The lower part of the frame (2) is joined at the rear to a vertical frame part (10) arranged in front of the seat back (5) and supported at the top of the back. The support frame may be clamped at the top to the pins (14,14') used to adjust the height of the headrest (15) and which home below into sockets in the upper part of the seat back. The two jaws (13,13') of the frame clamp can serve to clamp the pins in between jaw (13) being joined to frame via support element (12). The fixing part (6,6') at the front of the underframe may bear on the carbody guide rails (8,8') so as to swivel on this round axis (22) and thus join it to the underframe at the required angle. The underframe itself can swivel round a transverse joint axis (23) and lock onto the support frame at required angle. The jaw-connected (13) support (12) can otherwise swivel round axis (24) to lock onto frame at adjusted angle.