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Re: Elliptical gear calculations

• To: mathgroup at smc.vnet.net
• Subject: [mg110654] Re: Elliptical gear calculations
• From: Fred Klingener <gigabitbucket at BrockEng.com>
• Date: Wed, 30 Jun 2010 08:09:37 -0400 (EDT)
• References: <i0cjlk$8a5$1@smc.vnet.net>

On Jun 29, 6:59 am, dean k <deaken.... at gmail.com> wrote:
> Through two identical elliptical gears rotating about their centers, I
> would like to calculate the torque and angular velocity ratios as a
> function of the rotation angle of one of the gears.  I'm not a
> mathematician, but an engineer working on a personal project I thought
> would be interesting.  It is quickly becoming more interesting than I
> expected
...
First thing to do is to look at Harry Calkins Demonstration on
elliptical gears.

http://demonstrations.wolfram.com/EllipticGears/

That'll illustrate the geometry of the mesh and it'll let you convince
yourself of the relationship between the gears. As a basis for your
model, download the code and have a look at it. Harry knows a few
things about Mathematica.

Then someone (maybe you or I) should redo the tooth profiles. :-)

Hth,
Fred Klingener