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Gears.scad
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// Minor modifications of code by GregFrost for this: http://www.thingiverse.com/thing:3575
// and Reprappro: https://github.com/reprappro/Extruder-drive
include <measured_numbers.scad>
include <design_numbers.scad>
include <util.scad>
use <Nema17_and_Ramps_and_bearings.scad>
// Sweep.scad contains code from
// https://github.com/openscad/scad-utils
// and
// https://github.com/openscad/list-comprehension-demos
use <sweep.scad>
//////////// Functions /////////////
function mirror_point(coord) =
[
coord[0],
-coord[1]
];
function rotate_point(rotate, coord) =
[
cos(rotate)*coord[0] + sin(rotate)*coord[1],
cos(rotate)*coord[1] - sin(rotate)*coord[0]
];
function involute(base_radius, involute_angle) =
[
base_radius*(cos(involute_angle) + involute_angle*PI/180*sin(involute_angle)),
base_radius*(sin(involute_angle) - involute_angle*PI/180*cos(involute_angle)),
];
function rotated_involute(rotate, base_radius, involute_angle) =
[
cos(rotate)*involute(base_radius, involute_angle)[0] + sin(rotate)*involute(base_radius, involute_angle)[1],
cos(rotate)*involute(base_radius, involute_angle)[1] - sin(rotate)*involute(base_radius, involute_angle)[0]
];
function involute_intersect_angle(base_radius, radius) = sqrt(pow(radius/base_radius, 2) - 1)*180/PI;
//////////// Modules /////////////
module involute_gear_tooth(pitch_radius,
root_radius,
base_radius,
outer_radius,
half_thick_angle,
involute_facets){
min_radius = max(base_radius,root_radius);
pitch_point = involute(base_radius, involute_intersect_angle(base_radius, pitch_radius));
pitch_angle = atan2(pitch_point[1], pitch_point[0]);
centre_angle = pitch_angle + half_thick_angle;
start_angle = involute_intersect_angle(base_radius, min_radius);
stop_angle = involute_intersect_angle(base_radius, outer_radius);
res=(involute_facets!=0)?involute_facets:($fn==0)?5:$fn/4;
for(i=[1:res]){
polygon(points=[[0,0], rotate_point(centre_angle, involute(base_radius,start_angle+(stop_angle - start_angle)*(i-1)/res)),
rotate_point(centre_angle, involute(base_radius,start_angle+(stop_angle - start_angle)*i/res)),
mirror_point(rotate_point(centre_angle, involute(base_radius,start_angle+(stop_angle - start_angle)*i/res))),
mirror_point(rotate_point(centre_angle, involute(base_radius,start_angle+(stop_angle - start_angle)*(i-1)/res)))],
paths=[[0,1,2,3,4,0]]);
}
}
module gear_shape(number_of_teeth,
pitch_radius,
root_radius,
base_radius,
outer_radius,
half_thick_angle,
involute_facets){
union(){
rotate(half_thick_angle) circle($fn=number_of_teeth*2, r=root_radius);
for(i = [1:number_of_teeth]){
rotate([0,0,i*360/number_of_teeth]){
involute_gear_tooth(pitch_radius = pitch_radius,
root_radius = root_radius,
base_radius = base_radius,
outer_radius = outer_radius,
half_thick_angle = half_thick_angle,
involute_facets = involute_facets);
}
}
}
}
module gear(number_of_teeth = 15,
circular_pitch = false,
diametral_pitch = false,
pressure_angle = 28,
clearance = 0.2,
gear_thickness = 5,
rim_thickness = 8,
rim_width = 5,
hub_thickness = 10,
hub_diameter = 15,
bore_diameter = 5,
circles = 0,
backlash = 0,
twist = 0,
involute_facets = 0){
if(circular_pitch==false && diametral_pitch==false)
echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch");
// Convert diametrial pitch to our native circular pitch
circular_pitch = (circular_pitch!=false?circular_pitch:180/diametral_pitch);
// Pitch diameter: Diameter of pitch circle.
pitch_diameter = number_of_teeth*circular_pitch/180;
pitch_radius = pitch_diameter/2;
//echo("Teeth:", number_of_teeth, " Pitch radius:", pitch_radius);
// Base Circle
base_radius = pitch_radius*cos(pressure_angle);
// Diametrial pitch: Number of teeth per unit length.
pitch_diametrial = number_of_teeth/pitch_diameter;
// Addendum: Radial distance from pitch circle to outside circle.
