Dear all

This is the function of a logarithmic helix:
Funktion https://mathepedia.de/Reelle_Funktionen.html �(�)=�⋅��⋅�r(φ)=a⋅
ek⋅φ

How can I transform this "knowledge" to OpenScad, to receive a file in
which I can adjust the radients, the angles and the number of turns?

many thanks
Karl

P.S.

My aim is to create someting like that -->
https://www.kl-angelsport.de/images/thumbnail/produkte/medium/saenger_1907050.jpg

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This is the function of a logarithmic helix:

Funktion https://mathepedia.de/Reelle_Funktionen.html
�(�)=�⋅��⋅�r(φ)=a⋅ek⋅φ

How can I transform this "knowledge" to OpenScad, to receive a file in
which I can adjust the radients, the angles and the number of turns?

My aim is to create someting like that -->
https://www.kl-angelsport.de/images/thumbnail/produkte/medium/saenger_1907050.jpg

On 10/1/2023 11:37 PM, Karl Exler wrote:

This is the function of a logarithmic helix:
Funktion https://mathepedia.de/Reelle_Funktionen.html �(�)=�⋅��⋅�r(φ)=a⋅
ek⋅φ

My math isn't all that strong, and the article is in German and my German
extends only slightly past "Ich spreche kien Deutsch", but I think that's
the function of an exponential spiral.  It gives the radius of the spiral
for a particular angle phi around the spiral, with alpha being a scaling
factor on the radius and kappa being a scaling factor on the angle.

How can I transform this "knowledge" to OpenScad, to receive a file in
which I can adjust the radients, the angles and the number of turns?

Here's something that turns that formula into OpenSCAD and draws some
lines.  The next step (which I do not have time for at the moment) is to
sweep the points with a circle).  But see the important caveat below.

maxPhi = 7200;
alpha = 10;
kappa = 0.0005;
stretch = 0.1;

function toRect2(p) = [
p[0] * cos(p[1]),
p[0] * sin(p[1])
];

function logSpiralR(phi, alpha, kappa) = alpha * exp(kappa * phi);
function logSpiral(phi, alpha, kappa) =
toRect2([logSpiralR(phi, alpha, kappa), phi]);
function logHelix(phi, alpha, kappa, stretch) = concat(
logSpiral(phi, alpha, kappa),
phi * stretch);

for (phi=[0:maxPhi]) {
translate(logSpiral(phi, alpha, kappa)) square(2, center=true);
translate(logHelix(phi, alpha, kappa, stretch)) cube(2, center=true);
}

My aim is to create someting like that -->
https://www.kl-angelsport.de/images/thumbnail/produkte/medium/saenger_1907050.jpg

But that function produces a shape that expands to infinity, accelerating
its expansion, as you move along it, and that's not what this image shows.
I suspect that you want a function where the key piece is log() rather than
exp(), but again I'm out of time right now.

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Here's my approximation.  Only the stroke() command requires the
BOSL2 library:

    include <BOSL2/std.scad>
    $fn = 45;
    wire_d = 2;
    spring_l = 100;
    spring_d = 20;
    rod_d = 10;
    r_table = [
[0.00, 0],
[0.17, 0],
[0.50, 1],
[0.83, 0],
[1.00, 0],
    ];
    l_table = [
[0.00, -0.50],
[0.17, -0.45],
[0.20, -0.42],
[0.80, +0.42],
[0.83, +0.45],
[1.00, +0.50],
    ];
    loops = 17;
    lsteps = 45;
    tsteps = loops * lsteps;
    path = [
        for (i = [0:1:tsteps])
        let(
u = i / tsteps,
a = u * 360 * loops,
r = lookup(u, r_table) * spring_d/2 + wire_d/2 + rod_d/2,
z = lookup(u, l_table) * spring_l,
pt = [rcos(a), rsin(a), z]
        ) pt
    ];
rotate([0,90,0]) {
color("lightblue") stroke(path, width=wire_d);
cylinder(d=rod_d, h=spring_l+10, center=true);
    }

Screenshot 2023-10-03 at 6.05.28 PM.png

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Revised code to ensure "perfect" end wrap spacing of the spring wire if
you modify wire_d:

 include <BOSL2/std.scad>
 $fn = 45;
 wire_d = 2;
 spring_l = 100;
 spring_d = 20;
 rod_d = 10;
 loops = 17;
 tight_loops=3;

 tpart = tight_loops/loops;
 lpart = wire_d * tight_loops / 100;
 r_table = [
     [0.00, 0],
     [0.17, 0],
     [0.50, 1],
     [0.83, 0],
     [1.00, 0],
 ];
 l_table = [
     [0.00, -0.50],
     [0+tpart, -0.5+lpart],
     [1-tpart, +0.5-lpart],
     [1.00, +0.50],
 ];
 lsteps = 45;
 tsteps = loops * lsteps;
 path = [
     for (i = [0:1:tsteps])
     let(
         u = i / tsteps,
         a = u * 360 * loops,
         r = lookup(u, r_table) * spring_d/2 + wire_d/2 + rod_d/2,
         z = lookup(u, l_table) * spring_l,
         pt = [r*cos(a), r*sin(a), z]
     ) pt
 ];
 yrot(90) {
     color("lightblue")
         path_sweep(circle(d=wire_d), path);
     cylinder(d=rod_d, h=spring_l+10, center=true);
 }

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Revised code to ensure "perfect" end wrap spacing of the spring wire
if you modify wire_d:

    include <BOSL2/std.scad>
    $fn = 45;
    wire_d = 2;
    spring_l = 100;
    spring_d = 20;
    rod_d = 10;
    loops = 17;
    tight_loops=3;

    tpart = tight_loops/loops;
    lpart = wire_d * tight_loops / 100;
    r_table = [
        [0.00, 0],
        [0.17, 0],
        [0.50, 1],
        [0.83, 0],
        [1.00, 0],
    ];
    l_table = [
        [0.00, -0.50],
        [0+tpart, -0.5+lpart],
        [1-tpart, +0.5-lpart],
        [1.00, +0.50],
    ];
    lsteps = 45;
    tsteps = loops * lsteps;
    path = [
        for (i = [0:1:tsteps])
        let(
            u = i / tsteps,
            a = u * 360 * loops,
            r = lookup(u, r_table) * spring_d/2 + wire_d/2 + rod_d/2,
            z = lookup(u, l_table) * spring_l,
            pt = [rcos(a), rsin(a), z]
        ) pt
    ];
    yrot(90) {
        color("lightblue")
path_sweep(circle(d=wire_d), path);
        cylinder(d=rod_d, h=spring_l+10, center=true);
    }

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