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