I’ve made a couple of rowing models in the past. This one is the Shrimp Boat and is part of the Gizmos pack produced by Barnes and Nobel.
The models that I have produced so far have used a crank/slider mechanism to drive the oars. To do this I have used a tall box with the drive handle located low down so that the slider tube doesn’t need to swing back and forth excessively.

For a forthcoming project I need the box to be much shallower in relation to the length of the boat. To that end I have come up with this mechanism which uses a crank and a couple of linkages.
The black line (the locus) traces out the path the end of the push rod takes. It’s interesting just how un-circular the locus turns with only the addition of a couple of links, geometry is an amazingly flexible tool. With luck and experiment I’ll be able to tune the locus to just the movement I’m after.
Thinking about it, I probably want the locus to be exactly upside down from what it is now. When the push rod is at its highest the oars will be in the water and should be being pulled back flat and level. I’m sure that can be arranged.

The whole assembly should fit nicely in a shallow box just beneath the waves.