I don't know about the wheels, but Boston Whaler makes a "kayak" with pedals,
which turn a paddle wheel which sits below the kayak.

One of the obvious problems with this is it takes a lot more depth which
restricts where you can peddle. Personally, I wouldn't call this a kayak.
Maybe, since I last saw this model, they added the wheels.
Lynn

In the distance today while out paddling I saw two pedal-powered kayaks
(Georges River - Sydney Australia). Interestingly they both had a pair
of fixed wheels sticking up in the air behind the cockpit. I imagine
that they are some sort of transport system for when on land.

Does anyone know of a model like this?

One of the kayaks had a big "Shimano" on the side so I'm wondering if it
was a sponsored prototype or something.

RockyRoad