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+//===========================================
+//   Public Domain Epi- and Hypo- trochoids in OpenSCAD
+//   version 1.0
+//   by Matt Moses, 2011, mmoses152@gmail.com
+//   http://www.thingiverse.com/thing:8067
+//
+//   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.
+//
+//   An EPITROCHOID is a curve traced by a point 
+//   fixed at a distance "d" 
+//   to the center of a circle of radius "r"
+//   as the circle rolls 
+//   outside another circle of radius "R".
+//
+//   An HYPOTROCHOID is a curve traced by a point 
+//   fixed at a distance "d" 
+//   to the center of a circle of radius "r"
+//   as the circle rolls 
+//   inside another circle of radius "R".
+//
+//   An EPICYCLOID is an epitrochoid with d = r.
+//
+//   An HYPOCYCLOID is an hypotrochoid with d = r.
+//
+//   See http://en.wikipedia.org/wiki/Epitrochoid
+//   and http://en.wikipedia.org/wiki/Hypotrochoid
+// 
+//   Beware the polar forms of the equations on Wikipedia...
+//   They are correct, but theta is measured to the center of the small disk!!
+//===========================================
+
+// There are several different methods for extruding.  The best are probably
+// the ones using linear extrude.
+
+
+//===========================================
+//   Demo - draws one of each, plus some little wheels and sticks.
+//
+//   Fun stuff to try: 
+//   Animate, try FPS = 5 and Steps = 200
+//   R = 2, r = 1, d = 0.2
+//   R = 4, r = 1, d = 1
+//   R = 2, r = 1, d = 0.5
+//   
+//   What happens when you make d > r ??
+//   What happens when d < 0 ??
+//   What happens when r < 0 ??
+//
+//===========================================
+
+$fn = 30;
+
+thickness = 2;
+R = 4;
+r = 1;
+d = 1;
+n = 60; // number of wedge segments
+
+alpha = 360*$t;
+
+color([0, 0, 1])
+translate([0, 0, -0.5])
+	cylinder(h = 1, r= R, center = true);
+
+color([0, 1, 0])
+epitrochoid(R,r,d,n,thickness);
+
+color([1, 0, 0])
+translate([ (R+r)*cos(alpha) , (R+r)*sin(alpha), -0.5]) {
+	rotate([0, 0, alpha + R/r*alpha]) {
+		cylinder(h = 1, r = r, center = true);
+		translate([-d, 0, 1.5]) {
+			cylinder(h = 2.2, r = 0.1, center = true);
+		}
+	}
+}
+
+
+translate([2*(abs(R) + abs(r) + abs(d)), 0, 0]){
+color([0, 0, 1])
+translate([0, 0, -0.5])
+	difference() {
+		cylinder(h = 1, r = 1.1*R, center = true);
+		cylinder(h = 1.1, r= R, center = true);
+	}
+
+color([0, 1, 0])
+hypotrochoid(R,r,d,n,thickness);
+
+color([1, 0, 0])
+translate([ (R-r)*cos(alpha) , (R-r)*sin(alpha), -0.5]) {
+	rotate([0, 0, alpha - R/r*alpha]) {
+		cylinder(h = 1, r = r, center = true);
+		translate([d, 0, 1.5]) {
+			cylinder(h = 2.2, r = 0.1, center = true);
+		}
+	}
+}
+}
+
+// This just makes a twisted hypotrochoid
+translate([0,14, 0])
+hypotrochoidLinear(4, 1, 1, 40, 40, 10, 30);
+
+//   End of Demo Section
+//===========================================
+
+
+//===========================================
+// Epitrochoid
+//
+module epitrochoid(R, r, d, n, thickness) {
+	dth = 360/n;
+	for ( i = [0:n-1] ) {
+			polyhedron(points = [[0,0,0], 
