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  1. #1

    Lamé Equation (function) to drive a curve?

    I have been asked if I could model a curve using a Lamé equation. The equation actually has two different equations with two missing values, one being the Z direction and the other being the radius (that is my belief so far).

    Any ideas on how to get this into a model such that when the Z value is driven from 0 (or a negative number to start the curve on the correct trajectory) to say 7?

    Rh=3.36
    L2H=5.65
    Rleh=2.1
    n=3.5
    A = L2H * (1 - (Rleh/Rh)^n)^(1/n)

    Lame function:
    (R / Rh)^n + ( Z / A)^n = 1

    FYI: https://en.wikipedia.org/wiki/Lam%C3%A9_function
    Scott

  2. #2
    We figured it out. There was an error in the equation that was preventing it from working.

    In case anyone needs to know it in the future, here is what I put into the curve from equation (along with the notes to help):
    /* Original Lamé function: (R/Rmid)^n + (Z/A)^(n = 1)
    /* For Creo: T is the variable, we use this for the height in Z (CSYS based)
    /* So, for a curve that goes to 5.65 high, Z = T*5.65 or Z = L2H*T (to use the L2H value as the height)
    /* From the original formula, R is the radius, which we want to translate to X for cartesian coordinates
    /* Rmid: Radius at midplane
    /* L2H: Half length of the part
    /* Rtop: Radius at the top of the part
    /* n: exponent
    /* So, change the formula such that: (X/Rmid)^n + (Z/A)^(n = 1)
    /* Flip the equation such that we solve it for X = ((1-((Z/A)^n))^(1/n))*Rmid

    Rmid = 6.742/2
    L2H = 11.2874/2
    Rtop = 2.1
    n = 3.5
    A = L2H * (1 - ((Rtop/Rmid)^n))^(-1/n)
    Y = 0
    Z = L2H*T
    X = ((1-((Z/A)^n))^(1/n))*Rmid
    Attached Thumbnails Attached Thumbnails Lame.jpg  
    Scott

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