addendum = 1/pitch_diametrial;
//Outer Circle
outer_radius = pitch_radius + addendum;
// Dedendum: Radial distance from pitch circle to root diameter
dedendum = addendum + clearance;
// Root diameter: Diameter of bottom of tooth spaces.
root_radius = pitch_radius - dedendum;
backlash_angle = backlash/pitch_radius*180/PI;
half_thick_angle = (360/number_of_teeth - backlash_angle)/4;
// Variables controlling the rim.
rim_radius = root_radius - rim_width;
// Variables controlling the circular holes in the gear.
circle_orbit_diameter = hub_diameter/2 + rim_radius;
circle_orbit_curcumference = PI*circle_orbit_diameter;
// Limit the circle size to 90% of the gear face.
circle_diameter = min(0.70*circle_orbit_curcumference/circles,
(rim_radius-hub_diameter/2)*0.9);
difference(){
union(){
difference(){
linear_extrude(height = rim_thickness, convexity = 10, twist = twist)
gear_shape(number_of_teeth,
pitch_radius = pitch_radius,
root_radius = root_radius,
base_radius = base_radius,
outer_radius = outer_radius,
half_thick_angle = half_thick_angle,
involute_facets = involute_facets);
if(gear_thickness < rim_thickness)
translate([0,0,gear_thickness])
cylinder(r = rim_radius, h = rim_thickness-gear_thickness + 1);
}
if(gear_thickness > rim_thickness)
cylinder(r = rim_radius, h = gear_thickness);
if(hub_thickness > gear_thickness)
translate([0,0,gear_thickness])
cylinder(r = hub_diameter/2, h = hub_thickness - gear_thickness);
}
translate([0,0,-1])
cylinder(r = bore_diameter/2,
h = 2 + max(rim_thickness, hub_thickness, gear_thickness));
if(circles>0){
for(i=[0:circles-1])
rotate([0,0,i*360/circles])
translate([circle_orbit_diameter/2, 0, -1])
cylinder(r = circle_diameter/2, h = max(gear_thickness, rim_thickness) + 3);
}
}
}
module my_gear(teeth, height){
gear(number_of_teeth = teeth,
// Increasing circular_pitch this makes gears larger
// Should possibly be parameter in design_numbers.scad...
circular_pitch = Circular_pitch_top_gears,
pressure_angle = 30,
clearance = 0.2,
gear_thickness = height,
rim_thickness = height,
rim_width = 5,
hub_thickness = height,
hub_diameter = 15);
}
//my_gear(40,10);
module decoration_holes(){
for(i = [1:60:360]){
rotate([0,0,i])
translate([2*Snelle_radius/3,0,-1])
cylinder(r=8.5,h=Big);
}
}
module line_holes(){
rotate([90,0,33])
translate([0,Snelle_height/2,Snelle_radius/2])
cylinder(r = 0.95, h = 40);
rotate([90,0,27])
translate([0,Snelle_height/2,Snelle_radius/2])
cylinder(r = 0.95, h = 40);
}
// Sandwich is a sandwich gear on top of a snelle.
// These are modelled together, then split up before printing to make a cleaner edge.
// Sandwich height follows exactly 608 bearing thickness
module sandwich(worm=false, brim=Snelle_brim){
od = Bearing_608_outer_diameter;
bw = Bearing_608_width;
meltlength = 0.1;
difference(){
union(){
// sandwich gear
color(Printed_color_2)
if(worm){
translate([0, 0, Snelle_height])
worm_gear();
}else{
translate([0, 0, Snelle_height])
my_gear(Sandwich_gear_teeth, Sandwich_gear_height);
}
color(Printed_color_1){
// Snelle
cylinder(r = Snelle_radius, h = Snelle_height + meltlength, $fn=150);
cylinder(r = brim, h = Sandwich_edge_thickness, $fn=150);
}
}
// Dig out the right holes
// Bearing hole
translate([0, 0, -1.2])
cylinder(r = od/2 + 0.15, h = Sandwich_height); // 0.15 added to raduis during print...
cylinder(r = od/2-2, h = Big);
// Decoration/material saving holes
decoration_holes();
line_holes();
}
//Bearing_608();
}
//sandwich(brim=Snelle_radius+7);
//sandwich(worm=true);
//sandwich(worm=false);
module inverse_torx(h = Snelle_height + 2, r = Snelle_radius, female=false){
circs = 12;
difference(){
intersection(){
if(female){
cylinder(r=r+0.1, h=h, $fn=150);
} else {
cylinder(r=r, h=h, $fn=150);
}
for(i=[0:1:circs])
rotate([0,0,i*360/circs]){
translate([r-5,0,-1])
cylinder(r=r/4.2, h=h+2, $fn=50);
if(female){
rotate([0,0,360/(2*circs)])
translate([r-7,0,-1])
cylinder(r2=1, r1=r/1.9, h=h+2, $fn=50);
}
}
}
decoration_holes();
line_holes();
}
}
//inverse_torx();
// May not render correctly in preview...
