If the hands are Connected to and rotating with the back shoulder then, when viewed from above, a hitter will exhibit a Curved Hand Path.

The Exact Shape of the Hand Path

You'll notice that I use the term "Curved Hand Path" and not "Circular Hand Path" like Jack Mankin does. That is because only on inside pitches or perfectly-timed fastballs down the middle is the hand path best described as circular. On outside pitches, the hand path will be more of an oval shape as the hands work away from the body to get the head of the bat out to the ball. On pitches where the hitter is early, and has to make a late, Z-Axis Adjustment (e.g. a slider that wasn't seen out of the hand), the hand path will also be more elliptical as the hitter lets their hands travel as much as a foot forward toward the ball.

What the Curved Hand Path Looks Like

The clips below show the Curved Hand path in action.

Curved Hand Path
Inside Pitch

The video clip above shows Albert Pujols hitting a single to right field on a ball inside. Notice how his hands very quickly take a hard right turn as he gets them, and thus the head of the bat, inside of the ball.

Curved Hand Path
Outside Pitch

The video clip above shows Skip Schumaker hitting a double to left field on a ball outside. In this case, notice how his hands have to travel out away from his body in order to get the head of the bat out to where the ball is. This isn't a linear hand path, but it is much less circular than the one in the first clip.

Curved Hand Path
Ball Low and Inside

The video clip above shows Joe Mauer hitting a hard ground bat into the gap between first base and second base on a 95 MPH fastball low and in. This video clip shows the generally curved nature of his hand path.

Curved Hand Path
Ball Down the Middle

The video clip above shows Dan Uggla hitting a ground rule double into the Left Field corner on a fastball down the middle. This video clip also shows the generally curved nature of his hand path.