Using a basic, two-groove Archimedes trammel, is there a geometry or configuration that can draw a circle instead of an ellipse?
Examine the GIF of a trammel from Wikipedia and note the following:
The distance from the "pen" to the nearer block (pivot) is the same as the shortest distance from the center of the resulting ellipse to the ellipse. (The "short radius"; I forget the technical term.)
The distance from the pen to the further block is the "long radius" of the ellipse.
So to make a circle, both pivots would have to be coincident (at the same point), which would have to be fixed in the center rather than moving on the two tracks.
At that point you don't have a trammel anymore, you have a compass.
If you arrange the pen between the two pivots, equidistant from each, it will in fact trace a circle. That would follow the "two grooves" aspect of a trammel, but I don't think it could technically be called a trammel anymore. If you're willing to call that a trammel, then the answer would be "yes."