Mechanism for Moving Thread Core of a Plastic Injection Mould

Yellow rack is connected to the movable half mold.
When the movable half mold moves, the rack pinion drive and the screw drive (blue screw and orange fixed nut) make blue shaft carrying the pink thread core rotate and translate. Thus the thread core is inserted into or removed from the plastic injection part (not shown).
The blue gear must has enough length to enable its meshing with the rack when the blue screw translates.
Thread leads of thread core and the blue screw must be equal.