Help needed with calculating distances from circles

• DannyH
In summary, the problem is to remove material from linear tapered strips with a 1 inch round cutter, where the circles need to connect at half the section depth over the entire length of the strip. The link provided shows a visual representation of the problem. To calculate the distances between the circles, one can fix the first circle and use the known slope of the half-depth line to iteratively calculate the distances between successive circles. However, this method may be tedious and there may be a more efficient solution.
DannyH
I'm looking to find someone who can help me with my problem...

My problem is that I need to remove material from linear tapered strips with a 1 inch round cutter. The circles need to connect to each other at half the section depth over the entire length of the strip

--->

http://www.keone.com/hollow.gif

Because the diameter of the strips decreases the circles need to be placed closer to eatchother so that the circles keep connecting eatchother at the hart of the strip.

My problem is how to calculate the distances...

The picture in the link will make it more clear

Thanks alot!

Danny

Last edited by a moderator:
I don't know if there is a general formula, but if you fix the first circle at a certain point along the strip, you can calculate the distances between the successive circles iteratively. Take a look at the image I attached. Fixing the first circle defines the angle $$\theta_1$$. That first intersection is the only one you have to measure. If R is the radius of the circles (I guess .5" in your case?), then the distance between circles 1 and 2 is

$$d_{12} = 2 R \cos \theta_1$$

To find $$\theta_2$$, you can use the known slope "m" of the half-depth line. Just compute "rise over run" from the first intersection (circles 1 and 2) to the second (circles 2 and 3):

$$m = \frac{\Delta y}{\Delta x} = \frac{R\sin \theta_1 - R\sin \theta_2}{R\cos \theta_1 + R\cos \theta_2} = \frac{\sin \theta_1 - \sqrt{1 - \cos^2 \theta_2}}{\cos \theta_1 + \cos \theta_2}$$

Since $$\theta_1$$ is known, you can solve this quadratic equation for $$\cos \theta_2$$. Then the distance between circles 2 and 3 is

$$d_{23} = 2R \cos \theta_2$$

You can repeat this process to get the successive distances. This seems awfully tedious though. Maybe someone else will be inspired to come up with a better way.

Attachments

• circles.JPG
13.7 KB · Views: 432

Hello Danny,

I would be happy to help you with calculating distances from circles for your project. From what I understand, you need to remove material from linear tapered strips using a 1 inch round cutter, and the circles need to connect to each other at half the section depth over the entire length of the strip.

To calculate the distances, you will need to first determine the diameter of each circle based on the section depth of the strip. Then, you can use basic geometry to find the distance between each circle. This can be done by dividing the circumference of the circle by 2, and subtracting the diameter of the circle from that value. This will give you the distance between each circle.

If you would like further assistance, please provide more information on the dimensions of your strips and the desired section depth. Additionally, the picture in the link is not working, so if you could provide a different image or explain the design in more detail, I can provide a more accurate calculation.

I hope this helps and I look forward to hearing back from you.

1. How do I calculate the distance from a point to a circle?

To calculate the distance from a point to a circle, you can use the Pythagorean theorem. First, find the difference between the x and y coordinates of the point and the center of the circle. Then, square each difference and add them together. Finally, take the square root of the sum to find the distance.

2. Can I use the radius of the circle to calculate the distance?

Yes, you can use the radius of the circle to calculate the distance from a point. The distance will be the difference between the radius and the distance from the center of the circle to the point.

3. How do I find the coordinates of the point on the circle that is closest to a given point?

To find the coordinates of the point on the circle that is closest to a given point, you can draw a line from the center of the circle to the given point. This line will intersect the circle at the closest point. Use the Pythagorean theorem to find the distance from the center of the circle to the given point, and then use the radius to find the coordinates of the closest point.

4. Can I use the distance formula to find the distance between two circles?

No, the distance formula is used to find the distance between two points. To find the distance between two circles, you will need to find the distance between their centers and subtract the sum of their radii.

5. How can I use the distance from a point to a circle to determine if the point is inside, outside, or on the circle?

If the distance from the point to the circle is equal to the radius of the circle, then the point is on the circle. If the distance is greater than the radius, then the point is outside the circle. If the distance is less than the radius, then the point is inside the circle.

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