- This is a mock-up of
a type of belt drive called a crowned pulley. And it behaves in a really
counter-intuitive way. It's worth disambiguating the
word pulley at this point. Like when you think of the word pulley, you think of that device
that redirects force or multiplies a force, for
example, a snatch block. - Snatch block! - This isn't the snatch
block type of pulley. - Snatch block. (equipment clangs) - It just so happens that
in the world of belt drives this part and this part
are called pulleys. The thing that distinguishes
a crowned pulley is this curved profile here. what's surprising and counterintuitive about the crowned pulley is
that the band doesn't slip off. Like if I place the band
off center like this, you would expect that
when I start to turn it, it will slip further and further until it leaves the pulley altogether. Like if I pull a rubber band
against an inclined surface, it slides down the incline. But let's see what happens
with the crowned pulley. (drill whirring) It's quite the opposite. The band moves back towards
the middle of the pulley. How can that be? This isn't just a curiosity. It's actually really useful. I asked Tom Lipton. If he had any machines
with a crowned pulley. He very kindly sent me this
video of his belt sander. You might recognize Tom from
a collaboration I did with him on air bearings. Link to that video and his
channel in the description and in the card. It's worth just checking our intuition. Why do we think the rubber
band should slip off? Well, rubber bands are stretchy. When you pull them, they pull back. You feel a restoring force. If you'll permit me to
anthropomorphize the rubber band, when you extend it, it
wants to be short again. If you won't permit me to
anthropomorphize the rubber band, let's say that a shorter rubber band is energetically favorable. But either way you can see that as the rubber band
slips down the pulley, it gets shorter and that's
more energetically favorable. So we should expect that to happen. It's a bit like a ball
on the top of a hill. It's an unstable equilibrium. If you push it a little in one direction, it should roll all the way down the hill. Except that doesn't happen in this case. Our intuition is wrong. I want to say at this point that when you reach the end of this video you should go and check out
Matthias Wandel's channel. He made a video about
crowned pulleys 11 years ago. I don't tend to make videos
that have already been covered by other people unless
I can add something. I feel like I can in this case. But anyway, Matthias makes
some really interesting builds and you should check out his channel. The link is in the card
and the description. To understand why the crowned pulley behaves the way it does, consider what happens to a
rubber band when you stretch it but only holding onto one edge. You'll notice that the band arches. This part ends up higher
than it was before. And you have a curve here and here. You can see on the crowned pulley that this edge is more
stretched than this edge. So we should expect the rubber
band to curve upwards here. It's very subtle because
the difference in stretch between the two edges is
quite small in this case, but it is there. Because of that upward
curve of the rubber band, when you turn the crowned pulley, it comes into contact with
a piece of rubber band that is higher than the rubber band that's already on the pulley, and so it slowly shifts upwards. Just to prove that it is a belt effect, here's a rubber band that
is as wide as it is thick. And you'll notice it
does eventually slip off. We should also expect the
opposite counter-intuitive effect. If the profile has a concave curve, the rubber band should
ride up one of the sides when we intuitively expect it
to be drawn into the middle. And look, that's exactly what we find. I actually think the bowing
effect is easier to see on this one. And just for completeness,
here's a thin elastic band in the concave pulley not doing a thing. One question we haven't answered yet is, why does the rubber band bow when it's stretched from one edge? Well, you know me, I like to build physical models of things, so I've created this network of springs. It's not a perfect
analogy for a rubber band because, well, it's a
discretization of the rubber band. Like a rubber band is a
continuum of springiness but we have discreet springs here. But in any case, when you pull on the top-most row of springs, eventually these two springs here begin to pull on the
second row of springs. And so now these seven
springs are being pulled into a straight line. And as that line of springs straightens it pushes up on these four springs, and those springs push upwards
on the top row of springs, and so they bow upwards. But actually, why are
elastic bands stretchy in the first place? Why do they pull back? Surprisingly, it's because of entropy. You might know that elastic
bands are made of rubber, which is a polymer. In other words, long chain molecules like these long chains of beads here. So this is a kind of
model for the polymer. You'll notice that all of
the chains are jumbled up just like in an elastic band
when it's not stretched. When you stretch an elastic band, you line up those long chains like this. So why isn't our model of an elastic band contracting when we let go? Well it's because our model
doesn't have any heat yet. Heat is just molecular jiggle. So I can add heat to this model just by jiggling the chains with my hands. And you'll notice that when I do so, the ends contract inwards
just like a rubber band. The reason atomic jiggle causes the chains to become jumbled up is because the jumbled-up
state has higher entropy and systems tend towards higher entropy. The reason the jumbled
state is higher entropy and the reason systems
tend towards higher entropy would require a whole video to explain. Fortunately, I've already made that video. The link is in the card
and the description. I hope you check it out. But isn't that cool? The reason an elastic band stretches back is because of an entropic force. - Snatch block! - It's not a snatch block. Right? I wanna tell you about a Blinkist feature that I've been using a lot more recently. Blinkist are sponsoring this video. Blinkist is an app that
does something remarkable. It condenses non-fiction
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Tim Harford's books a while back. He's got a new one now
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get 25% off full membership. The link is also in the description, so check out Blinkist today. Thank you to Mitia Oven
for the idea for this video and thank you to Patrick Heard
for the 3D-printed parts. The YouTube algorithm thinks
you'll enjoy this video next. So why not give it a try? Go on, try it. Try it. (upbeat music)
If you enjoy this, you'll also like: https://www.youtube.com/watch?v=y7h4OtFDnYE
This is how belt drives on old farm equipment work. https://www.youtube.com/results?search_query=steam+threshing This is also why any raised curb, mound, or barrier next to a highway is so dangerous. As soon as your tire touches it the tire will automatically want to steer up the incline and off the road.
My vacuum has this same thing. Always wondered why
But what about the snatch block?
I don’t want to believe this
Disappointed it isn’t a spinning orange at the end