A friend of mine used to work for a firm making
labelling machines.  They had to build one to put a
label on a bottle with a wide oval shape (it was for
some sort of cosmetic, like hand-cream) where the major
axis was about 4x the minor.

He discovered (although I'm sure other people knew
before) that a pair of same-sized (circular) gears
mounted eccentrically and properly meshed have an
overall 1:1 ratio per revolution, but the movement of
the output is non-linear in relation to the input within
each revolution.  It was just what he needed to rotate
the bottle in time with the feeding of the label onto it
(that is it rotated the bottle to give a linear feed of
the circumference past a given point despite it being
non-circular).

Cheers,

Howard Winter
St.Albans, England

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