The following are some examples of elliptical drives built for bicycles or trikes.

Kingsbury K-Drive

A recent version is shown below (photograph by gNick Green):

K-drive (Click to see larger image)

Some History

Perhaps the reason there is no patent on the K-Drive is that in 1890 already, an almost identical mechanism had already been described:

Vietor Drive (Click to see larger image)

This illustration is from Fahrrad & Radfahrer by Wilhelm Wolf published, 1890 in Leipzig (reprinted in 1988 by Harenberg, ISBN 3-88379-106-1):

Title Page (Click to see larger image)

According to the description in the above text, the inventor was a certain Mr. Vietor from Osnabrück. It is stated that this kind of mechanism will allow the legs to move naturally as in walking. The following illustration, from the same source, indicates that apparently this was really the intention, with the "rider" almost standing upright in the pedals:

Vietor Trike (Click to see larger image)

Other examples