I am a complete nub, and am curious about Morse tapers, so I'm looking for an explanation of them
Welcome to the mechanical arts! There's a benefit to joining a shaft to a tool while keeping them exactly co-axial
(that way, if you keep the shaft from wobbling, the tool will also be non-wobbling), and many joints to rotating shafts are
improved by making one item a conical socket into which the other item is a conical plug. At sixty degrees apex full
angle, this is the familiar 'between centers' lathe workholding principle, and at smaller angles is how mills and
LeBlond lathes fit keyed toolholders and chucks for quickly dismounting. At still smaller angles (usually
specified in inches per foot) they become locking tapers, and that's where the old Morse Twist Drill
and Tool Company comes in.
Roughly making a conical socket, and (with the same setup) turning a matching exterior cone on a shank,
Morse tapers are so closely matched that the axial force of pushing them together, with the wedge-angle
advantage of the slight taper, is enough to put large pressures on the mating surface, and make a
drill (or other tool) never slip in its socket. Unlike other metalworking items, oil on a Morse taper is
a no-no.
Morse made these with simple tooling, in the absence of modern measurement, and that's why #1, #2, #3...
tapers are slightly different angles (they were aiming for 5%) on the order of 5/8 inch per foot. The
quality of drilled holes with a drill shaft and drill mated using these tapers was very good. So, the
original prototypes became standards (but not measurements of the prototypes, I mean the actual
century-and-a-half-ago manufactured models). The US adopted those standards (Bureau of Standards
presumably had the metal lumps in a case).
Drills getting stuck in the drill press was 'solved' by putting a tang on the small end, and slotting
the drill press spindle so that a wedge could be driven in to force the drill out.
In modern times, NIST has replaced the Bureau of Standards, and 'official' measurements of the
originals have replaced the metal lumps. It's still a viable standard, albeit not suitable
for robotic tool-swap.