+			[(R+r)*cos(dth*i) - d*cos((R+r)/r*dth*i), (R+r)*sin(dth*i) - d*sin((R+r)/r*dth*i), 0], 
+			[(R+r)*cos(dth*(i+1)) - d*cos((R+r)/r*dth*(i+1)), (R+r)*sin(dth*(i+1)) - d*sin((R+r)/r*dth*(i+1)), 0], 
+			[0,0,thickness], 
+			[(R+r)*cos(dth*i) - d*cos((R+r)/r*dth*i), (R+r)*sin(dth*i) - d*sin((R+r)/r*dth*i), thickness], 
+			[(R+r)*cos(dth*(i+1)) - d*cos((R+r)/r*dth*(i+1)), (R+r)*sin(dth*(i+1)) - d*sin((R+r)/r*dth*(i+1)), thickness]],
+			triangles = [[0, 2, 1], 
+			[0, 1,  3], 
+			[3, 1, 4], 
+			[3, 4, 5], 
+			[0, 3, 2], 
+			[2, 3, 5],
+			[1, 2, 4],
+			[2, 5, 4]]);
+	}
+}
+//===========================================
+
+
+//===========================================
+// Hypotrochoid
+//
+module hypotrochoid(R, r, d, n, thickness) {
+	dth = 360/n;
+	for ( i = [0:n-1] ) {
+			polyhedron(points = [[0,0,0], 
+			[(R-r)*cos(dth*i) + d*cos((R-r)/r*dth*i), (R-r)*sin(dth*i) - d*sin((R-r)/r*dth*i), 0], 
+			[(R-r)*cos(dth*(i+1)) + d*cos((R-r)/r*dth*(i+1)), (R-r)*sin(dth*(i+1)) - d*sin((R-r)/r*dth*(i+1)), 0], 
+			[0,0,thickness], 
+			[(R-r)*cos(dth*i) + d*cos((R-r)/r*dth*i), (R-r)*sin(dth*i) - d*sin((R-r)/r*dth*i), thickness], 
+			[(R-r)*cos(dth*(i+1)) + d*cos((R-r)/r*dth*(i+1)), (R-r)*sin(dth*(i+1)) - d*sin((R-r)/r*dth*(i+1)), thickness]],
+			triangles = [[0, 2, 1], 
+			[0, 1,  3], 
+			[3, 1, 4], 
+			[3, 4, 5], 
+			[0, 3, 2], 
+			[2, 3, 5],
+			[1, 2, 4],
+			[2, 5, 4]]);
+	}
+}
+//===========================================
+
+
+//===========================================
+// Epitrochoid Wedge with Bore
+//
+module epitrochoidWBore(R, r, d, n, p, thickness, rb) {
+	dth = 360/n;
+	union() {
+	for ( i = [0:p-1] ) {
+			polyhedron(points = [[rb*cos(dth*i), rb*sin(dth*i),0], 
+			[(R+r)*cos(dth*i) - d*cos((R+r)/r*dth*i), (R+r)*sin(dth*i) - d*sin((R+r)/r*dth*i), 0], 
+			[(R+r)*cos(dth*(i+1)) - d*cos((R+r)/r*dth*(i+1)), (R+r)*sin(dth*(i+1)) - d*sin((R+r)/r*dth*(i+1)), 0], 
+			[rb*cos(dth*(i+1)), rb*sin(dth*(i+1)), 0], 
+			[rb*cos(dth*i), rb*sin(dth*i), thickness],
+			[(R+r)*cos(dth*i) - d*cos((R+r)/r*dth*i), (R+r)*sin(dth*i) - d*sin((R+r)/r*dth*i), thickness], 
+			[(R+r)*cos(dth*(i+1)) - d*cos((R+r)/r*dth*(i+1)), (R+r)*sin(dth*(i+1)) - d*sin((R+r)/r*dth*(i+1)), thickness],
+			[rb*cos(dth*(i+1)), rb*sin(dth*(i+1)), thickness]],
+			triangles = [[0, 1, 4], [4, 1, 5],
+			[1, 2, 5], [5, 2, 6], 
+			[2, 3, 7], [7, 6, 2], 
+			[3, 0, 4], [4, 7, 3], 
+			[4, 5, 7], [7, 5, 6], 
+			[0, 3, 1], [1, 3, 2]]); 
+	}
+	}
+}
+//===========================================
+
+
+//===========================================
+// Epitrochoid Wedge with Bore, Linear Extrude
+//
+module epitrochoidWBoreLinear(R, r, d, n, p, thickness, rb, twist) {
+	dth = 360/n;
+	linear_extrude(height = thickness, convexity = 10, twist = twist) {
+	union() {
+	for ( i = [0:p-1] ) {
+			polygon(points = [[rb*cos(dth*i), rb*sin(dth*i)], 
+			[(R+r)*cos(dth*i) - d*cos((R+r)/r*dth*i), (R+r)*sin(dth*i) - d*sin((R+r)/r*dth*i)], 
+			[(R+r)*cos(dth*(i+1)) - d*cos((R+r)/r*dth*(i+1)), (R+r)*sin(dth*(i+1)) - d*sin((R+r)/r*dth*(i+1))], 
+			[rb*cos(dth*(i+1)), rb*sin(dth*(i+1))]],
