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// Parametric Involute Bevel and Spur Gears by GregFrost
// It is licensed under the Creative Commons - GNU LGPL 2.1 license.
// © 2010 by GregFrost, thingiverse.com/Amp
// http://www.thingiverse.com/thing:3575 and http://www.thingiverse.com/thing:3752
// Simple Test:
//gear (circular_pitch=700,
// gear_thickness = 12,
// rim_thickness = 15,
// hub_thickness = 17,
// circles=8);
//Complex Spur Gear Test:
//test_gears ();
// Meshing Double Helix:
//test_meshing_double_helix ();
module test_meshing_double_helix(){
test_meshing_double_helix ();
}
// Demonstrate the backlash option for Spur gears.
//test_backlash ();
// Demonstrate how to make meshing bevel gears.
//test_bevel_gear_pair();
module test_bevel_gear_pair(){
bevel_gear_pair ();
}
module test_bevel_gear(){bevel_gear();}
//bevel_gear();
pi=3.1415926535897932384626433832795;
//==================================================
// Bevel Gears:
// Two gears with the same cone distance, circular pitch (measured at the cone distance)
// and pressure angle will mesh.
module bevel_gear_pair (
gear1_teeth = 41,
gear2_teeth = 7,
axis_angle = 90,
outside_circular_pitch=1000)
{
outside_pitch_radius1 = gear1_teeth * outside_circular_pitch / 360;
outside_pitch_radius2 = gear2_teeth * outside_circular_pitch / 360;
pitch_apex1=outside_pitch_radius2 * sin (axis_angle) +
(outside_pitch_radius2 * cos (axis_angle) + outside_pitch_radius1) / tan (axis_angle);
cone_distance = sqrt (pow (pitch_apex1, 2) + pow (outside_pitch_radius1, 2));
pitch_apex2 = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius2, 2));
echo ("cone_distance", cone_distance);
pitch_angle1 = asin (outside_pitch_radius1 / cone_distance);
pitch_angle2 = asin (outside_pitch_radius2 / cone_distance);
echo ("pitch_angle1, pitch_angle2", pitch_angle1, pitch_angle2);
echo ("pitch_angle1 + pitch_angle2", pitch_angle1 + pitch_angle2);
rotate([0,0,90])
translate ([0,0,pitch_apex1+20])
{
translate([0,0,-pitch_apex1])
bevel_gear (
number_of_teeth=gear1_teeth,
cone_distance=cone_distance,
pressure_angle=30,
outside_circular_pitch=outside_circular_pitch);
rotate([0,-(pitch_angle1+pitch_angle2),0])
translate([0,0,-pitch_apex2])
bevel_gear (
number_of_teeth=gear2_teeth,
cone_distance=cone_distance,
pressure_angle=30,
outside_circular_pitch=outside_circular_pitch);
}
}
//Bevel Gear Finishing Options:
bevel_gear_flat = 0;
bevel_gear_back_cone = 1;
module bevel_gear (
number_of_teeth=11,
cone_distance=100,
face_width=20,
outside_circular_pitch=1000,
pressure_angle=30,
clearance = 0.2,
bore_diameter=5,
gear_thickness = 15,
backlash = 0,
involute_facets=0,
finish = -1)
{
echo ("bevel_gear",
"teeth", number_of_teeth,
"cone distance", cone_distance,
face_width,
outside_circular_pitch,
pressure_angle,
clearance,
bore_diameter,
involute_facets,
finish);
// Pitch diameter: Diameter of pitch circle at the fat end of the gear.
outside_pitch_diameter = number_of_teeth * outside_circular_pitch / 180;
outside_pitch_radius = outside_pitch_diameter / 2;
// The height of the pitch apex.
pitch_apex = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius, 2));
pitch_angle = asin (outside_pitch_radius/cone_distance);
echo ("Num Teeth:", number_of_teeth, " Pitch Angle:", pitch_angle);
finish = (finish != -1) ? finish : (pitch_angle < 45) ? bevel_gear_flat : bevel_gear_back_cone;
apex_to_apex=cone_distance / cos (pitch_angle);
back_cone_radius = apex_to_apex * sin (pitch_angle);
// Calculate and display the pitch angle. This is needed to determine the angle to mount two meshing cone gears.
