Coil springs

Coil springs#

See also: https://en.wikipedia.org/wiki/Coil_spring

See also: https://en.wikipedia.org/wiki/Spring_(device)

Spring 2#

An example in C#

var x = ((-3.75 * t + 100) * Math.Sin(t * Math.PI)) / 100;
var z = (20 * t) / 100;
var y = ((-3.75 * t + 100) * Math.Cos(t * Math.PI)) / 100;

Some text

Path_Spiral2_Aa \(\quad\) Path_Spiral2_Ba

Left figure: Spiral 2 (see also Wikipedia [1462], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=80^\circ\) and \(\phi = 90^\circ\).

Right figure: Spiral 2 (see also Wikipedia [1444], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=100^\circ\) and \(\phi = 90^\circ\).

Spring 6#

An example in C#

var x = (Math.Sqrt(10000 - 100 * t * t) * Math.Sin(t * Math.PI)) / 100;
var z = (20 * t) / 100;
var y = (Math.Sqrt(10000 - 100 * t * t) * Math.Cos(t * Math.PI)) / 100;

Some text

Path_Spiral6_Aa \(\quad\) Path_Spiral6_Ba

Left figure: Spiral 6 (see also Wikipedia [1462], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=80^\circ\) and \(\phi = 90^\circ\).

Right figure: Spiral 6 (see also Wikipedia [1444], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=100^\circ\) and \(\phi = 90^\circ\).

Spring 7a#

An example in C#

var x = (Math.Sqrt(10000 - 100 * t * t) * Math.Sin(t * Math.PI)) / 100;
var z = 209.22 * (Math.Tanh(0.1896 * t)) / 100;
var y = (Math.Sqrt(10000 - 100 * t * t) * Math.Cos(t * Math.PI)) / 100;

Some text

Path_Spiral7a_Aa \(\quad\) Path_Spiral7a_Ba

Left figure: Spiral 7a (see also Wikipedia [1462], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=80^\circ\) and \(\phi = 90^\circ\).

Right figure: Spiral 7a (see also Wikipedia [1444], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=100^\circ\) and \(\phi = 90^\circ\).

Spring 7b#

An example in C#

var x = (200 * Math.Cos(0.05 * t * Math.PI) * Math.Sin(t * Math.PI)) / 100;
var z = 209.22 * (Math.Tanh(0.1896 * t)) / 100;
var y = (200 * Math.Cos(0.05 * t * Math.PI) * Math.Cos(t * Math.PI)) / 100;

Some text

Path_Spiral7b_Aa \(\quad\) Path_Spiral7b_Ba

Left figure: Spiral 7b (see also Wikipedia [1462], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=80^\circ\) and \(\phi = 90^\circ\).

Right figure: Spiral 7b (see also Wikipedia [1444], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=100^\circ\) and \(\phi = 90^\circ\).

Spring 7c#

An example in C#

double e = Math.Exp(-(0.2 * t) * (0.2 * t));
var x = (200 * e * Math.Sin(t * Math.PI)) / 100;
var z = 209.22 * (Math.Tanh(0.1896 * t)) / 100;
var y = (200 * e * Math.Cos(t * Math.PI)) / 100;

Some text

Path_Spiral7c_Aa \(\quad\) Path_Spiral7c_Ba

Left figure: Spiral 7c (see also Wikipedia [1462], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=80^\circ\) and \(\phi = 90^\circ\).

Right figure: Spiral 7c (see also Wikipedia [1444], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=100^\circ\) and \(\phi = 90^\circ\).

Spring 7d#

An example in C#

double e = Math.Exp(-(0.2 * t) * (0.2 * t));
var x = ((200 - 140 * e) * Math.Sin(t * Math.PI)) / 100;
var z = 207.46 * (Math.Tanh(0.2 * t)) / 100;
var y = ((200 - 140 * e) * Math.Cos(t * Math.PI)) / 100;

Some text

Path_Spiral7d_Aa \(\quad\) Path_Spiral7d_Ba

Left figure: Spiral 7d (see also Wikipedia [1462], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=80^\circ\) and \(\phi = 90^\circ\).

Right figure: Spiral 7d (see also Wikipedia [1444], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=100^\circ\) and \(\phi = 90^\circ\).

Spring 8#

An example in C#

var x = (200 * Math.Cos(t) * Math.Cos(Math.Atan(0.15 * t))) / 100;
var z = -200 * Math.Sin(Math.Atan(0.15 * t)) / 100;
var y = (200 * Math.Sin(t) * Math.Cos(Math.Atan(0.15 * t))) / 100;

Some text

Path_Spiral8_Aa \(\quad\) Path_Spiral8_Ba

Left figure: Spiral 8 (see also Wikipedia [1462], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=80^\circ\) and \(\phi = 90^\circ\).

Right figure: Spiral 8 (see also Wikipedia [1444], Gray et al. [368], Krivoshapko and Ivanov [421]). Camera angles are \(\theta=100^\circ\) and \(\phi = 90^\circ\).

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