+			paths = [[0, 1, 2, 3]], convexity = 10); 
+	}
+	}
+	}
+}
+//===========================================
+
+
+//===========================================
+// Epitrochoid Wedge, Linear Extrude
+//
+module epitrochoidLinear(R, r, d, n, p, thickness, twist) {
+	dth = 360/n;
+	linear_extrude(height = thickness, convexity = 10, twist = twist) {
+	union() {
+	for ( i = [0:p-1] ) {
+			polygon(points = [[0, 0], 
+			[(R+r)*cos(dth*i) - d*cos((R+r)/r*dth*i), (R+r)*sin(dth*i) - d*sin((R+r)/r*dth*i)], 
+			[(R+r)*cos(dth*(i+1)) - d*cos((R+r)/r*dth*(i+1)), (R+r)*sin(dth*(i+1)) - d*sin((R+r)/r*dth*(i+1))]], 
+			paths = [[0, 1, 2]], convexity = 10); 
+	}
+	}
+	}
+}
+//===========================================
+
+
+//===========================================
+// Hypotrochoid Wedge with Bore
+//
+module hypotrochoidWBore(R, r, d, n, p, thickness, rb) {
+	dth = 360/n;
+	union() {
+	for ( i = [0:p-1] ) {
+			polyhedron(points = [[rb*cos(dth*i), rb*sin(dth*i),0], 
+			[(R-r)*cos(dth*i) + d*cos((R-r)/r*dth*i), (R-r)*sin(dth*i) - d*sin((R-r)/r*dth*i), 0], 
+			[(R-r)*cos(dth*(i+1)) + d*cos((R-r)/r*dth*(i+1)), (R-r)*sin(dth*(i+1)) - d*sin((R-r)/r*dth*(i+1)), 0], 
+			[rb*cos(dth*(i+1)), rb*sin(dth*(i+1)), 0], 
+			[rb*cos(dth*i), rb*sin(dth*i), thickness],
+			[(R-r)*cos(dth*i) + d*cos((R-r)/r*dth*i), (R-r)*sin(dth*i) - d*sin((R-r)/r*dth*i), thickness], 
+			[(R-r)*cos(dth*(i+1)) + d*cos((R-r)/r*dth*(i+1)), (R-r)*sin(dth*(i+1)) - d*sin((R-r)/r*dth*(i+1)), thickness],
+			[rb*cos(dth*(i+1)), rb*sin(dth*(i+1)), thickness]],
+			triangles = [[0, 1, 4], [4, 1, 5],
+			[1, 2, 5], [5, 2, 6], 
+			[2, 3, 7], [7, 6, 2], 
+			[3, 0, 4], [4, 7, 3], 
+			[4, 5, 7], [7, 5, 6], 
+			[0, 3, 1], [1, 3, 2]]); 
+	}
+	}
+}
+//===========================================
+
+
+//===========================================
+// Hypotrochoid Wedge with Bore, Linear Extrude
+//
+module hypotrochoidWBoreLinear(R, r, d, n, p, thickness, rb, twist) {
+	dth = 360/n;
+	linear_extrude(height = thickness, convexity = 10, twist = twist) {
+	union() {
+	for ( i = [0:p-1] ) {
+			polygon(points = [[rb*cos(dth*i), rb*sin(dth*i)], 
+			[(R-r)*cos(dth*i) + d*cos((R-r)/r*dth*i), (R-r)*sin(dth*i) - d*sin((R-r)/r*dth*i)], 
+			[(R-r)*cos(dth*(i+1)) + d*cos((R-r)/r*dth*(i+1)), (R-r)*sin(dth*(i+1)) - d*sin((R-r)/r*dth*(i+1))], 
+			[rb*cos(dth*(i+1)), rb*sin(dth*(i+1))]], 
+			paths = [[0, 1, 2, 3]], convexity = 10); 
+	}
+	}
+	}
+}
+//===========================================
+
+
+//===========================================
+// Hypotrochoid Wedge, Linear Extrude
+//
+module hypotrochoidLinear(R, r, d, n, p, thickness, twist) {
+	dth = 360/n;
+	linear_extrude(height = thickness, convexity = 10, twist = twist) {
+	union() {
+	for ( i = [0:p-1] ) {
+			polygon(points = [[0, 0], 
+			[(R-r)*cos(dth*i) + d*cos((R-r)/r*dth*i), (R-r)*sin(dth*i) - d*sin((R-r)/r*dth*i)], 
+			[(R-r)*cos(dth*(i+1)) + d*cos((R-r)/r*dth*(i+1)), (R-r)*sin(dth*(i+1)) - d*sin((R-r)/r*dth*(i+1))]],
+			paths = [[0, 1, 2]], convexity = 10); 
+	}
+	}
+	}
+}
+//===========================================