// Base Circle for forming the involute teeth shape.
base_radius = back_cone_radius * cos (pressure_angle);
// Diametrial pitch: Number of teeth per unit length.
pitch_diametrial = number_of_teeth / outside_pitch_diameter;
// Addendum: Radial distance from pitch circle to outside circle.
addendum = 1 / pitch_diametrial;
// Outer Circle
outer_radius = back_cone_radius + addendum;
// Dedendum: Radial distance from pitch circle to root diameter
dedendum = addendum + clearance;
dedendum_angle = atan (dedendum / cone_distance);
root_angle = pitch_angle - dedendum_angle;
root_cone_full_radius = tan (root_angle)*apex_to_apex;
back_cone_full_radius=apex_to_apex / tan (pitch_angle);
back_cone_end_radius =
outside_pitch_radius -
dedendum * cos (pitch_angle) -
gear_thickness / tan (pitch_angle);
back_cone_descent = dedendum * sin (pitch_angle) + gear_thickness;
// Root diameter: Diameter of bottom of tooth spaces.
root_radius = back_cone_radius - dedendum;
half_tooth_thickness = outside_pitch_radius * sin (360 / (4 * number_of_teeth)) - backlash / 4;
half_thick_angle = asin (half_tooth_thickness / back_cone_radius);
face_cone_height = apex_to_apex-face_width / cos (pitch_angle);
face_cone_full_radius = face_cone_height / tan (pitch_angle);
face_cone_descent = dedendum * sin (pitch_angle);
face_cone_end_radius =
outside_pitch_radius -
face_width / sin (pitch_angle) -
face_cone_descent / tan (pitch_angle);
// For the bevel_gear_flat finish option, calculate the height of a cube to select the portion of the gear that includes the full pitch face.
bevel_gear_flat_height = pitch_apex - (cone_distance - face_width) * cos (pitch_angle);
// translate([0,0,-pitch_apex])
difference ()
{
intersection ()
{
union()
{
rotate (half_thick_angle)
translate ([0,0,pitch_apex-apex_to_apex])
cylinder ($fn=number_of_teeth*2, r1=root_cone_full_radius,r2=0,h=apex_to_apex);
for (i = [1:number_of_teeth])
// for (i = [1:1])
{
rotate ([0,0,i*360/number_of_teeth])
{
involute_bevel_gear_tooth (
back_cone_radius = back_cone_radius,
root_radius = root_radius,
base_radius = base_radius,
outer_radius = outer_radius,
pitch_apex = pitch_apex,
cone_distance = cone_distance,
half_thick_angle = half_thick_angle,
involute_facets = involute_facets);
}
}
}
if (finish == bevel_gear_back_cone)
{
translate ([0,0,-back_cone_descent])
cylinder (
$fn=number_of_teeth*2,
r1=back_cone_end_radius,
r2=back_cone_full_radius*2,
h=apex_to_apex + back_cone_descent);
}
else
{
translate ([-1.5*outside_pitch_radius,-1.5*outside_pitch_radius,0])
cube ([3*outside_pitch_radius,
3*outside_pitch_radius,
bevel_gear_flat_height]);
}
}
if (finish == bevel_gear_back_cone)
{
translate ([0,0,-face_cone_descent])
cylinder (
r1=face_cone_end_radius,
r2=face_cone_full_radius * 2,
h=face_cone_height + face_cone_descent+pitch_apex);
}
translate ([0,0,pitch_apex - apex_to_apex])
cylinder (r=bore_diameter/2,h=apex_to_apex);
}
}
module involute_bevel_gear_tooth (
back_cone_radius,
root_radius,
base_radius,
outer_radius,
pitch_apex,
cone_distance,
half_thick_angle,
involute_facets)
{
// echo ("involute_bevel_gear_tooth",
// back_cone_radius,
// root_radius,
// base_radius,
// outer_radius,
// pitch_apex,
// cone_distance,
// half_thick_angle);
