Corrections spotted by tests
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Elmo
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gears.scad
40
gears.scad
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@ -1,6 +1,6 @@
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//test_involute_curve();
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test_gears();
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demo_3d_gears();
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//test_gears();
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//demo_3d_gears();
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// Geometry Sources:
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// http://www.cartertools.com/involute.html
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@ -15,14 +15,14 @@ module gear(number_of_teeth,
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pressure_angle=20, clearance = 0)
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{
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if (circular_pitch==false && diametral_pitch==false) echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch");
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//Convert diametrial pitch to our native circular pitch
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circular_pitch = (circular_pitch!=false?circular_pitch:180/diametral_pitch);
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// Pitch diameter: Diameter of pitch circle.
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pitch_diameter = number_of_teeth * circular_pitch / 180;
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pitch_radius = pitch_diameter/2;
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// Base Circle
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base_diameter = pitch_diameter*cos(pressure_angle);
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base_radius = base_diameter/2;
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@ -32,24 +32,24 @@ module gear(number_of_teeth,
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// Addendum: Radial distance from pitch circle to outside circle.
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addendum = 1/pitch_diametrial;
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//Outer Circle
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outer_radius = pitch_radius+addendum;
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outer_diameter = outer_radius*2;
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// Dedendum: Radial distance from pitch circle to root diameter
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dedendum = addendum + clearance;
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// Root diameter: Diameter of bottom of tooth spaces.
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root_radius = pitch_radius-dedendum;
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root_diameter = root_radius * 2;
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half_thick_angle = 360 / (4 * number_of_teeth);
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union()
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{
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rotate(half_thick_angle) circle($fn=number_of_teeth*2, r=root_radius*1.001);
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for (i= [1:number_of_teeth])
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//for (i = [0])
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{
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@ -76,32 +76,32 @@ module involute_gear_tooth(
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)
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{
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pitch_to_base_angle = involute_intersect_angle( base_radius, pitch_radius );
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outer_to_base_angle = involute_intersect_angle( base_radius, outer_radius );
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base1 = 0 - pitch_to_base_angle - half_thick_angle;
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pitch1 = 0 - half_thick_angle;
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outer1 = outer_to_base_angle - pitch_to_base_angle - half_thick_angle;
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b1 = polar_to_cartesian([ base1, base_radius ]);
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p1 = polar_to_cartesian([ pitch1, pitch_radius ]);
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o1 = polar_to_cartesian([ outer1, outer_radius ]);
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b2 = polar_to_cartesian([ -base1, base_radius ]);
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p2 = polar_to_cartesian([ -pitch1, pitch_radius ]);
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o2 = polar_to_cartesian([ -outer1, outer_radius ]);
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// ( root_radius > base_radius variables )
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pitch_to_root_angle = pitch_to_base_angle - involute_intersect_angle(base_radius, root_radius );
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root1 = pitch1 - pitch_to_root_angle;
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root2 = -pitch1 + pitch_to_root_angle;
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r1_t = polar_to_cartesian([ root1, root_radius ]);
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r2_t = polar_to_cartesian([ -root1, root_radius ]);
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// ( else )
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r1_f = polar_to_cartesian([ base1, root_radius ]);
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r2_f = polar_to_cartesian([ -base1, root_radius ]);
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if (root_radius > base_radius)
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{
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//echo("true");
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@ -115,7 +115,7 @@ module involute_gear_tooth(
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r1_f, b1,p1,o1,o2,p2,b2,r2_f
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], convexity = 3);
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}
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}
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// Mathematical Functions
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@ -157,7 +157,7 @@ module demo_3d_gears()
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translate([0,0,10]) linear_extrude(height = 10, center = true, convexity = 10, twist = 45)
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gear(number_of_teeth=17,diametral_pitch=1);
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}
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//spur gear
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translate([0,-50]) linear_extrude(height = 10, center = true, convexity = 10, twist = 0)
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gear(number_of_teeth=17,diametral_pitch=1);
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@ -170,4 +170,4 @@ module test_involute_curve()
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{
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translate(polar_to_cartesian([involute_intersect_angle( 0.1,i) , i ])) circle($fn=15, r=0.5);
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}
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}
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}
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@ -32,13 +32,13 @@ module test_bevel_gear_pair(){
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module test_bevel_gear(){bevel_gear();}
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bevel_gear();
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//bevel_gear();
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pi=3.1415926535897932384626433832795;
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//==================================================
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// Bevel Gears:
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// Two gears with the same cone distance, circular pitch (measured at the cone distance)
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// Two gears with the same cone distance, circular pitch (measured at the cone distance)
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// and pressure angle will mesh.
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module bevel_gear_pair (
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@ -49,7 +49,7 @@ module bevel_gear_pair (
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{
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outside_pitch_radius1 = gear1_teeth * outside_circular_pitch / 360;
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outside_pitch_radius2 = gear2_teeth * outside_circular_pitch / 360;
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pitch_apex1=outside_pitch_radius2 * sin (axis_angle) +
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pitch_apex1=outside_pitch_radius2 * sin (axis_angle) +
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(outside_pitch_radius2 * cos (axis_angle) + outside_pitch_radius1) / tan (axis_angle);
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cone_distance = sqrt (pow (pitch_apex1, 2) + pow (outside_pitch_radius1, 2));
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pitch_apex2 = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius2, 2));
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@ -68,7 +68,7 @@ module bevel_gear_pair (
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cone_distance=cone_distance,
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pressure_angle=30,
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outside_circular_pitch=outside_circular_pitch);
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rotate([0,-(pitch_angle1+pitch_angle2),0])
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translate([0,0,-pitch_apex2])
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bevel_gear (
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@ -125,7 +125,7 @@ module bevel_gear (
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// Calculate and display the pitch angle. This is needed to determine the angle to mount two meshing cone gears.
