A machine tool for machining a part by on-head and continuous grinding tool profiling includes a part holder support driven into rotation by first driving means around a first axis in a vertical plane, a machining system provided with a grinding tool for machining the part, and a knurl for profiling the grinding tool. The first driving means are incorporated into a cradle driven into rotation by second driving means along a second axis perpendicular to the vertical plane. The machining system includes a bearing structure translationally mobile along three axes equipped with a main spindle for rotating the grinding tool, and a rotating device bound to the bearing structure and provided with a secondary spindle integral with the knurl moving around the axis of rotation of the grinding pool.