After meeting with the mechanical engineering professor, we developed a multi-axle gear hub that is similar to a manual automotive transmission. This design, shown below in the low gear reverse drive, utilizes three axles and allows for low and high gear reverse drive and for 1:1 direct drive. We showed this to our Rowheels sponsor and his main concern was that this is a non-concentric design, as our power input (blue) and output (green) were in different planes. 

To address our sponsors concern, we simply redesigned this gear box to move the power output to the purple axle, giving us a concentric design. We can shift between the two reverse gears by pulling the orange shifting rod via a cable which then slides the blue synchronizer along the blue input shaft and allows it to mesh with either gear ratio. 

To shift into direct drive, the blue input shaft is slid into connection with the purple output shaft via a second shifting mechanism. Having these separate shifting mechanisms is a safety precaution for the user, as shifting from reverse to forward drive while in motion could jam the gears and jerk the user forward. 

Here is our preliminary SolidWorks design of this multi-axle gear hub and Gantt chart. We believe this hub can be manufactured with off the shelf components, such as the ICP dog clutch shown below and we are in the process of getting these pieces to create a working three-speed prototype.