A head for the continuous precision machining on three-dimensional bodies includes a fastening means to a flange of a machining equipment, having a first mechanical rotation axis, an intermediate means having a second mechanical rotation axis in series to the first mechanical rotation axis. The second mechanical rotation axis is orthogonal to the first mechanical rotation axis which intersects at a point of intersection. A terminal processing means has in series with the first and second mechanical rotation axes a third mechanical translating axis. The intermediate means has an arc configuration of a circumference with its centre at the point of intersection. The first mechanical rotation axis and the third mechanical translating axis are radially oriented to the arc.