Added ability to make spiral bevel gears.

involute_gears.scad

@@ -2,8 +2,8 @@
 // Public Domain Parametric Involute Spur Gear (and involute helical gear and involute rack)
 // version 1.1
 // by Leemon Baird, 2011, Leemon@Leemon.com
-// Corrected and tweaked by Revar Desmera, 2017, revarbat@gmail.com
 // http://www.thingiverse.com/thing:5505
+// Tweaked, and improved by Revar Desmera, 2017-2019, revarbat@gmail.com
 //
 // This file is public domain.  Use it for any purpose, including commercial
 // applications.  Attribution would be nice, but is not required.  There is
@@ -57,6 +57,83 @@
 //////////////////////////////////////////////////////////////////////////////////////////////
 
 
+//gear_tooth_profile(mm_per_tooth=5, number_of_teeth=20, pressure_angle=20);
+module gear_tooth_profile(
+	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
+	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
+	bevelang        = 0.0
+) {
+	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
+	scale([1, 1/cos(bevelang), 1])
+	translate([0,-r,0])
+	polygon(
+		points=[
+			polar(r-1, -181/number_of_teeth),
+			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),
+			polar(r-1, 181/number_of_teeth),
+		]
+	);
+}
+
+
+// Creates a 2D involute spur gear, with reasonable defaults for all the parameters.
+// Normally, you should just specify the first 2 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().
+//   mm_per_tooth  = This is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
+//   number_of_teeth = Total number of teeth along the rack
+//   teeth_to_hide = Number of teeth to delete to make this only a fraction of a circle
+//   pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
+//   clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
+//   backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
+// Example:
+//   gear2d(mm_per_tooth=5, number_of_teeth=20);
+//   linear_extrude(height=5*20/PI/2/2, scale=0.5) gear2d(mm_per_tooth=5, number_of_teeth=20);
+module gear2d(
+	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
+	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
+	bevelang        = 0.0
+) {
+	p  = mm_per_tooth * number_of_teeth / PI / 2; //radius of pitch circle
+	c  = p + mm_per_tooth / PI - clearance;       //radius of outer circle
+	r  = p-(c-p)-clearance;                       //radius of root circle
+	union() {
+		circle(r=r-0.5, $fn=number_of_teeth);
+		for (i = [0:number_of_teeth-teeth_to_hide-1] ) {
+			rotate(i*360/number_of_teeth) {
+				translate([0,r,0]) {
+					gear_tooth_profile(
+						mm_per_tooth    = mm_per_tooth,
+						number_of_teeth = number_of_teeth,
+						pressure_angle  = pressure_angle,
+						clearance       = clearance,
+						backlash        = backlash,
+						bevelang        = bevelang
+					);
+				}
+			}
+		}
+	}
+}
+
+
 // Creates 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,
@@ -65,56 +142,68 @@
 //   number_of_teeth = Total number of teeth along the rack
 //   thickness = Thickness of rack in mm (affects each tooth)
 //   hole_diameter = Diameter of centeral shaft hole.
-//   twist = 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 = Number of teeth to delete to make this only a fraction of a circle
 //   pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
 //   clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
 //   backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
+//   twist = Teeth rotate this many degrees from bottom of gear to top.  360 makes the gear a screw with each thread going around once
+//   scale = Scale of top of gear compared to bottom.  Useful for making crown gears.
+//	 slices = Number of slices to divide gear into.  Useful for refining gears with `twist`.
 // Example:
-//   gear(mm_per_tooth=5, number_of_teeth=20, thickness=5, hole_diameter=5);
+//   gear(mm_per_tooth=5, number_of_teeth=20, thickness=10*cos(45), hole_diameter=5, twist=-30, bevelang=45, slices=12, $fa=1, $fs=1);
+//   gear(mm_per_tooth=5, number_of_teeth=20, thickness=8, hole_diameter=5, $fa=1, $fs=1);
 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
+	backlash        = 0.0,   //gap between two meshing teeth, in the direction along the circumference of the pitch circle
+	bevelang        = 0.0,   //angle of bevelled gear face.
+	twist           = undef, //teeth rotate this many degrees from bottom of gear to top.  360 makes the gear a screw with each thread going around once
+	slices          = undef  //Number of slices to divide gear into.  Useful for refining gears with `twist`.
 ) {
 	p  = mm_per_tooth * number_of_teeth / PI / 2; //radius of pitch circle
+	p2 = p - (thickness*tan(bevelang));
 	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() {
-		linear_extrude(height = thickness, center = true, convexity = 10, twist = twist, slices = ceil(abs(twist)/5)+1)
+		linear_extrude(height=thickness, center=true, convexity=10, twist=twist, scale=p2/p, slices=slices) {
-			for (i = [0:number_of_teeth-teeth_to_hide-1] )
+			gear2d(
-				rotate([0,0,i*360/number_of_teeth])
+				mm_per_tooth    = mm_per_tooth,
-					polygon(
+				number_of_teeth = number_of_teeth,
-						points=[
+				teeth_to_hide   = teeth_to_hide,
-							polar(hole_diameter/10, -181/number_of_teeth),
+				pressure_angle  = pressure_angle,
-							polar(r, -181/number_of_teeth),
+				clearance       = clearance,
-							polar(r, r<b ? k : -180/number_of_teeth),
+				backlash        = backlash,
-							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),
+				bevelang        = bevelang
-							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),
-							polar(hole_diameter/10, 181/number_of_teeth),
-						],
-						paths=[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]]
 			);
+		}
+		if (hole_diameter > 0) {
 			cylinder(h=2*thickness+1, r=hole_diameter/2, center=true);
 		}
-};	
+		if (bevelang != 0) {
+			h = (c-r)*sin(bevelang);
+			translate([0,0,-thickness/2]) {
+				difference() {
+					cube([2*c/cos(bevelang),2*c/cos(bevelang),2*h], center=true);
+					cylinder(h=h, r1=r, r2=c, center=false);
+				}
+			}
+		}
+	}
+}
+
+
 //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)/PI*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
 
+
 // Creates a rack, which is a straight line with teeth.
 // The same as a segment of teeth from an infinite diameter gear.
 // The "pitch circle" is a line along the X axis.
@@ -154,7 +243,8 @@ module rack (
 					],
 					paths=[[0,1,2,3,4,5,6,7]]
 				);
-};	
+}
+
 
 //These 5 functions let the user find the derived dimensions of the gear.
 //A gear fits within a circle of radius outer_radius, and two gears should have
@@ -168,6 +258,7 @@ function pitch_radius    (mm_per_tooth=5,number_of_teeth=11) = mm_per_tooth * nu
 function outer_radius    (mm_per_tooth=5,number_of_teeth=11,clearance=0.1)    //The gear fits entirely within a cylinder of this radius.
 	= mm_per_tooth*(1+number_of_teeth/2)/PI  - clearance;
 
+
 //////////////////////////////////////////////////////////////////////////////////////////////
 //example gear train.
 //Try it with OpenSCAD View/Animate command with 20 steps and 24 FPS.