4 Replies Latest reply on Sep 21, 2010 7:22 AM by Sreenath Varma

    Equation driven curves

    Sreenath Varma

      Dear All--

       

      The following was originally posted by Mahir Abrahim under Equation driven curves: cool equation, in response to: Kevin De Smet on May 6, 2010.

       

      Wave Spring with radius R, height A, and n waves

      x: R*cos(2*pi*t)

      y: R*sin(2*pi*t)

      z: A*sin(n*2*pi*t)

      t1: 0

      t2: .999 (SW won't do a closed loop)

       

      How did he arrive at this equation. Is it the way it is made. If so, where can I find references to the same, else what are those sources from which this can be derived.

       

      cheers

        • Re: Equation driven curves
          Harold Brunt

          If I understand it correctly the formula is basically a circle x^2 + y^2 = R^2 plus the z (height) component. If you solve for x and y you get x(t) = cos(t) and y(t)= sin(t) with t being the postion of the rotation. Then add the z component of z(t) = sin(t) for the basic formulas.

            • Re: Equation driven curves
              Sreenath Varma

                          _           _
                         |rCosU + a|   
              P(u) =  |rSinU +  b|    U belongs to [0,2pi]
                         |_           _|

               

              This is the parametric equation of a circle with centers a,b and radius r.
              If you require a helix an additional Z parameter will come into picture denoted by hU, where h is the height
              of the helix.

               

                          _                       _
                         |rCos(2*pi*n*U) + a|   
              P(u) =  |rSin(2*pi*n*U) +  b|    U belongs to [0,1]
                         |_      hU             _|

               

              We multiply U with (2*pi*n) where n is the number of revolution.
              In Z direction, we multiply "U" by the height of the helix (: h in this case)
              Circle is nothing, but a helix in 2D.

               

              But how do you solve for wave spring. What are the laws governing the shape.

               

              Please bear with my matrix. No Office tools are installed in mine, so had to get around with notepad.