Moving Background on Gears

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

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:

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.