We (me anyway) are accustomed to thinking of gears as being circular.
However, pairs of unlikely looking gears matched to each other can remain in
mesh throughout a rotation cycle, just as circular gears do, but impart a
wide range of useful relationships between the input and output parts. eg
linear forward motion to a slider with quick return, stop and dwell motion
etc

This company provides a wide range of non-circular gears.
Interesting examples provided.

        http://www.cunningham-ind.com/

____________________
ref from Ken Mardle.

SAMPLE

Elliptical Gears:        An ellipse is defined by a set of points in a
plane, such that the sum of the distances from two fixed points - the foci -
to any point in the set is a constant. This enables elliptical gears cut
about their foci to run at a constant center distance. The velocity ratio
resulting from elliptical gears varies between 1/K and K during one cycle of
speed change, where K is the maximum gear ratio. Multilobe gears can be
derived from unilobe gears. In appropriate situations, elliptical gears may
be cascaded to obtain varying speed-change characteristics, giving an
effective ratio of from 1 to K^2 . Bilobe gears (oval gears) have been used
in flowmeters and pumps. Using precision elliptical bilobe gears, flowmeters
can have good linearity over a wide range of flow rates and viscosities

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