//these 4 functions are used by gear
function polar(r,theta)   = r*[sin(theta), cos(theta)];                            //convert polar to cartesian coordinates
function iang(r1,r2)      = sqrt((r2/r1)*(r2/r1) - 1)/3.1415926*180 - acos(r1/r2); //unwind a string this many degrees to go from radius r1 to radius r2
function q7(f,r,b,r2,t,s) = q6(b,s,t,(1-f)*max(b,r)+f*r2);                         //radius a fraction f up the curved side of the tooth 
function q6(b,s,t,d)      = polar(d,s*(iang(b,d)+t));                              //point at radius d on the involute curve
pi = 3.1415926;
module space(
   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
   hole_diameter   = 3,    //diameter of the hole in the center, in mm
   thickness       = 6,    //thickness of gear 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
	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
){
   p  = mm_per_tooth * number_of_teeth / pi / 2;     //radius of pitch circle
	c  = p + mm_per_tooth / pi - clearance;        //radius of outer circle
	b  = p*cos(pressure_angle);                    //radius of base circle
	r  = p-(c-p)-clearance;                        //radius of root circle
	t  = mm_per_tooth/2-backlash/2;                //tooth thickness at pitch circle
	k  = -iang(b, p) - t/2/p/pi*180;               //angle to where involute meets base circle on each side of tooth

   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<b ? k : -180/number_of_teeth),
								polar(r, r<b ? -k : 180/number_of_teeth),
								polar(r, 181/number_of_teeth)
							],
 							paths=[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]
						);
}

module tooth(
   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
   hole_diameter   = 3,    //diameter of the hole in the center, in mm
   thickness       = 6,    //thickness of gear 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
	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
){
   p  = mm_per_tooth * number_of_teeth / pi / 2;     //radius of pitch circle
	c  = p + mm_per_tooth / pi - clearance;        //radius of outer circle
	b  = p*cos(pressure_angle);                    //radius of base circle
	r  = p-(c-p)-clearance;                        //radius of root circle
	t  = mm_per_tooth/2-backlash/2;                //tooth thickness at pitch circle
	k  = -iang(b, p) - t/2/p/pi*180;               //angle to where involute meets base circle on each side of tooth

   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<b ? k : -180/number_of_teeth),
								q7(0/5,r,b,c,k, 1),q7(1/5,r,b,c,k, 1),q7(2/5,r,b,c,k, 1),q7(3/5,r,b,c,k, 1),q7(4/5,r,b,c,k, 1),q7(5/5,r,b,c,k, 1),
								q7(5/5,r,b,c,k,-1),q7(4/5,r,b,c,k,-1),q7(3/5,r,b,c,k,-1),q7(2/5,r,b,c,k,-1),q7(1/5,r,b,c,k,-1),q7(0/5,r,b,c,k,-1),
								polar(r, r<b ? -k : 180/number_of_teeth),
								polar(r, 181/number_of_teeth)
							],
 							paths=[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]
						);
}

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
) {

	p  = mm_per_tooth * number_of_teeth / pi / 2;  //radius of pitch circle
	c  = p + mm_per_tooth / pi - clearance;        //radius of outer circle
	b  = p*cos(pressure_angle);                    //radius of base circle
	r  = p-(c-p)-clearance;                        //radius of root circle
	t  = mm_per_tooth/2-backlash/2;                //tooth thickness at pitch circle
	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])
			     tooth(mm_per_tooth, number_of_teeth, hole_diameter, thickness, twist, pressure_angle, clearance, backlash);
			cylinder(h=2*thickness+1, r=hole_diameter/2, center=true, $fn=20);
		}
	
};	

n1 = 11; //red gear number of teeth

mm_per_tooth = 9; //all meshing gears need the same mm_per_tooth (and the same pressure_angle)
thickness    = 6;
hole         = 3;
height       = 12;

//color([1.00,0.75,0.75]) tooth(mm_per_tooth,n1,thickness);
//color([1.00,0.75,0.75]) gear(mm_per_tooth,n1,thickness,hole);
color([1.00,0.75,0.75]) space();