module sandwich_gear(worm=false){
difference(){
sandwich(worm=worm);
translate([0,0,-1])
color(Printed_color_2)
cylinder(r=Big, h=Snelle_height + 1);
color("blue")
inverse_torx(female=true);
}
}
// Give space to worm so it doesn't lock up
//rotate([180,0,0])
//sandwich_gear(false);
//sandwich_gear(true);
// May not render correctly in preview...
module snelle(){
color(Printed_color_2)
difference(){
sandwich();
translate([0,0,Snelle_height-0.01])
cylinder(r=Big, h=Big);
}
color("red")
inverse_torx();
}
//snelle();
module snelle_line_buildup_visualization(){
module snelle(){
difference(){
color(Printed_color_2)
rotate([0,0,-103])
snelle();
translate([0,0,-1])
cylinder(r=Big, h=1.7);
}
}
module rectangular_torus(){
color("gold")
difference(){
cylinder(r=Snelle_radius+3, h=Snelle_height-1,$fn=300);
translate([0,0,-1])
cylinder(r=Snelle_radius, h=Snelle_height+2,$fn=300);
}
}
module line(){
translate([Snelle_radius+3,0,Snelle_height/2])
rotate([90,0,0])
cylinder(r=0.7, h=150);
}
module letters(){
translate([0,0,Snelle_height]){
color("white")
translate([0,-2.5,0])
cube([Snelle_radius+3, 5, 0.2]);
color("black")
translate([Snelle_radius/2,-2,0])
text("R", font="Times New Roman:style=Italic", size=4);
rotate([0,0,45]){
color("white")
translate([0,-2.5,0])
cube([Snelle_radius, 5, 0.2]);
color("black")
translate([Snelle_radius/2,-2,0])
text("r", font="Times New Roman:style=Italic", size=4);
}
}
}
rectangular_torus();
letters();
}
//snelle_line_buildup_visualization();
module motor_gear(height = Motor_protruding_shaft_length, shaft_radius = Motor_gear_shaft_radius_BC){
swgh = Sandwich_gear_height - 0.4; // allow some space for easier printing
melt = 0.1;
teeth = Motor_gear_teeth;
module the_bore(){
difference(){
translate([0, 0, -1])
cylinder(r = Nema17_motor_shaft/2 + 0.21, h = height + 2);
// D-wall in bore
translate([-6/2, Nema17_motor_shaft/2 - Shaft_flat, 0])
cube([6,3,height]);
}
// Phase in
translate([0,0,-0.1])
cylinder(r1=Nema17_motor_shaft/2+0.8, r2=1.6, h=3.0);
translate([0,0,height - 2.9])
cylinder(r2=Nema17_motor_shaft/2+0.8, r1=1.6, h=3.0);
// Mark the direction of the flat D-side
translate([-1,0,-1])
cube([2,10,1.5]);
}
difference(){
union(){
translate([0,0,height - swgh])
my_gear(teeth, swgh);
// Shaft cylinder
cylinder(r = shaft_radius, h = height - swgh + melt, $fn=40);
}
the_bore();
}
}
//motor_gear();
module motor_gear_a(){
motor_gear(Motor_gear_a_height, Motor_gear_shaft_radius_A);
}
//motor_gear_a();
module motor_gear_b(){
motor_gear(Motor_gear_b_height, Motor_gear_shaft_radius_BC);
}
//motor_gear_b();
module motor_gear_c(){
motor_gear(Motor_gear_c_height, Motor_gear_shaft_radius_BC);
}
//motor_gear_c();
// Visualization only
module gear_friends(){
translate([Four_point_five_point_radius,0,-5]) motor_gear();
sandwich();
}
//gear_friends();
// A gear with 90 degree valleys and a twist
module worm_gear(angle=Worm_largest_angle){
// phi_length = twist*(PI/180)*Worm_disc_radius
// angle = atan(phi_length/Sandwich_gear_height)
// tan(angle) = phi_length/Sandwich_gear_height
// = twist*(PI/180)*(Worm_disc_radius/Sandwich_gear_height)
// twist = tan(angle)*(180/PI)*(Sandwich_gear_height/Worm_disc_radius)
// twist = tan(angle)*Sandwich_gear_height
//echo(Worm_disc_radius);
//echo((PI/180));
//echo((PI/180)*Worm_disc_radius);
linear_extrude(height = Sandwich_gear_height,
convexity = 10,
