A 3D probe measuring instrument, in particular for probing work pieces in machine tools, comprising: a housing; a probe arm protruding from the housing and carrying a probe tip, the probe arm being displaceable relative to the housing in the direction of a measuring axis and pivotable to all sides around the measuring axis by means of a first universal joint; a probe lever connected to the probe arm and having a joint head which is formed at its end facing the probe arm and has an outer control surface which is rotatably supported on an inner control surface of the housing to form the first universal joint for pivoting the probe arm, wherein the probe lever has at its end facing away from the probe arm a further control surface for a second universal joint; and a measuring device for detecting a value characterizing the displacement and/or pivoting of the probe arm, wherein the measuring device comprises an elongated toothed rack of a gear mechanism which is oriented along the measuring axis, slideably mounted and coupled to the probe lever via the second universal joint, wherein the toothed rack carries a coupling element which is displaceable together therewith, wherein the coupling element is a separate component from the toothed rack, which is detachably mounted on a front end of a toothed rack, or is integrally formed on the toothed rack, wherein the coupling element has a control surface of the second universal joint which cooperates with the further control surface in order to couple the probe lever to the toothed rack, and wherein the probe arm, the probe lever and the toothed rack are arranged centrally to the measuring axis in the rest state. a housing; a probe arm protruding from the housing and carrying a probe tip, the probe arm being displaceable relative to the housing in the direction of a measuring axis and pivotable to all sides around the measuring axis by means of a first universal joint; a probe lever connected to the probe arm and having a joint head which is formed at its end facing the probe arm and has an outer control surface which is rotatably supported on an inner control surface of the housing to form the first universal joint for pivoting the probe arm, wherein the probe lever has at its end facing away from the probe arm a further control surface for a second universal joint; and a measuring device for detecting a value characterizing the displacement and/or pivoting of the probe arm, wherein the measuring device comprises an elongated toothed rack of a gear mechanism which is oriented along the measuring axis, slideably mounted and coupled to the probe lever via the second universal joint, wherein the toothed rack carries a coupling element which is displaceable together therewith, wherein the coupling element is a separate component from the toothed rack, which is detachably mounted on a front end of a toothed rack, or is integrally formed on the toothed rack, wherein the coupling element has a control surface of the second universal joint which cooperates with the further control surface in order to couple the probe lever to the toothed rack, and wherein the probe arm, the probe lever and the toothed rack are arranged centrally to the measuring axis in the rest state.