Steve, as you surmise, the half-moon shaped 
expanders (#23) fit in the angled slots of the 
clutch shaft (the "screw #24") and when the 
star knob (#37) is tightened, it pulls the two 
expanders (#23) in and against the inside of 
the shoes (#22). These in turn push against 
the inside of the worm gear (#21). 

It has been awhile since I have been inside an 
apron but IIRC, the clutch pinion gear (#19) 
has two square-like projections on one end. 
These are the driving "dogs" of the clutch. The 
shoes (#22) fit on either side of these dogs. 

The coil spring (#20) pushes the inside of the 
clutch pinion gear (#19) and against the cross 
pin (#26) in the clutch shaft screw (#24). This 
gives pressure (to open) in the clutch by pushing 
the expanders (#23) away from the shoes (#22).

Remember, the worm gear (#21) is constantly 
turning (so long as the leadscrew is turning). When 
the clutch is disengaged, the clutch pinion gear (#19),
shoes (#22), expanders (#23), shaft (screw #24),
etc. are NOT turning with the worm gear (#21). 

When the star knob (#37) is tightened, the clutch 
shaft (#24) is pulled in. The expanders (#23) push 
against the shoes (#22) and force them outward, 
locking them with the worm gear (#21). These 
shoes (#22) in turn are mechanically engaged with 
the dogs on pinion gear (#19). So, with the clutch 
engaged, the clutch pinion gear (#19) is locked with 
the worm gear (#21) and in turn, will power the rest 
of the apron (depending on the selector lever on the 
apron).

The two pins (#26) are a later addition to the clutch. 
Or maybe I should say, when the clutch shaft (screw 
#24) was modified, the two pins (#26) became 
necessary. Older versions of the clutch shaft (screw 
#24) had 4 projections formed on the outside in two 
pairs (and hence no pins were necessary). Their pur-
pose is to keep the clutch shaft and expanders co-
ordinated with the shoes and give something for the 
coil spring (#20) can push against

Lastly, the "hair pin" spring (#25) is placed on the end 
of the clutch shaft (#24) and the ends are "tucked in" 
between the two expanders (#23). And the star knob 
retaining screw (#30) is screwed on (left hand threads).

Good Luck!
-Blue Chips-