This is not my shaper but it is a nice picture!
This is a hand shaper and it is the same as the motorised one I have and the picture nicely shows the area of concern.
The swivel head will not lock securely, you can see the square headed stud at the top and a slotted head grub screw on the side.
I originally thought there was something terribly worn in this area but careful cleaning and resetting the slide gibs solved that. The problem now is that the head will often rotate slightly under load which of course spoils the cut.
Loosening the square head and backing the grub screw allows the head to be pulled out, it is a nice snug fit with no sign of wear. There is a small 'vee' grove around the inner piece which is what the grub screw (which is pointed) engages to keep the head in place. The square headed stud has a brass end on it which is rather odd as it too meets with the 'vee' grove which of course mangles the brass bit and does not get a good lock.
So I am a bit lost as how to fix this, maybe a chisel shaped brass piece which does not try to rotate as the stud is tightened? Something like John Bogstandard showed for his carriage lock?
This really is the only thing on this little shaper which prevents it doing good work, except I have not yet figured out how to set it up for every occasion.