--- /dev/null
+// Parametric Involute Bevel and Spur Gears by GregFrost
+// It is licensed under the Creative Commons - GNU GPL license.
+// © 2010 by GregFrost
+// http://www.thingiverse.com/thing:3575
+
+// 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:
+//meshing_double_helix ();
+
+// Demonstrate the backlash option for Spur gears.
+//test_backlash ();
+
+// Demonstrate how to make meshing bevel gears.
+bevel_gear_pair ();
+
+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)
+{
+ 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 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);
+}
+
HCoop / clinton / prusa3.git / commitdiff