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Ratio for 2 tangent circles with fixed centers

Question asked by David Lewis on Jun 17, 2020
Latest reply on Jun 18, 2020 by Jim Riddell

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I know the center locations for two circles of unknown diameter that are tangent to each other, and I know what their ratio is to one another. I want to make sure the diameters are viable for the build when the circles have a ratio of 8-to-1.

I can't drive either of the diameters, but to be clear, I know that I can measure the distance between the centers, divide by 9 and multiply the product by 16.

I'm asking if this is possible without intermediate dimensions. I prefer to include the absolute minimum construction geometry or intermediate dimensions in sketches, and I'd like to know if this is possible without it.

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Teemu Jääskeläinen Jun 18, 2020 3:25 AM
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Draw a line. Split the line with the Segment tool in to 9 equal segments. Draw a circle that spans one segment and another circle that spans 8 segments.
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Jim Riddell Jun 18, 2020 4:15 AM
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You mean something like this?
The diameter of the smaller (or larger, if you modify the equation) is set or chosen from something given and the distance between the two circles which have a tangent relation between them is set to = (d1/2) * 9.
Then you could throw in a driven dimension for the horizontal & vertical coordinates or just do a 'measure' between centers to be able to locate.
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- Teemu Jääskeläinen @ Jim Riddell on Jun 18, 2020 4:39 AM
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  If you draw a line and split it with the segment tool, the segments get and equal relation, meaning they will always be equal in length with each other. You can drag on one of the segments and the other segments will grow and shrink accordingly. No need for dimensions or equations.
  
  I'm not at the computer right now but I will post a screenshot later.
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  - Jim Riddell @ Teemu Jääskeläinen on Jun 18, 2020 4:49 AM
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    Teemu Jääskeläinen wrote:
    
    If you draw a line and split it with the segment tool, the segments get and equal relation, meaning they will always be equal in length with each other. You can drag on one of the segments and the other segments will grow and shrink accordingly. No need for dimensions or equations.
    
    I'm not at the computer right now but I will post a screenshot later.
    I read the OP as knowing there was a *fixed* distance between the centers and they want to determine functional 8:1 diameters, i.e. gears. If you drag a segment or the endpoint then that distance is no longer fixed, you don't know what you have except for two circles that are 8:1 floating in space.
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    - Teemu Jääskeläinen @ Jim Riddell on Jun 18, 2020 4:59 AM
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      Then you dimension the initial line with the known distance. Then you segment the line. Then you use the segments as the radiis of the circles in the wanted ratio.
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      - Jim Riddell @ Teemu Jääskeläinen on Jun 18, 2020 5:16 AM
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        Teemu Jääskeläinen wrote:
        
        Then you dimension the initial line with the known distance. Then you segment the line. Then you use the segments as the radiis of the circles in the wanted ratio.
        That will not work if you are purchasing stock gear sets. I approach problems such as this from a practical applied engineering and design input.
        For example, if I am building a house I may use 2x4s (which are actually 1.75x3.75) instead of specifying studs that are *exactly* as thick as the insulation necessary for the application.
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Jim Riddell Jun 18, 2020 4:20 AM
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I threw in a fixed horizontal dimension and a driven vertical dimension but you might have to modify the fixed one if your diameters change drastically.
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Jim Riddell Jun 18, 2020 4:23 AM
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I forgot to mention - the reverse is also true. Given two tangent circles, if you know the distance between centers then you can calculate the diameters of both circles. (I imagined the problem as defining gear sets originally.)
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Ratio for 2 tangent circles with fixed centers

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