min_radius = max (base_radius*2,root_radius*2);
pitch_point =
involute (
base_radius*2,
involute_intersect_angle (base_radius*2, back_cone_radius*2));
pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
centre_angle = pitch_angle + half_thick_angle;
start_angle = involute_intersect_angle (base_radius*2, min_radius);
stop_angle = involute_intersect_angle (base_radius*2, outer_radius*2);
res=(involute_facets!=0)?involute_facets:($fn==0)?5:$fn/4;
translate ([0,0,pitch_apex])
rotate ([0,-atan(back_cone_radius/cone_distance),0])
translate ([-back_cone_radius*2,0,-cone_distance*2])
union ()
{
for (i=[1:res])
{
assign (
point1=
involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i-1)/res),
point2=
involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i)/res))
{
assign (
side1_point1 = rotate_point (centre_angle, point1),
side1_point2 = rotate_point (centre_angle, point2),
side2_point1 = mirror_point (rotate_point (centre_angle, point1)),
side2_point2 = mirror_point (rotate_point (centre_angle, point2)))
{
polyhedron (
points=[
[back_cone_radius*2+0.1,0,cone_distance*2],
[side1_point1[0],side1_point1[1],0],
[side1_point2[0],side1_point2[1],0],
[side2_point2[0],side2_point2[1],0],
[side2_point1[0],side2_point1[1],0],
[0.1,0,0]],
triangles=[[0,1,2],[0,2,3],[0,3,4],[0,5,1],[1,5,2],[2,5,3],[3,5,4],[0,4,5]]);
}
}
}
}
}
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,
flat=false)
{
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_exturde_flat_option(flat=flat, 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)
linear_exturde_flat_option(flat=flat, height=gear_thickness)
circle (r=rim_radius);
if (flat == false && hub_thickness > gear_thickness)
translate ([0,0,gear_thickness])
linear_exturde_flat_option(flat=flat, height=hub_thickness-gear_thickness)
circle (r=hub_diameter/2);
}
translate ([0,0,-1])
linear_exturde_flat_option(flat =flat, height=2+max(rim_thickness,hub_thickness,gear_thickness))
circle (r=bore_diameter/2);
if (circles>0)
{
for(i=[0:circles-1])
rotate([0,0,i*360/circles])
translate([circle_orbit_diameter/2,0,-1])
linear_exturde_flat_option(flat =flat, height=max(gear_thickness,rim_thickness)+3)
circle(r=circle_diameter/2);
}
}
}
module linear_exturde_flat_option(flat =false, height = 10, center = false, convexity = 2, twist = 0)
{
if(flat==false)
{
linear_extrude(height = height, center = center, convexity = convexity, twist= twist) child(0);
}
else
{
child(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 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;
union ()
{
for (i=[1:res])
assign (
point1=involute (base_radius,start_angle+(stop_angle - start_angle)*(i-1)/res),
point2=involute (base_radius,start_angle+(stop_angle - start_angle)*i/res))
{
assign (
side1_point1=rotate_point (centre_angle, point1),
side1_point2=rotate_point (centre_angle, point2),
side2_point1=mirror_point (rotate_point (centre_angle, point1)),
side2_point2=mirror_point (rotate_point (centre_angle, point2)))
{
polygon (
points=[[0,0],side1_point1,side1_point2,side2_point2,side2_point1],
paths=[[0,1,2,3,4,0]]);
}
}
}
}
// Mathematical Functions
//===============
// Finds the angle of the involute about the base radius at the given distance (radius) from it's center.
