A three-dimensional measuring device, comprising an arm having a free end provided with an interface body and a handle enabling an operator to point the measuring member at a zone of the object that is to be measured. The handle is secured to a fastener base having an end portion that includes a slideway extending transversely relative to the longitudinal direction of the handle in order to co-operate with a slideway of the interface body, the interface body and the end portion of the fastener support having both complementary abutment means so as to define a mutual engagement position of the slideways and also complementary locking means that oppose disengagement of the slideways, the complementary locking means including a control lever that is hinged to the end portion of the fastener base between an activation position for activating the locking means and an inactivation position for inactivating the locking means. |