The rotating background is built on 2 gears as shown in Figure 1. Note in the figure that gear 2 and rotating body 3 have the same angular velocity but different linear velocities on the edges of the parts.
...
Body | Radius | N | Linear Velocity (in/s) | Angular Velocity (rad/s) |
1 | .805” | 6 | 4.83 | 2π |
2 | 1.315” | 12 | 3.945 | π |
3 | 4” | N/A | 12 | π |
The gear mechanism was easy enough to implement, but I had to add thicker card stock to Gear 2, its associated axle and the top of the box because the gears were not meshing properly. I had more difficulty when I added the background because it was very large and unstable. The background's movements affected the orientation of the horizontal gear below (gear 2), so I had to add a support layer below the backdrop to keep it level. The layer is yellow in the video below:
...