An adjustable collet holder for use with a lathe is provided. The adjustable collet holder may include a set of hold down screws to hold it in place once adjusted. Adjustment may be achieved by adjusting multiple set screws to change both angular and concentricity orientations of a collet receiver relative to a body of the collet holder.

A tool unit includes a base that is mountable on and demountable from a first turret, a slider that is disposed on the base, holds a cutting tool in a state in which a direction of the linear cutting blade of the cutting tool is inclined with respect to a Z-direction by a predetermined angle when seen from an X-direction, and is able to move in a Y-direction perpendicular or substantially perpendicular to both the X-direction and Z-direction, and a drive transmission that is disposed on the base and is connected to a tool drive unit to move the slider.

A tool system includes a machine-proximal shank configured to be introduced into a driven tool receptacle and containing a device for transferring a rotating movement to be picked up from the driven tool receptacle. A tool-proximal shank is configured as a tool holder or to have a tool holder releasably connected thereto. A gear mechanism disposed between the machine-proximal shank and the tool-proximal shank is configured to transfer a rotating movement transmitted by the device in a reduced manner to the tool-proximal shank. At least one insert seat configured on the tool holder for receiving an interchangeable cutting insert is provided on an end face of the tool holder extending transversely to a longitudinal axis of the tool holder. A method for machining a workpiece is also provided.