I'm not really sure what the point behind your question is, as even though you say your stroke is "simple, very simple", I would bet it looks much more like a pendulum than a piston.
I think Neil is correct...the small amount the arcs travel is virtually negligible, and results in a straight line at the bottom, but if you still are looking for a "biomechanical" description of how a circle (or arc) can have a staright line as a component...it can't. And you already know that. But considering the small amount the arc translates on the vertical axis, I would surmise that a combination of wrist movement, grip pressure, and simple 'cushion' of the fingers would allow for unconscious (or is it subconscious?) correction to at least the point of negligibility of outcome.
I think Neil is correct...the small amount the arcs travel is virtually negligible, and results in a straight line at the bottom, but if you still are looking for a "biomechanical" description of how a circle (or arc) can have a staright line as a component...it can't. And you already know that. But considering the small amount the arc translates on the vertical axis, I would surmise that a combination of wrist movement, grip pressure, and simple 'cushion' of the fingers would allow for unconscious (or is it subconscious?) correction to at least the point of negligibility of outcome.