Abstract: The contact surfaces between a seat and a base member are planar. This base member defines a shouldered bore for a retaining plate connected to the seat by locking and unlocking screws. This seat is integral with a pivot which is in two parts, whereof one is slidingly mounted in the said plate parallel to its rotation axis, while the other is off-centered relative to this axis in order to support at least one central bearing for the table. These improvements are applicable to machine tools having a rotary circular table and a tool-holder spindle, whose axes must be brought into the same plane by precise regulation.