Shifting and translation blocking system for a rod, especially for car head-rests

The assembly (1) for adjusting and locking a sliding rod with notches consists of a sleeve (5) that receives the rod, and a lock with a mobile component (12) associated with the sleeve, a locking element (33) that engages with a first notch in the rod, a second mobile component (14) and locking element (34) to engage with a second notch, and a spring (32) for relative movement of the two components (12, 14). At least one of the locking elements (33, 34) can be made in one piece with a mobile component (12, 14), which can be fitted with a reinforcing member.