//////////////////////////////////////////////////////////////////////////////////////////////
// Public Domain Parametric Involute Spur Gear (and involute helical gear and involute rack)
// version 1.1
// by Leemon Baird, 2011, Leemon@Leemon.com
//http://www.thingiverse.com/thing:5505
//
// This file is public domain. Use it for any purpose, including commercial
// applications. Attribution would be nice, but is not required. There is
// no warranty of any kind, including its correctness, usefulness, or safety.
//
// This is parameterized involute spur (or helical) gear. It is much simpler and less powerful than
// others on Thingiverse. But it is public domain. I implemented it from scratch from the
// descriptions and equations on Wikipedia and the web, using Mathematica for calculations and testing,
// and I now release it into the public domain.
//
// http://en.wikipedia.org/wiki/Involute_gear
// http://en.wikipedia.org/wiki/Gear
// http://en.wikipedia.org/wiki/List_of_gear_nomenclature
// http://gtrebaol.free.fr/doc/catia/spur_gear.html
// http://www.cs.cmu.edu/~rapidproto/mechanisms/chpt7.html
//
// The module gear() gives an involute spur gear, with reasonable defaults for all the parameters.
// Normally, you should just choose the first 4 parameters, and let the rest be default values.
// The module gear() gives a gear in the XY plane, centered on the origin, with one tooth centered on
// the positive Y axis. The various functions below it take the same parameters, and return various
// measurements for the gear. The most important is pitch_radius, which tells how far apart to space
// gears that are meshing, and adendum_radius, which gives the size of the region filled by the gear.
// A gear has a "pitch circle", which is an invisible circle that cuts through the middle of each
// tooth (though not the exact center). In order for two gears to mesh, their pitch circles should
// just touch. So the distance between their centers should be pitch_radius() for one, plus pitch_radius()
// for the other, which gives the radii of their pitch circles.
//
// In order for two gears to mesh, they must have the same mm_per_tooth and pressure_angle parameters.
// mm_per_tooth gives the number of millimeters of arc around the pitch circle covered by one tooth and one
// space between teeth. The pitch angle controls how flat or bulged the sides of the teeth are. Common
// values include 14.5 degrees and 20 degrees, and occasionally 25. Though I've seen 28 recommended for
// plastic gears. Larger numbers bulge out more, giving stronger teeth, so 28 degrees is the default here.
//
// The ratio of number_of_teeth for two meshing gears gives how many times one will make a full
// revolution when the the other makes one full revolution. If the two numbers are coprime (i.e.
// are not both divisible by the same number greater than 1), then every tooth on one gear
// will meet every tooth on the other, for more even wear. So coprime numbers of teeth are good.
//
// The module rack() gives a rack, which is a bar with teeth. A rack can mesh with any
// gear that has the same mm_per_tooth and pressure_angle.
//
// Some terminology:
// The outline of a gear is a smooth circle (the "pitch circle") which has mountains and valleys
// added so it is toothed. So there is an inner circle (the "root circle") that touches the
// base of all the teeth, an outer circle that touches the tips of all the teeth,
// and the invisible pitch circle in between them. There is also a "base circle", which can be smaller than
// all three of the others, which controls the shape of the teeth. The side of each tooth lies on the path
// that the end of a string would follow if it were wrapped tightly around the base circle, then slowly unwound.
// That shape is an "involute", which gives this type of gear its name.
//
//////////////////////////////////////////////////////////////////////////////////////////////
//An involute spur gear, with reasonable defaults for all the parameters.
//Normally, you should just choose the first 4 parameters, and let the rest be default values.
//Meshing gears must match in mm_per_tooth, pressure_angle, and twist,
//and be separated by the sum of their pitch radii, which can be found with pitch_radius().
module gear (
mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
number_of_teeth = 11, //total number of teeth around the entire perimeter
thickness = 6, //thickness of gear in mm
hole_diameter = 3, //diameter of the hole in the center, in mm
twist = 0, //teeth rotate this many degrees from bottom of gear to top. 360 makes the gear a screw with each thread going around once
teeth_to_hide = 0, //number of teeth to delete to make this only a fraction of a circle
pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
clearance = 0.0, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
backlash = 0.0 //gap between two meshing teeth, in the direction along the circumference of the pitch circle
) {
assign(pi = 3.1415926)
assign(p = mm_per_tooth * number_of_teeth / pi / 2) //radius of pitch circle
assign(c = p + mm_per_tooth / pi - clearance) //radius of outer circle
assign(b = p*cos(pressure_angle)) //radius of base circle
assign(r = p-(c-p)-clearance) //radius of root circle
assign(t = mm_per_tooth/2-backlash/2) //tooth thickness at pitch circle
assign(k = -iang(b, p) - t/2/p/pi*180) { //angle to where involute meets base circle on each side of tooth
difference() {
for (i = [0:number_of_teeth-teeth_to_hide-1] )
rotate([0,0,i*360/number_of_teeth])
linear_extrude(height = thickness, center = true, convexity = 10, twist = twist)
polygon(
points=[
[0, -hole_diameter/10],
polar(r, -181/number_of_teeth),
polar(r, r