Another key feature of our structure is the ratcheting wheels (Figure 5). We added ratcheting wheels to both the front and the rear to prevent the seal from surrendering any ground already covered. By using Lego pieces and lasercamming our own wheels, we had the freedom to decide their size and ensure that the ratchets would engage with the Lego pawls with accuracy. We used a rubber band to add a medium force between the pawl and ratchet, keeping it engaged with the teeth at all times.

Figure 5: Ratcheting wheel; Figure 6: Nails in the rubber added traction

Although the ratcheting mechanism worked well, the friction between the wheels and the surface was not always large enough and the wheels sometimes slipped. We increased friction by adding rubber bands around the rear wheels, but still saw the front wheels slipping. Although we tried putting rubber bands in the front as well, we eventually transitioned to rubber Lego wheels for more consistent gripping. Finally, we found that poking nails through the rubber Lego front wheels resulted in the correct amount of grip and eliminated slippage on all wheels (Figure 6).

A series of iterations were focused on motor mounting as we worked to find the correct location for the motor without sacrificing stability. By moving the gear to the outside of the main support beams, we were able to center the motor in the middle of our seal (Figure 7).

However, placing the motor on top elevated the center of mass.  Fortunately, this did not present an issue because we had already widened the wheels to broaden the seal and increase stability. In future iterations, we would attach the motor on the underside of our seal for a more elegant design. To control our motor, we fashioned a flexible switch from paper clips, which allowed us to easily turn our robot on and off (Figure 8).

Figure 7:  Moving gear to the outside; Figure 8:  Paperclip switch; Figure 9: Rear linkage connection

Another series of changes focused on the alignment of our seal. After we discovered Eggman's tendency to veer to the left, we realized he needed a more rigid frame. Since one linkage was driving the front left and another linkage was driving the rear right, the design is not symmetrical about its central axis. This coupled with the fact that the rotation of the two linkages was 180 degrees out of phase resulted in a lot of wobble and instability in the design.  Therefore, we took a lot of time in order to minimize the degrees of freedom in the joints.  We added support beams between the linkages and tightened them so that the frame would be less wobbly and also added a second support beam in the rear. To further stabilize the structure, we glued all the washers to the linkages (Figure 9).

We used a free body diagram analysis (Figure 10) to select an appropriate motor and gear ratio.  In order to size our motor to the most conservative prediction, we assumed the worst-case conditions.  We assumed that in the absolute worst case, the Eggman would have to lift himself perpendicular from a flat surface counteracting 100% of the gravity force.  In addition, he would have to pull his weight forward overcoming all of static friction.  Although static friction would never be overcome in actual operation (Eggman locomotes via rolling not sliding), we used static friction so that our calculations represented the highest possible forces in the x-direction.  In actual operating conditions the forces Eggman would have to exert to counteract gravity would be smaller because of the 10 degree slope.  Using these assumptions, we calculated that the highest required torque would be 0.416 Nm (see Appendix A for detailed calculations).   We knew if Eggman was designed to withstand these torques, he would have no problem in real operation since he never actually needs to lift his entire weight - he simply extends, then pulls himself forward via wheels.

For our final design, we bought a Tamiya Planetary Gearbox Set so that we would have the flexibility to change the gear ratio if necessary.  We decided to use the Tamiya gear reduction of 100:1 and add an extra gear reduction outside the motor of 5:3, giving an overall gear reduction of 167:1.  This resulted in an adequate speed of locomotion up the slope in under thirty seconds.  At this gear ratio, we measured an output torque of 0.84 Nm at stall conditions.  Although this is above our worst-case design requirement, we decided it would be beneficial to have a safety factor of available torque over the worst-case scenario in order to account for frictional losses in the design.

Figure 12: Velocity vs. time for rear (left) and front (right) four bar linkages

We used Solidworks to visualize and refine our movement. Once we had a working Lego prototype, we translated our model into Solidworks. In Solidworks, we found that these Lego links were in fact unstable due to unforeseen collisions with other pieces (Figure 13). By simulating the movement of each design iteration, we were able to experiment with different linkage dimensions so that we could find the smooth galumphing motion that we were looking for in a stable design (Figure 14).

Not only did Solidworks aid with the overall movement, but also with seal features like the fins. During this process, we were able to move the assembly to ensure that our fins did not collide with any other parts.

Figure 13: Assembly with collision piece in green (left) revised assembly (right)

Figure 14: One Solidworks simulation where we saw an unstable configuration.

Figure 15: Seal in extended position; Figure 16: Seal in compressed position

The operating point seen in Table 1 is the maximum current required by the seal in its motion cycle, corresponding to the point of maximum torque requirement.  Taking the 1.55 A measurement and running through calculations based on InoLoad, Istall, and ωnoLoad, we were able to conclude that the highest torque required to power the seal was .27 Nm.

Table 2 highlights how the addition of the tail impacted the performance of the seal.  Based on the current of 1.2 A, we realized our power train was operating a little to the left of the efficiency peak of 18.2% (Figure 1 Appendix B). Both with and without the tail, the operating current was close to the peak efficiency, so we decided to keep the more authentic galumphing motion despite the extra power consumption.

Adding the tail supported some of the weight, increasing the normal force and therefore the friction force at the tail-ground interface.  On one hand this was bad because the required output of the motor increased.  On the other hand, this could be a beneficial side effect because the tail provided more grip on the terrain and decreased slippage.  This was the dominant reason in keeping the tail in this location.