A cutterhead of the kind described above includes a housing rotatable about a central axis and a spool is rotatably journalled in this housing.  An adequate supply of cutting filament is wound on the spool.  The free end of the cutting filament pulled off the spool is guided out of the housing through a housing opening.  The portion of the filament disposed outside of the housing is subjected to centrifugal force and constitutes the rotating cutting element with which grass or other vegetation is cut. 
The supply spool for the cutting filament is rotatably mounted in the housing and is provided with an indexing device which includes a blocking lever.  The blocking lever is pivotally journalled in the housing and has a switching arm which coacts with switching stops of a switching disc or a slide so as to cause the blocking lever to move out of its blocking position with respect to the switching stops of the spool and into a outer position wherein the spool is released.  The spool then rotates relative to the housing and a predetermined increment of wound cutting filament is released. 
In the known embodiment, the filament taken off the spool is guided around the pivotable blocking lever such that a filament redirecting location is formed at a spacing from the axis of the blocking lever.  The rotating cutting filament is subjected to centrifugal force and has a different magnitude dependent upon the cutting length thereof.  For this reason, the filament redirecting location defines a point of application for the centripetal force which acts in a direction opposite to the centrifugal force acting on the blocking lever and tends to move the blocking lever inwardly into its blocked position.  Since the mass of the indexing device is not changeable but only the mass of the free end of the cutting filament, the cutterhead described above will respond only to the mass of the free end of the cutting filament which, in turn, is directly a function of its length. 
In the known configuration, the blocking lever is configured as a one-arm lever and has a free pivotable end lying opposite the bearing axis.  On this end, the blocking lever has a section over which the cutting filament unwound from the spool is guided and thereby forms the redirecting location of the cutting filament on which a centripetal force acts in a direction opposite to the centrifugal force and this centripetal force tends to press the blocking lever inwardly into the blocking position with respect to the spool.  This free pivotable end of the blocking lever together with its redirecting element for the filament conjointly defines a switching arm which coacts with the switching stops of the spool in such a manner that the switching arm blocks the spool against rotation in an inner position and releases the spool in an outer position. 
It is a disadvantage of this cutterhead that its automatic readjustment is not always assured especially when the cutting filament is greatly worn down.  This makes it necessary for the operator to perform the readjustment operation manually especially when the remainder of the cutting filament is very worn, that is, greatly shortened.