Calculate the diameter + circumference of a circle (straight line on circumference)

[mitchellleary]

Hi,

im hoping someone can help me on this forum.

I am trying to calculate the necessary circumference and resulting diameter of a circle that would accommodate a straight line of 5cms anywhere along its circumference.

Im wondering if there is an equation to calculate this and would appreciate your help on this.

Thanks,

mitch

 

[mmm4444bot]

I am trying to calculate the necessary circumference and resulting diameter of a circle that would accommodate a straight line of 5cms anywhere along its circumference.

No part of any circle's circumference is straight. Can you explain in more detail the meaning of "accommodate a straight line"? :cool:

 

[mitchellleary]

No part of any circle's circumference is straight. Can you explain in more detail the meaning of "accommodate a straight line"? :cool:

Yes, I realised that no part of the circumference of a circle is straight as I posted it and that it needs more explanation. Apologies for that.

So i am conducting an experiment and I have to attached a rectangle 5cm x 1cm to the edge of a circular rotor. Unattached to this circle, there will be 4 x "gates" located at 4 equidistant corresponding points of a separate circle that will match up with my rectangles of 5cm x 1cm.
The "gates" will be slightly larger to allow the passage of my rectangle through the gates(maybe 5.1cm x 1.1cm). The rotor will turn and my rectangle will need to pass through the 4 gates smoothly without touching the sides.

i need to work out what circumference and diameter of circle (to construct my rotor) could accommodate my rectangle passing through the gates as the rotor turns.

I hope that's a bit clearer? If not, I'll try and explain further.

Thanks for your reply.

mitch

 

[mmm4444bot]

… I have to

 

[tkhunny]

A picture would be excellent

 

[mitchellleary]

Did you give only two dimensions because the rectangular object is a relatively thin sheet? Which of the three dimensions is attached to the rotor?


I'm sorry -- how many rectangular objects are there?

Also, I'm assuming that 4 x "gates" means 4 gates.


I'm thinking of multiple possibilities, for what two circular surfaces would look like, with "gates" and "rectangles". One circle is inside the other, yes?

Can you upload a couple rough sketches? One, a birds-eye view, looking down on the circles, would help. Scroll down, on the page where you type your post, and look for the Manage Attachments button. :cool:

Hi guys,

Thanks for your replies, and apologies for my late reply. I had a busy day yesterday.

Ok, so I tried to attach my sketch to this thread but apparently, it only allows images of 94kb and lower which is insanely small. My image is only 150kb.

If you take a look, there are 4 gates and 4 rectangles (whose full dimensions are 5cm x 1cm x 1cm). The 4 gates sit on one rotor disc and the 4 rectangles sit on the other rotor disc. I had only mentioned 1 rectangle(now cuboid) as if one fits through each gate, all 4 will.
The 2 rotor discs will come together, face to face. The disc with the gates will stay stationary and the disc with the cuboids will rotate. The cuboids must be able to pass through each gate that is just slightly larger than the aforementioned cuboids without problem or collision.

So taking all of this into consideration, what would the circumference and diameter of the rotor discs need to be to accommodate the cuboids being able to pass through the gates as the rotor turns.

Thanks again for your time and help.

Much appreciated,

Mitch

 

[mitchellleary]

Thanks mmm4444bot for editing and adding my image into my thread. Much appreciated.

What are your thoughts now based on the drawings?

Thanks,

Mitch

 

[mmm4444bot]

The cuboids' footprint is a washer.

Let r be the distance from the center of the circle to the midpoint of each cuboid's nearest side.

Then, r is the inner radius of the washer.

Let R be the outer radius of the washer. From Pythagorean Theorem, we get:

R = sqrt(2.5^2 + (r + 1)^2)

I have assumed the length of the gates' walls to be 5 cm, also.

I used 0.1 cm for clearance.

The outer gate walls would be positioned R+0.1 cm from the center of the circle.

The inner gate walls would be positioned 0.1 cm less than the distance from the center of the circle to a 5cm chord (on the inner arc).

Let S = the segment height

S = r - sqrt(r^2 - 2.5^2)

Hence, the inner gate walls would be positioned r - S - 0.1 cm from the center of the circle.

Here's a concrete example (all measurements rounded): Pick 15 cm for the cuboid's distance from the center of the circle.

r = 15 cm

R = 16.19 cm

S = 0.21 cm

R + 0.1 = 16.29 cm

r - S - 0.1 = 14.69 cm

In other words, if the inner edge of each cuboid is placed 15 cm from the circle's center (measured to the midpoint of the 5 cm side), then the footprint traced out by the spinning cuboids has the shape of a washer, where the inner radius is 15 cm and the outer radius is 16.19 cm.

The inner gates' outer edge could be positioned 14.69 cm from the circle's center, and the outer gates' inner edge could be positioned 16.29 cm from the circle's center.

If the inner gates' length were shortened (i.e., made less than 5 cm), then each inner gate could move closer to the inner arc of the washer.

 

[mitchellleary]

The cuboids' footprint is a washer.

Let r be the distance from the center of the circle to the midpoint of each cuboid's nearest side.

Then, r is the inner radius of the washer.

Let R be the outer radius of the washer. From Pythagorean Theorem, we get:

R = sqrt(2.5^2 + (r + 1)^2)

I have assumed the length of the gates' walls to be 5 cm, also.

I used 0.1 cm for clearance.

The outer gate walls would be positioned R+0.1 cm from the center of the circle.

The inner gate walls would be positioned 0.1 cm less than the distance from the center of the circle to a 5cm chord (on the inner arc).

Let S = the segment height

S = r - sqrt(r^2 - 2.5^2)

Hence, the inner gate walls would be positioned r - S - 0.1 cm from the center of the circle.

Here's a concrete example (all measurements rounded): Pick 15 cm for the cuboid's distance from the center of the circle.

r = 15 cm

R = 16.19 cm

S = 0.21 cm

R + 0.1 = 16.29 cm

r - S - 0.1 = 14.69 cm

In other words, if the inner edge of each cuboid is placed 15 cm from the circle's center (measured to the midpoint of the 5 cm side), then the footprint traced out by the spinning cuboids has the shape of a washer, where the inner radius is 15 cm and the outer radius is 16.19 cm.

The inner gates' outer edge could be positioned 14.69 cm from the circle's center, and the outer gates' inner edge could be positioned 16.29 cm from the circle's center.

If the inner gates' length were shortened (i.e., made less than 5 cm), then each inner gate could move closer to the inner arc of the washer.

Thanks very much mmm4444bot. Your description is very clear and that's exactly the assistance I was looking for. I really appreciate your help.

I highly recommend your knowledge and skills!

Thanks again!
T