Of course, there's a reason for that because we're trying to turn a circular motion into a linear movement. Adding more "linkages," apparently helps that out.
Greg's tutorial shows the movement towards the end, but if you want to build one yourself, it's a great video to watch nonetheless.
I did find a thread on HauntForum which led me to this design of a Grave Peeper by stokstad that uses the gear motor to create a straight up-and-down motion. Laying that down flat would seem to give me the straight reaching motion I'm looking for (it's also very cool the head turning mechanism stokstad designed into his Peeper).
Does anyone know of any other links that would discuss converting a round motion into a linear one?