An engagement mechanism for a driver instrument (24) can comprise a mobile shaft (121, 221), a collet (122, 222) and an angled engagement interface (124; 136A-D). The mobile shaft comprises a first shaft portion (128, 228) located at a proximal end of ON the mobile shaft, a driver portion (126, 226) located at a distal end of the mobile shaft, and an internal passageway (180, 280) extending from the proximal end to the distal end. The collet comprises a second shaft portion (134, 234) disposed within the passageway at co the first shaft portion, and flexible arms (132A-D, 232A-D) extending from the second shaft portion within the driver portion. The angled engagement interface is positioned between the driver portion and the flexible arms, and is configured to permit the driver portion to push or deflect the flexible arms radially inward when the first shaft portion is slid along the second shaft portion. The angled engagement interface can include bearings (224A-D) and a frusto-conical contact surface (124; 282A-D).