//source: http://www.mathhelpforum.com/math-help/geometry/136011-circle-involute-solving-y-any-given-x.html
function involute_intersect_angle (base_radius, radius) = sqrt (pow (radius/base_radius, 2) - 1) * 180 / pi;
// Calculate the involute position for a given base radius and 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 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)),
];
// Test Cases
//===============
module test_gears()
{
translate([17,-15])
{
gear (number_of_teeth=17,
circular_pitch=500,
circles=8);
rotate ([0,0,360*4/17])
translate ([39.088888,0,0])
{
gear (number_of_teeth=11,
circular_pitch=500,
hub_diameter=0,
rim_width=65);
translate ([0,0,8])
{
gear (number_of_teeth=6,
circular_pitch=300,
hub_diameter=0,
rim_width=5,
rim_thickness=6,
pressure_angle=31);
rotate ([0,0,360*5/6])
translate ([22.5,0,1])
gear (number_of_teeth=21,
circular_pitch=300,
bore_diameter=2,
hub_diameter=4,
rim_width=1,
hub_thickness=4,
rim_thickness=4,
gear_thickness=3,
pressure_angle=31);
}
}
translate ([-61.1111111,0,0])
{
gear (number_of_teeth=27,
circular_pitch=500,
circles=5,
hub_diameter=2*8.88888889);
translate ([0,0,10])
{
gear (
number_of_teeth=14,
circular_pitch=200,
pressure_angle=5,
clearance = 0.2,
gear_thickness = 10,
rim_thickness = 10,
rim_width = 15,
bore_diameter=5,
circles=0);
translate ([13.8888888,0,1])
gear (
number_of_teeth=11,
circular_pitch=200,
pressure_angle=5,
clearance = 0.2,
gear_thickness = 10,
rim_thickness = 10,
rim_width = 15,
hub_thickness = 20,
hub_diameter=2*7.222222,
bore_diameter=5,
circles=0);
}
}
rotate ([0,0,360*-5/17])
translate ([44.444444444,0,0])
gear (number_of_teeth=15,
circular_pitch=500,
hub_diameter=10,
rim_width=5,
rim_thickness=5,
gear_thickness=4,
hub_thickness=6,
circles=9);
rotate ([0,0,360*-1/17])
translate ([30.5555555,0,-1])
gear (number_of_teeth=5,
circular_pitch=500,
hub_diameter=0,
rim_width=5,
rim_thickness=10);
}
}
module meshing_double_helix ()
{
test_double_helix_gear ();
mirror ([0,1,0])
translate ([58.33333333,0,0])
test_double_helix_gear (teeth=13,circles=6);
}
module test_double_helix_gear (
teeth=17,
circles=8)
{
//double helical gear
{
twist=200;
height=20;
pressure_angle=30;
gear (number_of_teeth=teeth,
circular_pitch=700,
pressure_angle=pressure_angle,
clearance = 0.2,
gear_thickness = height/2*0.5,
rim_thickness = height/2,
rim_width = 5,
hub_thickness = height/2*1.2,
hub_diameter=15,
bore_diameter=5,
circles=circles,
twist=twist/teeth);
mirror([0,0,1])
gear (number_of_teeth=teeth,
circular_pitch=700,
pressure_angle=pressure_angle,
clearance = 0.2,
gear_thickness = height/2,
rim_thickness = height/2,
rim_width = 5,
hub_thickness = height/2,
hub_diameter=15,
bore_diameter=5,
circles=circles,
twist=twist/teeth);
}
}
module test_backlash ()
{
backlash = 2;
teeth = 15;
translate ([-29.166666,0,0])
{
translate ([58.3333333,0,0])
rotate ([0,0,-360/teeth/4])
gear (
number_of_teeth = teeth,
circular_pitch=700,
gear_thickness = 12,
rim_thickness = 15,
rim_width = 5,
hub_thickness = 17,
hub_diameter=15,
bore_diameter=5,
backlash = 2,
circles=8);
rotate ([0,0,360/teeth/4])
gear (
number_of_teeth = teeth,
circular_pitch=700,
gear_thickness = 12,
rim_thickness = 15,
rim_width = 5,
hub_thickness = 17,
hub_diameter=15,
bore_diameter=5,
backlash = 2,
circles=8);
}
color([0,0,128,0.5])
translate([0,0,-5])
cylinder ($fn=20,r=backlash / 4,h=25);
}