twist = -tan(angle)*(180/PI)*(Sandwich_gear_height/Worm_disc_radius))
difference(){
// There is a radius and a virtual radius for worm gears in design_numbers.scad
// Cutting off the outermost virtual band has the same effect as if
// it was never there in the first place
circle(r=Worm_disc_radius, $fn=Sandwich_gear_teeth);
for(i=[0:Degrees_per_worm_gear_tooth:359.9]){
rotate([0,0,i])
// Worm_disc_virtual_radius affects Worm_disc_tooth_valley_r
translate([Worm_disc_tooth_valley_r,0])
rotate([0,0,-45])
square([30,30]);
}
}
}
//worm_gear(61);
//translate([0,Worm_disc_radius,0])
//rotate([0,61,0]) cylinder(r=2, h=10, center=true);
module placed_worm_gear(ang=0){
rotate([90,0,0])
translate([Worm_disc_tooth_valley_r+Worm_radius,0,-Sandwich_gear_height/2])
rotate([0,0,ang])
worm_gear();
}
//%placed_worm_gear();
// This is the worm for the worm drive
module worm(step=0.2, with_details=true){
stop_angle = Worm_spiral_turns*Degrees_per_worm_gear_tooth; // where main path stops
// XY-Translations of top (phase in), main (touch gear) and bottom (phase out) spirals
function translate_top_xy(v) = Worm_radius
- virtual_side*v/Degrees_per_worm_gear_tooth;
function translate_main_xy(v) = Worm_radius + Worm_disc_tooth_valley_r*(1 - cos(v));
function translate_bottom_xy(v) = Worm_radius
+ Worm_disc_tooth_valley_r*(1 - cos(v))
- 6*(v - stop_angle)/(Degrees_per_worm_gear_tooth);
module fill_interior(){
function my_circle(r) = [for (i=[0:Worm_spiral_turns*step*360/stop_angle:359.9])
r * [cos(i), sin(i)]];
// Scale profile to fill interior
towerpath1 = [for (v=[-Degrees_per_worm_gear_tooth : (stop_angle+2*Degrees_per_worm_gear_tooth)/20 : stop_angle + Degrees_per_worm_gear_tooth+0.01])
// Move downwards
translation([0, // x
0,
-Worm_disc_tooth_valley_r*sin(v)]) *
// Scale in xy to fill interior
scaling([(translate_main_xy(v)+virtual_side*(1 - cos(v)))/translate_main_xy(0),
(translate_main_xy(v)+virtual_side*(1 - cos(v)))/translate_main_xy(0),
0])
];
sweep(my_circle(Worm_smallest_radius), // Smallest radius at z=0
towerpath1);
}
// Worm gear tooth side including tip
virtual_side = sqrt(2)*(Worm_disc_virtual_radius - Worm_disc_tooth_valley_r);
// Extra sidelength needed to connect spiral with itself vertically
reduced_side = virtual_side-Worm_edge_cut; // might need hand tuning to compile
thread_profile = [
//[-reduced_side*sqrt(2),0,0], // With this corner, it's essentially a square
[-reduced_side/Sqrt2,0,-reduced_side/Sqrt2],
[-Worm_edge_cut,0,-Worm_edge_cut], // Round off outer edge
[-Worm_edge_cut,0,+Worm_edge_cut], // Virtual valley-hitting point in origo
[-reduced_side/Sqrt2,0,reduced_side/Sqrt2]
];
//p = [translation([0,0,0]),translation([0,1,0])];
//sweep(thread_profile,p);
// Top spiral
path0 = [for (v=[Degrees_per_worm_gear_tooth : -step : step])
rotation([0,0,-v*360/Degrees_per_worm_gear_tooth]) * // Rotate around z axis
translation([translate_top_xy(v), // x
0,
+Worm_disc_tooth_valley_r*sin(v)]) * // z
rotation([0,-v,0]) // Rotate shape around valley-hitting point
];
// Main path touching gear
path1 = [for (v=[0 : step : stop_angle + step])
rotation([0,0,v*360/Degrees_per_worm_gear_tooth]) *
translation([translate_main_xy(v), // x
0,
-Worm_disc_tooth_valley_r*sin(v)]) * // z
rotation([0,-v,0])
];
// Bottom spiral
path2 = [for (v=[stop_angle + 2*step : step : stop_angle
+ Degrees_per_worm_gear_tooth])
rotation([0,0,v*360/Degrees_per_worm_gear_tooth]) *
