Tool (10) for the precision machining of surfaces (F) optically active, in particular free form surfaces and toric surfaces on spectacle lenses (L), with a base (12) body which can be fixed in a tool spindle of a machine tool, an elastic membrane (14), having a machining section (16), below which is disposed a bellows section (18), whereby the membrane (14) is fixed in the body base (12) suitably shaped for rotary entrainment, a chamber of a pressure medium (20) delimited by the base body (12) and the membrane (14), which can be requested optionally via a channel (22 ) with a pressure medium to establish during machining of the surface (F) optically activated by the machining section (16) a pressure of machining, and a guide element (24) guided displaceably in the longitudinal direction the base body (12) which is connected activamen like the machining section (16) of the membrane (14), so that the machining section (16) is displaceable in the longitudinal direction of the guide element (24) and is fastened in the transverse direction relative to the element guide (24), although it can perform a tilting movement relative to the guide element (24) causing an elastic deformation of the gaiter section (18).
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