Abstract: A rigid connector secured to the front end of the core of the flexible shaft of this invention has a front portion axially receivable in a noncircular well in a driving shaft of a driving device and has a radially projecting circumferential flange rearwardly adjacent to that portion. Secured to the front of its sheath is the rear one of two telescoped tubular parts, each of which has a counterbore that opens to the other and defines an internal annular shoulder. One tubular part is threaded into the counterbore in the other, and the flange is axially slidable in the counterbore in that one, between the shoulders. The front portion of the front tubular part is formed for detachable securement directly to a conventional fixed collar on the driving device.