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Math Help - Equation for 3 Circles before 1 circle makes contact with other 2

  1. #1
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    Equation for 3 Circles before 1 circle makes contact with other 2

    Hello =)

    I have a real life circle problem on my hands, and although Im not the best at math I can apply simplified equations to my hobby. I have a picture below with 3 circles:

    C1 Diameter = 25
    C1 is a metal tube with Diameter 25mm and length 300mm. However length is irrelevant to my problem I just want you to get a good picture of what Im trying to work out.

    C2 Diameter = 25
    C2 is also a metal tube as described above.

    C3 Diameter = 50
    C3 is a shopping trolley wheel

    Y = 5
    Y is the distance between the right arc of C1 and left arc of C2. These two circles will never touch, by design the tubes are bolted not to touch. And they are also leveled one will never be higher than other.

    X = ?
    This is the distance Im trying to work out.

    The only way I can describe X is: The drop of C3 before it makes contact with C1 & C2.


    If anyone can help me or direct me to where I can find an equation to always be able to workout 'X' if C1, C2, C3 & Y where to change in value.

    Thanks in advance

    Wolve
    Attached Thumbnails Attached Thumbnails Equation for 3 Circles before 1 circle makes contact with other 2-circle_problem.jpg  
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  2. #2
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    earboth's Avatar
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    Re: Equation for 3 Circles before 1 circle makes contact with other 2

    Quote Originally Posted by wolve View Post
    Hello =)

    I have a real life circle problem on my hands, and although Im not the best at math I can apply simplified equations to my hobby. I have a picture below with 3 circles:

    C1 Diameter = 25
    C1 is a metal tube with Diameter 25mm and length 300mm. However length is irrelevant to my problem I just want you to get a good picture of what Im trying to work out.

    C2 Diameter = 25
    C2 is also a metal tube as described above.

    C3 Diameter = 50
    C3 is a shopping trolley wheel

    Y = 5
    Y is the distance between the right arc of C1 and left arc of C2. These two circles will never touch, by design the tubes are bolted not to touch. And they are also leveled one will never be higher than other.

    X = ?
    This is the distance Im trying to work out.

    The only way I can describe X is: The drop of C3 before it makes contact with C1 & C2.


    If anyone can help me or direct me to where I can find an equation to always be able to workout 'X' if C1, C2, C3 & Y where to change in value.

    Thanks in advance

    Wolve
    1. I've modified your sketch a little bit. (see attachment)

    2. The green line h has a length of:

    h = 25+\sqrt{75^2-27.5^2}\approx 94.776

    3. The red line z has a length of:

    z = h - 50 \approx 44.776

    4. Thus x has a length of:

    x = 50 - z = 50 - (h - 50) = 100 - h \approx 5.224
    Attached Thumbnails Attached Thumbnails Equation for 3 Circles before 1 circle makes contact with other 2-tricirculus.png  
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  3. #3
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    Re: Equation for 3 Circles before 1 circle makes contact with other 2

    Hi earboth,

    Thank you very much for your solution, this will definitely help me now and in future projects =)

    Once again Thank you
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