, • a first coupling element coupled to the support element so as to rotate about a first axis of rotation parallel to said geometrical axis, and • a second coupling element carrying the reference device and coupled to the first coupling element so as to rotate with respect to it about a second axis of rotation parallel to said geometrical axis, • a guiding mechanism associated with the support device for guiding the arrangement of the reference device onto the pin, towards a checking condition of the apparatus, and • a control device for controlling automatic displacements of the apparatus from a rest position to the checking condition, and vice versa, characterized in that the guiding mechanism comprises a constraining linkage between the support element and the second coupling element, with • a third coupling element coupled to the second coupling element so as to rotate about a third axis of rotation parallel to said geometrical axis and spaced apart from the second axis of rotation, • a fourth coupling element coupled to the support element so as to rotate about a fourth axis of rotation parallel to said geometrical axis and spaced apart from the first axis of rotation, • the third coupling element and the fourth coupling element being connected to each other so as to mutually rotate about a fifth axis of rotation parallel to said geometrical axis. • a reference device adapted to cooperate with the pin to be checked, • a measuring device, movable with the reference device, • a support device for supporting the reference device and the measuring device, the support device comprising • a support element adapted to be fixed to the grinding-wheel slide, • a first coupling element coupled to the support element so as to rotate about a first axis of rotation parallel to said geometrical axis, and • a second coupling element carrying the reference device and coupled to the first coupling element so as to rotate with respect to it about a second axis of rotation parallel to said geometrical axis, • a support element adapted to be fixed to the grinding-wheel slide, • a first coupling element coupled to the support element so as to rotate about a first axis of rotation parallel to said geometrical axis, and • a second coupling element carrying the reference device and coupled to the first coupling element so as to rotate with respect to it about a second axis of rotation parallel to said geometrical axis, • a guiding mechanism associated with the support device for guiding the arrangement of the reference device onto the pin, towards a checking condition of the apparatus, and • a control device for controlling automatic displacements of the apparatus from a rest position to the checking condition, and vice versa, • a third coupling element coupled to the second coupling element so as to rotate about a third axis of rotation parallel to said geometrical axis and spaced apart from the second axis of rotation, • a fourth coupling element coupled to the support element so as to rotate about a fourth axis of rotation parallel to said geometrical axis and spaced apart from the first axis of rotation, • the third coupling element and the fourth coupling element being connected to each other so as to mutually rotate about a fifth axis of rotation parallel to said geometrical axis.