> One interesting thing I've seen is that the drive sheaves (as on a tractor
> with a belt PTO) are often slightly convex in shape, not flat or concave
as
> I would expect.  Apparently that shape actually helps to keep the belt
> centered on the sheave?

The surface curve is called the "crown" of a pulley and it is a
self-centring device for the belt.   It does look exactly opposite what you
might expect, but imagine a canvas or leather belt stretched tightly over
the crowned pulley.   The centre of the belt will be in tight contact with
the surface but the edges of the belt will be somewhat relaxed and not
stretched so tightly because of the crown.   The belt will be slightly
distorted by extra tension in the middle.   As the pulley turns, if the belt
were to begin to move toward the right, the left side of the belt would
begin to tighten as it moves up over the crown.   The right side will become
even more relaxed as this happens.   With the left side so tense, it begins
to pull the belt back to the left.   Now, as the right side of the belt
starts to rise over the crown, it becomes the more tense part of the belt
width and the tension causes the belt to drift back the other way.   It is
sort of like steering a bicycle, pulling left then right to keep going
straight.  When I demonstrate starting up the mill for visitors, I love to
sling a belt on a big 5' pulley with only about half of the belt on the
surface, doing it quickly and then turning away to go to the "water gate"
control lever to start the mill.   The visitors worry and think I have made
a mistake of not noticing the poor belt placement and start to call out for
me to fix it as the pulleys begin to turn, and then the belt neatly climbs
magically up and over the crown and the whole place begins to sing the music
of happy machinery.

Flat pulleys rely on perfect alignment of the shafts, but crowned pulleys
are very forgiving.   Wouldn't it be nice if the crowned heads were that way
too.

Not meaning to be too picky, but a "sheave" is actually a pulley with a
concave groove in the circumference to contain the belting medium, such as a
rope.   It also refers to a grooved wheel that will ride on a track.   Of
course, a sheave is also a slice of bread and the act of back-turning or
backing up a boat.   Go figure.   Appearances aren't everything.

cp powered up in bc

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