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// Base Circle for forming the involute teeth shape.
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base_radius = back_cone_radius * cos (pressure_angle);
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base_radius = back_cone_radius * cos (pressure_angle);
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// Diametrial pitch: Number of teeth per unit length.
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pitch_diametrial = number_of_teeth / outside_pitch_diameter;
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@ -143,9 +143,9 @@ module bevel_gear (
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root_cone_full_radius = tan (root_angle)*apex_to_apex;
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back_cone_full_radius=apex_to_apex / tan (pitch_angle);
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back_cone_end_radius =
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outside_pitch_radius -
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dedendum * cos (pitch_angle) -
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back_cone_end_radius =
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outside_pitch_radius -
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dedendum * cos (pitch_angle) -
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gear_thickness / tan (pitch_angle);
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back_cone_descent = dedendum * sin (pitch_angle) + gear_thickness;
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@ -158,9 +158,9 @@ module bevel_gear (
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face_cone_height = apex_to_apex-face_width / cos (pitch_angle);
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face_cone_full_radius = face_cone_height / tan (pitch_angle);
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face_cone_descent = dedendum * sin (pitch_angle);
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face_cone_end_radius =
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face_cone_end_radius =
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outside_pitch_radius -
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face_width / sin (pitch_angle) -
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face_width / sin (pitch_angle) -
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face_cone_descent / tan (pitch_angle);
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// 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.
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@ -198,7 +198,7 @@ module bevel_gear (
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{
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translate ([0,0,-back_cone_descent])
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cylinder (
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$fn=number_of_teeth*2,
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$fn=number_of_teeth*2,
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r1=back_cone_end_radius,
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r2=back_cone_full_radius*2,
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h=apex_to_apex + back_cone_descent);
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@ -211,7 +211,7 @@ module bevel_gear (
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bevel_gear_flat_height]);
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}
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}
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if (finish == bevel_gear_back_cone)
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{
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translate ([0,0,-face_cone_descent])
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@ -223,7 +223,7 @@ module bevel_gear (
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translate ([0,0,pitch_apex - apex_to_apex])
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cylinder (r=bore_diameter/2,h=apex_to_apex);
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}
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}
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}
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module involute_bevel_gear_tooth (
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@ -247,9 +247,9 @@ module involute_bevel_gear_tooth (
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min_radius = max (base_radius*2,root_radius*2);
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pitch_point =
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pitch_point =
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involute (
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base_radius*2,
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base_radius*2,
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involute_intersect_angle (base_radius*2, back_cone_radius*2));
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pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
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centre_angle = pitch_angle + half_thick_angle;
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@ -310,7 +310,7 @@ module gear (
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involute_facets=0,
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flat=false)
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{
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if (circular_pitch==false && diametral_pitch==false)
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if (circular_pitch==false && diametral_pitch==false)
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echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch");
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//Convert diametrial pitch to our native circular pitch
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@ -387,7 +387,7 @@ module gear (
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circle (r=bore_diameter/2);
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if (circles>0)
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{
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for(i=[0:circles-1])
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for(i=[0:circles-1])
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rotate([0,0,i*360/circles])
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translate([circle_orbit_diameter/2,0,-1])
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linear_exturde_flat_option(flat =flat, height=max(gear_thickness,rim_thickness)+3)
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@ -488,15 +488,15 @@ function involute_intersect_angle (base_radius, radius) = sqrt (pow (radius/base
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// Calculate the involute position for a given base radius and involute angle.
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function rotated_involute (rotate, base_radius, involute_angle) =
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function rotated_involute (rotate, base_radius, involute_angle) =
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[
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cos (rotate) * involute (base_radius, involute_angle)[0] + sin (rotate) * involute (base_radius, involute_angle)[1],
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cos (rotate) * involute (base_radius, involute_angle)[1] - sin (rotate) * involute (base_radius, involute_angle)[0]
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];
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function mirror_point (coord) =
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function mirror_point (coord) =
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[
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coord[0],
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coord[0],
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-coord[1]
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];
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@ -506,7 +506,7 @@ function rotate_point (rotate, coord) =
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cos (rotate) * coord[1] - sin (rotate) * coord[0]
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];
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function involute (base_radius, involute_angle) =
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function involute (base_radius, involute_angle) =
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[
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base_radius*(cos (involute_angle) + involute_angle*pi/180*sin (involute_angle)),
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base_radius*(sin (involute_angle) - involute_angle*pi/180*cos (involute_angle)),
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@ -523,7 +523,7 @@ module test_gears()
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gear (number_of_teeth=17,
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circular_pitch=500,
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circles=8);
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rotate ([0,0,360*4/17])
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translate ([39.088888,0,0])
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{
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@ -587,7 +587,7 @@ module test_gears()
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circles=0);
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}
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}
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rotate ([0,0,360*-5/17])
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translate ([44.444444444,0,0])
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gear (number_of_teeth=15,
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@ -598,7 +598,7 @@ module test_gears()
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gear_thickness=4,
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hub_thickness=6,
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circles=9);
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rotate ([0,0,360*-1/17])
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translate ([30.5555555,0,-1])
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gear (number_of_teeth=5,
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@ -612,7 +612,7 @@ module test_gears()
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module meshing_double_helix ()
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{
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test_double_helix_gear ();
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mirror ([0,1,0])
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translate ([58.33333333,0,0])
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test_double_helix_gear (teeth=13,circles=6);
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@ -676,7 +676,7 @@ module test_backlash ()
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bore_diameter=5,
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backlash = 2,
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circles=8);
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rotate ([0,0,360/teeth/4])
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gear (
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number_of_teeth = teeth,
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