From 754ca14785e74551b251d7e17152a7a607de7984 Mon Sep 17 00:00:00 2001 From: Elmom Date: Thu, 28 Apr 2011 11:40:13 +0300 Subject: [PATCH] Added trochoids.scad from thingiverse, needs cleaning --- trochoids.scad | 290 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 290 insertions(+) create mode 100644 trochoids.scad diff --git a/trochoids.scad b/trochoids.scad new file mode 100644 index 0000000..a0d00bb --- /dev/null +++ b/trochoids.scad @@ -0,0 +1,290 @@ +//=========================================== +// 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); + } + } + } +} +//===========================================