Disclosed is a tap driver for rigid tapping, which includes predetermined tension and compression factors to self-synchronize the tap driver. In the preferred embodiment, the tap driver includes helical coils imparted in the tap driver body which allow the attachment body to synchronize axially in response to a force of a predetermined magnitude imparted on the tap. An additional embodiment of this invention provides such a tap driver body wherein the body allows for lateral flexure and movement to compensate for feed error and location error.