How do I construct a set of concentric circles with millimeter precision?

[inflation]

How do I construct a set of "concentric" circles with millimeter precision?

I would need a few real life circular objects with the following specifications:

They should all be "semi-concentric" so that they all share the same central axis (at right angle to the planes of the circles), but lie on different heights. That is to say, they could lie on the surface of the same regular cone, however more of a "bowl" shape would do just fine too.

The circles do not need to be of a certain size given in advance. It is only that I need to know what size they have. What I mean is that any perfect cone with circles marked on it at different heights over apex, would be perfect for me, if only I know the specifications of those circles marked on in. Though I'd prefer if they have something like 0.1 to 1 meter radius or height (simply because objects of 100 meter or 0.01 meter might be impractical to handle).

Materials are not important to me, if only they are fairly clarly visible to the naked eye. Like if they are all on the inside of a cone, I could see them all by looking down on them. I only need it to look at, to take photos of. So it needs to be stable for at least a minute or so.

Precision needs to be something like 1%, so that errors in specification of the circle sizes and height differences rarerly are greater than 1 millimeter per decimeter.


How should I practically construct such a set of circles with simple means?
Or, what ready made everyday object could I use?


If I draw circles on transparent plastics sheets, I have the problems of:
- placing the sheets at know heights over each other.
- centrating them all on the same central axis.
- avoiding that the sheets bend by the force of gravity.

If I take a closer look at bowl-shaped objects at home, I have two problems:
1) They have at least millimeter sized defects. If I but a glass bowl on my glass table, it wobbles and I can slide a coin under it from one side.
2) Even with a perfect bowl, how should I proceed in order to mark visble precision circles on its (inside) surface, and at precision height differences from each others to?


I'd be happy for any advice on this maybe unusual kind of question, thank you!

 

[FredGarvin]

They should all be "semi-concentric" so that they all share the same central axis (at right angle to the planes of the circles), but lie on different heights.

There is no such thing as semi-concentric. The description you gave is the definition of concentricity.

The circles do not need to be of a certain size given in advance. It is only that I need to know what size they have. What I mean is that any perfect cone with circles marked on it at different heights over apex, would be perfect for me, if only I know the specifications of those circles marked on in. Though I'd prefer if they have something like 0.1 to 1 meter radius or height (simply because objects of 100 meter or 0.01 meter might be impractical to handle).

I have read this 5 times now and I still don't quite understand what you are asking. Please restate this.

Precision needs to be something like 1%, so that errors in specification of the circle sizes and height differences rarerly are greater than 1 millimeter per decimeter.

Well, if you are talking about a circle of 10 cm, then a 1 mm variation in radius or diameter should not be to terribly difficult. You could do this by hand if you are careful.

How should I practically construct such a set of circles with simple means?

Take a plate of plastic, drill a hole in the center. Use a string and a fine razor at the end of it. Swing the circle using the string as the radius. If you do it right, you can get a very accurate circle. To vary the size, vary the length of the string.

 

[inflation]

There is no such thing as semi-concentric. The description you gave is the definition of concentricity.

But the circles must not be in the same plane. They must be in parallell planes on different heights. Maybe that still is defined as concentric, though.

I have read this 5 times now and I still don't quite understand what you are asking. Please restate this.

Yes, that was ill explained. Here I try again:

I do not need to give size speifications in advance, such that the radii must be for example 89, 124, 186 and 223 mm. They could be almost anything, if only I know afterwards what they are. If the first circles radius is 93 or 89 mm is completely irrelevant to me, if only I know about it.

Well, if you are talking about a circle of 10 cm, then a 1 mm variation in radius or diameter should not be to terribly difficult. You could do this by hand if you are careful.

Take a plate of plastic, drill a hole in the center. Use a string and a fine razor at the end of it. Swing the circle using the string as the radius. If you do it right, you can get a very accurate circle. To vary the size, vary the length of the string.

Yes, but then I want to put the circles on top of each other at known heights between each others. That third dimension makes it more difficult than a normal geometric drawing exercise.

From the side, the cirles could look something like this:

________

 ______
   __