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In order to ensure efficiency with our robot we wanted to determine the total area that would be cleaned by the moving squeegee arm. Below is a drawing of the expected area that is to be cleaned.
(Insert pic of ellipse/inf symbol with squeegee arm reach on top of path)
To calculate this we have to determine the dimensions of the ellipse that is formed around our figure 8 path. To do this we used measuring tape to determine the major and minor axis lengths with our final prototype. We moved our gears to simulate the path and made markings at the edges of the ellipse. From here we were able to easily take our ellipse dimensions.
Ellipse Dimensions:
| Major Axis Length (in) | Minor Axis Length (in) |
|---|---|
| 13.75 | 2.19 |
Now we have to consider the extra area that is cleaned by our extended squeegee arm. For this we can just add the squeegee arm length to the major and minor axis lengths. With a squeegee arm length of 4 inches we can add that to our the axes lengths.
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Ellipse Dimensions with Squeegee arm
| Major Axis Length (in) | Minor Axis Length (in) |
|---|---|
| 17.75 | 6.19 |
Now we just have to use the area of an ellipse formula to solve for our area. Here a = major axis and b = minor axis.
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