PURPOSE: To mechanically machine a concave spherical surface having a minute diameter by connecting a minute diameter needle like tool to a rotary shaft, making the tool rotate round its own weight to be its own axis in an inclining posture under a light load caused by its own weight to be brought in contact with a work, so that the tool and the work can make mutually relative rotation.

CONSTITUTION: The top end of a needle like tool 24 made of metal, ceramics, synthetic resin, etc. suspended from a rotary shaft 15 is brought in slight contact with the center of the cavity of a work W to be machined and held at the work W to be prevented from sliding by means of a drill-like sensor and a guide plate. At this time, a thread like connecting body 20 made of silk yarn, cotton yarn, hemp yarn, nylon yarn tungsten wire, etc., is suspended nearly vertically, the axis of the tool 24 is aligned with the center of the work W, and when the rotary shaft 15 is rotated, the yarn 20 is twisted but when the twist of the yarn reaches its limited state, the yarn starts to rotate round its own axis to make the tool 24 rotate round the circumference of its own axis. Hereupon, if a head 10 is slightly lowered in a Z direction, the tool 24 is inclined relative to the work W and is rotated round its own axis while applying a slight load caused by its own weight to the work W round the inclined axis and the work W is relatively rotated like an arrow mark so that is concave spherical face may be machined.