Parametric Helical Coil (Spring)
thingiverse
An experiment to create an accurate helical coil in OpenSCAD using linear_extrude. In order for this to work, a polygon representing the end section of the spring must first be calculated. To derive this equation, follow these steps: 1) Start with a circle representing the cross-section of round wire. 2) This wire will be angled by the spring's pitch angle; therefore, the cross-section gets stretched into an ellipse by scaling one axis. 3) Then this ellipse gets distorted by wrapping it around the mean coil diameter. 4) Finally use extrude this shape vertically while twisting it. It was a mathematically intriguing challenge, and the result appears visually appealing.
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