so I've got here a wooden case on some wheels you can see it rolls very
smoothly you can roll it back and forth
now if you assume these wheels are round well you'd be wrong
there are actually triangles so these are actually called reuleaux triangles
they're solids of constant width so if you can roll around on triangles just
like you can with circles then why have you been using circles for wheels for so
long well let me show you the problem with using these Rolo triangles as
wheels so let's find...so let's set the triangle like this and find the very
center of it the center from the top from the bottom I'm gonna say it's about
right there now watch what happens to that Center as it rolls so even though
this glass is staying at the same height watch what happens to that piece of tape
there so you'll notice that the piece of tape was actually moving up and down and
up and down as it rolled so if you were to follow the point of the triangle as
it rolled you'd find that it traces out a square but you'll notice that if you
point to the center of masses the triangle as it's tracing out that square
it moves in a circle so it moves up and down as it rolls normally we don't just
set wheels on the ground and then set something on top of them and have them
roll but we want to fix the wheels to the vehicle and so if we try to fix the
reuleaux triangles to the vehicle we have to set an axle through them and the
problem is is that there's not a constant center of mass at a constant
height that height is always changing so that means if you're gonna hook an axle
to it that axle has to be able to move freely up and down and up and down in
order to keep the top fixed at a fixed height
now when these wheels are just loosely rolling on the ground that's fine
because there's no axle having to hold them in place but if you want to put an
axle through it you got to make sure that it can loosely move up and down and
I've actually seen a YouTube video of someone who made a reuleaux triangle
bike and basically they have the axles able to adjust up and down as it was
rolling and so the guy on the bike was just moving smoothly I'll put a link in
the description to that video so it definitely is possible to make wheels
out of triangles that rolls smoothly but the problem is you have to have more
complex axles for them now these reuleaux triangles don't make great
wheels because the center of mass moves in a circle like that as it rolls it
moves up and down but one cool thing about that is that means that you can
actually change a rotational axis a fixed rotational axis into reciprocating
motion like this so notice in this mechanism here is changing this
rotational motion into a basically a square motion notice how it moves in an
exact square whereas if you were just to use a wheel or something it would move
in a circle now if you want to draw a two-dimensional reuleaux triangle it's
pretty easily actually you just start with a regular triangle and then get
some circle and just connect two points of the triangle here and then connect
these two points
and then these two points
and you have yourself a reuleaux triangle now what's interesting about
these curves of constant width is you don't have to start with the triangle to
make them you can start with a shape with any number of sides and if you want
to make a shape that doesn't have its center of mass changing position then
you just have to increase the number of sides as your number of sides approach
infinity then your center of mass stays right in the center and that's called a
circle or a wheel so it turns out it is actually a good idea to use a circle for
wheels hey everyone thanks for watching another
episode of the action lab I hope you liked it if you did don't forget to
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and thanks for watching and I'll see you next time