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.
Figure 1. Rotating Background on Gear B setup where the vertical input gear is gear 1, the horizontal orange gear is gear 2 and the background is rotating body 3.
Gear 2 has twice as many teeth as Gear 1, which results in an angular velocity reduction on the scale of 1/2. In other words, for every rotation of gear 1, gear 2 only goes through half a rotation. This relationship is shown in the video below.
Various values for the Gear system are shown in Table 1.
Table 1. Gear Values
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 layer below the backdrop to keep it level. The layer is yellow in the video below:
To re-emphasize the difficulty of continual gear meshing, I have added the following video. In the video, you can see how gear 2 shifts to the left and right depending on the wobble of body 3 instead of remaining vertical and meshing with gear 1.