Square and Elliptical Gears

[Adam Y.]

So anyone care to explain to me what is special about square and elliptical gears? I know the gear ratio must be chaning but I want to know how. Also, please do not say that there is no such thing because there is. I saw it in a musuem.

[ahecht]

Square and eliptical gears are special because you can not only get dynamic ratios, but you can also get motions that you would normally need a linkage for.

Basically, a non-circular gear set works as follows:

If you have any two moving bodies, you can always define what are called "instant centers", which is a point that both bodies appear to rotate about in that instant. If you then plot the path that the instant center takes as the bodies move, you have a centrode.

Now, if you have a four bar linkage, you have two centrodes (since each centrode is defined by an instant center for two moving bodies). If you follow the logic though (which can be a bit complex without a further understanding of kinematics), you will see that if you make both centrodes into physical objects and roll them against each other, you will get the exact same motion and variations in angular velocity and mechanical advantage that you got from the four-bar linkage.

If your linkage had two fixed points (as most do), your non-circular gear set will also have two fixed points, which you can use to put a shaft through.

A side effect of all this is that, since circualr gears are just special cases of non-circular gears, that all gear systems are actually four-bar linkages in disguise. I know that this has probably not helped at all, and to understand it, you would probably need to take a course in kinematics. Perhaps someone else can explain it better...

[Arefin Bari]

this website tells you what a elliptical gear is... go down to page 5... also this
has description and examples too... check it out...

[Al Skierkiewicz]

Originally Posted by Adam Y.

So anyone care to explain to me what is special about square and elliptical gears? I know the gear ratio must be chaning but I want to know how. Also, please do not say that there is no such thing because there is. I saw it in a musuem.

Adam,
I see you are from Long Island so I don't know if you have been to the Museum of Science and Industry in Chicago. They have several unusual gear clusters on display in the stairwells. There are square, elliptical, and I believe triangular gears as well as linear motion convertors. If this is the exhibit to which you are referring, the gearsets shown are for demo and are not practical. As you have pointed out the ratio is variable as the the two gears mesh at different diameters as they rotate. The noise output is very high and the engagement clearance seemed to be very high as well, so backlash was pretty bad. The demonstrations were prepared for the Chicago World's Fair in 1933 according to the museum site. I know they have been on display since the 1950's.
Is it possible these are the gears you saw?

[Adam Y.]

There are square, elliptical, and I believe triangular gears as well as linear motion convertors.

The exhibit had a linear motion converter also but no triangular gears. They also had some type of gear set called scroll gears.

I see you are from Long Island so I don't know if you have been to the Museum of Science and Industry in Chicago. They have several unusual gear clusters on display in the stairwells. There are square, elliptical, and I believe triangular gears as well as linear motion convertors. If this is the exhibit to which you are referring, the gearsets shown are for demo and are not practical.

I have never been there but it sounds interesting. The museum exhibit Im talking about is in Boston. They also have an extremely large assortment of linkeages and engineering devices on display like the geneva mechanism. Im not sure how old the exhibit is but it does seem fairly worn. I can't even read some of the devices name. The only thing that fascinated me about this is that they really didn't give an explanation why the gears are rarely used and trying to count the changing revolutions of an gear is impossible by eye.

[ahecht]

Originally Posted by Adam Y.

The museum exhibit Im talking about is in Boston. They also have an extremely large assortment of linkeages and engineering devices on display like the geneva mechanism.

I've seen that exhibit as well, and it is pretty neat, although most of the stuff there was designed for show. There is also an interesting CVT design there (using a wheel on a disk).

The main reason that non-circular gears haven't been used is that they are very hard to design and make without the help of computers and CNC machines. Unlike gears, you can't just use a single gear cutter to cut all the teeth, since each tooth is a different shape.

[Holtzman]

Ovalized sprockets have made there way into the cycling community. Recently, U.S. Cyclist Bobby Julich used an unusual shaped chain ring to win the bronze medal in the Athens Olympics. For cycling, the odd shaped chain ring is designed to take advantage of the greater power produced in the down stroke of a cyclists pedaling action.

Since the motors in the KOP obviously do not produce different power outputs within one revolution, these ovalized chain rings don't offer any realistic purpose for a FIRST robot, that I can think of anyway.(although I'm sure someone can come up with something wacky...ie pneumatically powered crankshaft

[patrickrd]

I've always found square and elliptical gears, and similar mechanisms amazing. I'm pretty good with geometry but I don't know how people figure out the shape of the teeth on those types of things.

One of the great (way under-known and under-rated) things that Cornell University has is the Reuleaux Collection of Mechanisms and Machines. I lived in the mechanical engineering department; everyday I would walk by display cases of hundreds of mechanisms, most you'd never even think of if you spent your entire life trying... Several nobody has figured out what they are useful for at all. Anyway basically Reuleaux (French, I believe) spent much of his life designing and building (all made by hand) this collection of mechanisms... Gears, linkages, etc... And eventually the collection was obtained by Ezra Cornell sometime at the turn of the 20th century. Given a desired input and output (linear or rotary, dynamic speed or constant), you can probably find a mechanism there that does what you need, or you can combine them to get a new mechanism. They're in the process of putting the entire library online with 3d models and videos, so definately check it out:

http://kmoddl.library.cornell.edu/model.php

And if you ever visit Cornell's campus, walk through the second floor of Upson Hall to see them all for yourself. Also, there are some cool ones (but not quite as cool as the Reuleaux collection) at Boston's museum of science.

There's even a mechanism that could be used to machine an almost perfect square hole

[JVN]

Coolest application of elliptical gears I've ever heard of:

One Christmas, the engineers at DEKA constructed a clock for Dean Kamen made from elliptical gears.

The result?
The clock moves slower during the 8 hours of "work day" than during the rest of the day (during which time it speeds up to compensate).

Hilarious.
The perfect gift for ANY boss.

[Al Skierkiewicz]

Originally Posted by patrickrd

I've always found square and elliptical gears, and similar mechanisms amazing. I'm pretty good with geometry but I don't know how people figure out the shape of the teeth on those types of things.
They're in the process of putting the entire library online with 3d models and videos, so definately check it out:

http://kmoddl.library.cornell.edu/model.php

I checked this out and it is very cool! Thanks Patrick!