Designing rectangular gears

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In the book Five Hundred and Seven Mechanical Movements, Henry Brown shows a diagram of two rectangular gears (drawing #30) that when meshed together provide varying speed for the driven gear.

Anyone have any thoughts or references to a process for producing these gears?

covers the design and fabrication of elliptical gears. Similar issues I suspect.

From the drawing a least, it appears that each tooth is of consistent depth, so treating it as circular wouldn't really get it.

Just curious.

-jeff

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Hi Jeff:

Believe it or not, you can trace a tooth profile of almost any curve desired and then create a mating tooth that will drive with a smooth angular velocity. There is nothing special about an involute. As long as the common normal intersects the line of centers at a fixed point, the two tooth profiles are considered conjugate and the gears will mate with pure rolling contact. It just depends on how simple and interchangeable you want them to be.

Gears have been made in the past with several profile systems, the two standardized ones being the epicyclic and the involute. The involute, as you know, is generated by an unwinding "string" on the base circle; the epicyclic curve is generated by following the outer edge of a smaller circle rolling on the base circle. All modern industrial gearing is now of the involute type. Epicyclic gearing is used only in the manufacture of watch and clock gears. The biggest advantages of the involute system are ease of manufacture (an involute rack has straight faces) and the fact that a slight change in center distance will not affect the speed ratio between two gears.

OK, now lets talk about elliptical gears. The tooth profile of an involute gear could indeed be generated by wrapping a string around a "base ellipse", just like a circular one. And, in fact, this gear would mate with even an ordinary circular spur gear of similar pressure angle and pitch. Obviously since the base is an ellipse, the individual tooth profiles for each tooth will change depending on their location because the instantaneous radius of the base ellipse is not constant (as with an ordinary spur gear). For this reason it would be difficult to machine. It would probably require EDM machining, sintering, or extrusion.

I'm not sure what this rectangular gear you're talking about looks like, but I'm imagining that it is a rectangle with rounded corners. This would be an odd gear indeed. If the sides are straight they would be interlocking racks. Once they mesh you're screwed, since you lose angular driving power. A more practical (?) design would be with convex sides (like a TV screen). It would be the equivalent of several different circular spur gears. The convex sides would have their own pitch diameter and the corners would have another. As long as you keep the same diameteral pitch with all of them, you should have a perfectly good gear.

Don

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Thanks Don for the extremely accessible explanation.

The gears in question do indeed have teeth that form a rounded corner.

In the drawing I'm looking at, the left hand gear is cocked 90 deg to the right hand gear. They indeed appear to mesh fully as both complete a cycle. _ /\| | Hi Jeff:

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Only? Not quite true. I'm using epicylic gearing (actually cogged belt and sprockets) in my oval-turning lathe.

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How do you figure that this is epicyclic gearing? First of all, it's not even gearing, it's a belt and sprocket (gears drive other gears). And second, a timing belt pulley would technically require involute teeth anyway.

Don

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Its my understanding that anything with a 'sun' and 'planet' configuration is an epicyclic mechanism. Perhaps we are talking about two different things?

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Oh, I see what you're thinking of. I was referring to epicyclic gear teeth, not an epicyclic mechanism. This is an alternate tooth

*profile*. Instead of tracing the tooth shape with an unwinding string, like involute teeth, the profile is generated by a circle rolling around the base circle. It's used in clock work because you can have much fewer teeth on pinions without "undercutting".

Don

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I can't give you a reference, but I've seen actual physical gears of this description someplace--(perhaps the museum of science in Boston, or the Exploratorium in SF?) Making them's not a lost art...

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"Jeff" wrote in news:nofbb.1101\$ snipped-for-privacy@twister.southeast.rr.com:

Try some net searching on the phrase "non-circular gears". One company that manufactures nothing but is

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configuration

So I was. Thanks for educating me. :)

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I have seen square gears in action (motorized) at a local science center. There is a web site that uses square gears as a logo:

I have seen the gears with several teeth on each side. The logo shows just 4 teeth per gear.

Jim Y

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I think the the tooth profile is called "Cycloidal" Epicyclic refers to a gear train

configuration

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I think the profile you described is called Cycloidal. Epicyclic refers to a gear train.

configuration

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No. A cycloid is a path generated by a circle on a straight line. An epicycloid is a path generated by a circle on a circle, which is how this tooth profile is produced. They have always been called epicyclic gears. Open up a book on gears some time.

Don

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