Parametric tyre

// A parametric tyre: a rounded carcass swept around the axis, with a tread cut into the
// crown. Everything follows from the three sizes at the top, so a wheel for an RC car and
// one for a desk toy come out of the same source.

/* [Size] */
// Diameter measured over the tread, the outside of the tyre.
outer_diameter = 60; // [20:1:200]
// Diameter of the rim seat, the hole the tyre sits on.
rim_diameter = 34; // [10:1:160]
// Width across the tyre, bead to bead.
width = 22; // [4:1:80]

/* [Tread] */
// Blocks around the tyre. Zero leaves a slick.
tread_blocks = 24; // [0:1:80]
// How deep each groove is cut into the crown.
tread_depth = 1.8; // [0:0.1:6]
// How far the blocks lean across the tread, in degrees.
tread_angle = 18; // [0:1:60]
// Groove width as a share of the space between blocks.
tread_gap = 0.38; // [0.1:0.01:0.7]

/* [Shape] */
// How round the shoulders are. Zero is a square edge, one is a half circle.
shoulder = 0.55; // [0:0.05:1]
// Facets around the tyre. More is smoother and slower.
smoothness = 96; // [24:8:192]

/* [Colour] */
// Colour the tyre is shown in. Display only, the STL carries no colour.
color_tyre = "DimGray"; // [DimGray, Black, SlateGray, Silver, Gainsboro, White, FireBrick, SteelBlue, ForestGreen, Goldenrod]

/* [Hidden] */
outer_radius = outer_diameter / 2;
rim_radius = rim_diameter / 2;
half_width = width / 2;
// The shoulder never eats more than the tyre has to give, in either direction.
shoulder_radius = shoulder * min(half_width, outer_radius - rim_radius) * 0.9;
// One groove and one block share the pitch, so the gap scales with the block count.
pitch = tread_blocks > 0 ? 360 / tread_blocks : 360;
groove_width = 2 * PI * outer_radius * (pitch / 360) * tread_gap;

// The cross section, revolved later: flat where it meets the rim, rounded at the crown.
module section() {
  hull() {
    translate([rim_radius, -half_width]) square([0.01, width]);
    translate([outer_radius - shoulder_radius, -half_width + shoulder_radius])
      circle(r = shoulder_radius, $fn = 32);
    translate([outer_radius - shoulder_radius, half_width - shoulder_radius])
      circle(r = shoulder_radius, $fn = 32);
  }
}

module carcass() {
  rotate_extrude($fn = smoothness) section();
}

// A groove is a block leaned across the crown. Cutting them is cheaper than building the
// blocks themselves, and it keeps the crown curve intact between them.
module grooves() {
  for (index = [0 : max(tread_blocks - 1, 0)]) {
    rotate([0, 0, index * pitch])
      translate([outer_radius, 0, 0])
        rotate([tread_angle, 0, 0])
          cube([tread_depth * 2, groove_width, width * 3], center = true);
  }
}

module tyre() {
  if (tread_blocks > 0 && tread_depth > 0) {
    difference() {
      carcass();
      grooves();
    }
  } else {
    carcass();
  }
}

color(color_tyre) tyre();