Hi, I'm Henry Segerman, and we'll get to this thing later on.
But first, let's look at gears.
There are lots of different kinds of geared mechanism.
Here are three of them: spur gears, bevel
gears, and this is a worm drive.
In all of these mechanisms, there are two "gear" parts and a third
"frame" part that the gears are attached to and rotate relative to.
The difference between these three types of mechanism
is the position of the axles around which the gears rotate.
A pair of spur gears rotate in a common plane,
so their axles are parallel to each other.
In bevel gears, the axles are at an angle
and meet at a point, here.
In a worm drive the two axles are skew
relative to each other, neither parallel nor meeting at a point.
There are lots of
other kinds of geared mechanisms with skew axles.
This is "Triple helix", a design I made with Saul Schleimer.
Ignore one of the three gears for the moment - in fact, I'll take it out.
Then we have two gears rotating in a frame.
The gear axles are skew relative to each other, like in the worm drive.
But here the two gears rotate
at the same speed, while in the worm drive one is much slower than the other.
All right, what else can we do beyond gears that rotate?
There are three basic kinds of motion: rotation,
translation (or sliding), and screw motion, which is a combined motion
of a rotation together with a translation along the axis of rotation.
The gears we've seen so far all move by rotating relative to their frames.
What if you want one of the gears to translate instead?
This is what the rack and pinion mechanism does.
It's another kind of gearing with two gears mounted to a frame.
One of the gears, the "pinion" is just another spur gear,
while the rack is a kind of gear that translates rather than rotates.
Okay, so that's a rotation with a translation.
And we already did two rotating gears.
What about a geared mechanism that has two translating gears?
Here's another design I made
with Saul Schleimer which we call "Borromean racks".
If you hold one of the three rack parts fixed and call it the frame,
then the other two parts
translate relative to the frame and moving one moves the other.
So this fits the bill.
It's a translate/translate geared mechanism.
I don't know of any examples of this
kind of mechanism used in a real-life tool or industrial application,
but do let me know in the comments if you know of one.
I wouldn't be surprised if there are puzzle mechanisms
that work like this - again, I'd love to hear about them.
To be clear on the rules: It should be a one-degree of freedom mechanism
with three parts where the two gear parts both slide relative to the frame part.
We can make a table of the different kinds of geared mechanism.
In the rotate/rotate box we have spur gears,
bevel gears, worm drives and triple helix.
The rotate/translate box has the rack
and pinion and the translate/translate box has Borromean racks.
Let's expand the table out to include screw motions.
Now I know of two common mechanism used in everyday tools
that fit into the rotate/screw and the translate/screw boxes.
I'll show you what they are in a minute,
but if you want to see if you can figure them out for yourself,
pause the video and comment below with what you think the tools are.
Be careful though.
Just because something looks like a screw
doesn't mean that it moves with a screw motion.
In the worm drive, for example, the worm gear certainly
looks like a screw, but it rotates relative to its frame.
It doesn't follow a screw motion.
Okay, ready?
Here's the first one. A corkscrew.
The frame is this red part.
And then there's the cork extractor and the two levers.
Let's ignore one of the levers to get down to three parts.
Here the extractor and the lever are the two gears that work inside of the frame.
To really make this work, we also need a cork for the screw to go into,
that needs to be fixed relative to the frame, but I'll just use my hand.
The cork extractor follows a screw motion relative to the frame
as it screws into the cork,
and this causes the lever to rotate relative to the frame.
So that's a rotate/screw geared mechanism.
It's interesting, though, that when you come to pull the cork out,
you rotate the levers down and the cork extractor slides out.
It does not screw out.
So depending on which part of the cork extraction process you're in, you're
either doing rotate/screw on the way in or rotate/translate on the way out.
Now, for the translate/screw box in the table,
we have an adjustable spanner.
This one is a little subtle.
If I hold the handle still, then as the worm gear rotates, the jaw slides.
So this looks like it should be a rotate/translate gearing.
And it is, if we take the handle to be the frame of the mechanism.
However, we could instead take the jaw to be the frame.
If I hold the jaw still, then as I move the mechanism, the handle slides
relative to the jaw and this time the worm gear follows a screw motion.
So we have a translate/screw gearing.
Going back to our table, again this one fits into two of the boxes,
although this time we're not using the tool in a different way,
we're just choosing a different one of the three parts to be the frame
of the mechanism.
Okay, now for the final box, the screw/screw box.
For this one, I don't know of any examples of this kind of gearing anywhere,
so that's why I had to make one.
Again, please leave a comment if you've seen anything else that does this.
The frame is this cylindrical cage into which the two gears screw.
Their teeth engage, so when one gear moves, so does the other.
Each gear is like an ordinary rack
from a rack and pinion mechanism, that got twisted into a helix.
Two ordinary racks wouldn't make a very interesting mechanism
since they would just push each other in the same direction.
With the twisted helices though, the two gears mesh at a place where their teeth
are both moving in the same direction, but then they diverge afterwards.
The same thing happens with the rack and pinion, and with spur gears.
The teeth are pushing in the same direction at one point
and then they diverge and head off in different directions.
And I think you could drive these helical gears with a suitable spur gear or rack
to get more examples of rotate/screw and translate/screw geared mechanisms.
Usually the shapes of the teeth on spur gears, racks, bevel gears and so on
are precisely designed to transfer force in the most efficient way.
I didn't do anything that clever with these.
The tooth shape is just based on a sine wave,
but it seems to work well enough for this demo.
I imagine that there could be a fun research project in
working out what the shapes of the teeth on these helical gears really should be.
Alright, that's it.
Thanks for watching.