translation([translate_bottom_xy(v), // x
0,
-Worm_disc_tooth_valley_r*sin(v)]) * // z
rotation([0,-v,0])
];
height_downwards = Worm_disc_tooth_valley_r*sin(stop_angle+Degrees_per_worm_gear_tooth);
height_upwards = 5;
module worm_axle(h){
big_radius = Worm_smallest_radius*(translate_main_xy(stop_angle + Degrees_per_worm_gear_tooth)+virtual_side*(1 - cos(stop_angle + Degrees_per_worm_gear_tooth)))/translate_main_xy(0);
small_radius = big_radius - h + 1;
cylinder(h=h,r1=small_radius,r2=big_radius, $fs = step*big_radius);
}
//translate([0,0,height_downwards]) // Put bottom plane on z=0
difference(){
union(){
// Axle
translate([0,0,-height_downwards-Worm_axle_length])
worm_axle(Worm_axle_length+0.01);
// Spiral
if(with_details){
mirror([1,0,0]) // Right-handed threading to push with greatest force _down_ into bottom_plate
sweep(thread_profile, concat(path0, path1, path2));
fill_interior();
}else{
mirror([1,0,0]) // Right-handed threading to push with greatest force _down_ into bottom_plate
sweep(thread_profile, path1);
}
}
// Cut in half, see interior
//translate([0,-25,-40])
//cube([30,50,50]);
if(with_details){
// Motor shaft D-shaped bore
h = height_downwards + height_upwards + Worm_axle_length + 2;
rotate([0,0,45])
translate([0,0,-height_downwards - Worm_axle_length - 1])
difference(){
cylinder(r = 5.4/2, h = h+2, $fn=40);
translate([2.2,-(h+4),-2])
cube(2*(h+4));
}
// Phase in the D-shape
translate([0,0,-height_downwards - Worm_axle_length - 1]){
cylinder(d1=8, d2=5, h=3);
}
// Cut bottom (except Worm_axle)
translate([0,0,-Worm_axle_length - height_downwards])
difference() {
cylinder(h=Worm_axle_length,r=50);
worm_axle(Worm_axle_length);
}
// Cut top
translate([-50,-50,height_upwards])
cube(100);
// Screw hole and nut lock
for(i=[0,120,240]){
rotate([0,0,i]){
translate([0,0,-height_downwards+6.3-Worm_axle_length]){
rotate([0,90,45]){
scale([1.06,1.06,3])
M3_screw(6,true);
rotate([0,0,90])
translate([0,4,5])
rotate([90,0,0])
translate([-5.6/2,0,1]){
point_cube([5.6,2.5,9],120);
// Phase in nutlock
translate([5.6/2,2.5/2, 7.1])
linear_extrude(height=3,convexity=3,scale=[2.4, 2.7])
translate([-(5.6/1.5)/2,-(2.5/1.5)/2])
square([5.6/1.5,2.5/1.5]);
}
}
}
}
}
}
}
}
//worm(step=0.07);
module animate_roating_worm(){
rotate([0,0,360*$t])
rotate([0,5,0])
translate([0,0,10])
color(Printed_color_2)
worm(step=0.062);
}
//animate_roating_worm();
// ang is angle of worm plate, not worm itself
module placed_worm(ang = 0){
rotate([0,0,-ang*Sandwich_gear_teeth])
worm();
%placed_worm_gear(ang);
}
//placed_worm(ang=-12);
module sstruder_gear(){
difference(){
union(){
gear(
number_of_teeth = Sstruder_gear_teeth,
circular_pitch = Sstruder_gear_circular_pitch,
diametral_pitch = false,
pressure_angle = 30,
clearance = 0.2,
gear_thickness = Sstruder_gear_thickness,
rim_thickness = Sstruder_gear_thickness,
rim_width = 5,
hub_thickness = Sstruder_gear_thickness,
hub_diameter = 15,
bore_diameter = Nema17_motor_shaft,
circles = 0,
backlash = 0,
twist = 0,
involute_facets = 0
);
translate([Nema17_motor_shaft/2 - Shaft_flat,-5/2,0])
cube([1.5,5,Sstruder_gear_thickness]);
//base
//difference(){
// cylinder(r=6.3,h=1.0,$fn=64);
// cylinder(r=Nema17_motor_shaft/2,h=1.001,$fn=64);
//}
}
//lead in
translate([0,0,-0.01])
cylinder(r1=Nema17_motor_shaft/2+0.25,
r2=Nema17_motor_shaft/2-1,h=2,$fn=64);
}
}
//sstruder_gear();