An auxiliary device for a machining tool that converts a standard rotary machining tool into an oscillation-machining tool. The device has a chuck, or other workpiece gripping device, at an upper end of a shaft. The shaft may be rotated around an axis parallel to the axis of the rotary machining tool and may be oscillated along the rotary axis. The degree of oscillation may be adjusted dependent on the length of the surface to be machined.