As Ian said, a spindle stop for a lathe is just a gizmo that acts as a position stop for parts held in the lathe chuck (which is why it's also called a chuck depth stop), so parts can be turned without resetting for each one.
Mine isn't as flash as Harold Hall's, but does the job. It was based on a design in David Fenners Mini Lathe book, using whatever off-cuts were around the workshop at the time. I mostly use it for turning axles to length and also turning the axle journals and wheel seats. It also gets used when making frame spacers.
Starting from the right, the cylindrical pad is the actual stop and sits in the lathe spindle behind the chuck. It is screwed onto a length of allthread and fixed with a locknut. The next cylindrical part to the left is a spacer that is a sliding fit in the spindle bore, so the pad can't flop around. It also has a locknut. The stop pad is usually up in the morse taper seat, so has to be sized to fit through the small end of the taper.
The three parts on the end at the left make up an expanding arbor that locks the whole device in the spindle bore. The arbor locking bolt is drilled and threaded for the allthread so it can be screwed in and out to position the stop. There's a locknut on the all thread out of sight behind the locking bolt to keep it in position once set.
The only critical dimensions are the o.d. of the spacer and the o.d. of the mandrel as they have to be a sliding fit in the spindle bore.
Since I work on the KISS principle when it comes to jigs and fixtures, it isn't particularly pretty, but you can't see it when fitted in place and it works.
Regards,
Graeme