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Corrections spotted by tests

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This commit is contained in:
Elmo 2010-08-23 20:51:25 +08:00 committed by Eero af Heurlin
parent d83ad01668
commit f0960f9337
2 changed files with 46 additions and 46 deletions
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40
gears.scad
View file

@ -1,6 +1,6 @@
//test_involute_curve(); //test_involute_curve();
test_gears(); //test_gears();
demo_3d_gears(); //demo_3d_gears();
// Geometry Sources: // Geometry Sources:
// http://www.cartertools.com/involute.html // http://www.cartertools.com/involute.html
@ -15,14 +15,14 @@ module gear(number_of_teeth,
pressure_angle=20, clearance = 0) pressure_angle=20, clearance = 0)
{ {
if (circular_pitch==false && diametral_pitch==false) echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch"); 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 //Convert diametrial pitch to our native circular pitch
circular_pitch = (circular_pitch!=false?circular_pitch:180/diametral_pitch); circular_pitch = (circular_pitch!=false?circular_pitch:180/diametral_pitch);
// Pitch diameter: Diameter of pitch circle. // Pitch diameter: Diameter of pitch circle.
pitch_diameter = number_of_teeth * circular_pitch / 180; pitch_diameter = number_of_teeth * circular_pitch / 180;
pitch_radius = pitch_diameter/2; pitch_radius = pitch_diameter/2;
// Base Circle // Base Circle
base_diameter = pitch_diameter*cos(pressure_angle); base_diameter = pitch_diameter*cos(pressure_angle);
base_radius = base_diameter/2; base_radius = base_diameter/2;
@ -32,24 +32,24 @@ module gear(number_of_teeth,
// Addendum: Radial distance from pitch circle to outside circle. // Addendum: Radial distance from pitch circle to outside circle.
addendum = 1/pitch_diametrial; addendum = 1/pitch_diametrial;
//Outer Circle //Outer Circle
outer_radius = pitch_radius+addendum; outer_radius = pitch_radius+addendum;
outer_diameter = outer_radius*2; outer_diameter = outer_radius*2;
// Dedendum: Radial distance from pitch circle to root diameter // Dedendum: Radial distance from pitch circle to root diameter
dedendum = addendum + clearance; dedendum = addendum + clearance;
// Root diameter: Diameter of bottom of tooth spaces. // Root diameter: Diameter of bottom of tooth spaces.
root_radius = pitch_radius-dedendum; root_radius = pitch_radius-dedendum;
root_diameter = root_radius * 2; root_diameter = root_radius * 2;
half_thick_angle = 360 / (4 * number_of_teeth); half_thick_angle = 360 / (4 * number_of_teeth);
union() union()
{ {
rotate(half_thick_angle) circle($fn=number_of_teeth*2, r=root_radius*1.001); rotate(half_thick_angle) circle($fn=number_of_teeth*2, r=root_radius*1.001);
for (i= [1:number_of_teeth]) for (i= [1:number_of_teeth])
//for (i = [0]) //for (i = [0])
{ {
@ -76,32 +76,32 @@ module involute_gear_tooth(
) )
{ {
pitch_to_base_angle = involute_intersect_angle( base_radius, pitch_radius ); pitch_to_base_angle = involute_intersect_angle( base_radius, pitch_radius );
outer_to_base_angle = involute_intersect_angle( base_radius, outer_radius ); outer_to_base_angle = involute_intersect_angle( base_radius, outer_radius );
base1 = 0 - pitch_to_base_angle - half_thick_angle; base1 = 0 - pitch_to_base_angle - half_thick_angle;
pitch1 = 0 - half_thick_angle; pitch1 = 0 - half_thick_angle;
outer1 = outer_to_base_angle - pitch_to_base_angle - half_thick_angle; outer1 = outer_to_base_angle - pitch_to_base_angle - half_thick_angle;
b1 = polar_to_cartesian([ base1, base_radius ]); b1 = polar_to_cartesian([ base1, base_radius ]);
p1 = polar_to_cartesian([ pitch1, pitch_radius ]); p1 = polar_to_cartesian([ pitch1, pitch_radius ]);
o1 = polar_to_cartesian([ outer1, outer_radius ]); o1 = polar_to_cartesian([ outer1, outer_radius ]);
b2 = polar_to_cartesian([ -base1, base_radius ]); b2 = polar_to_cartesian([ -base1, base_radius ]);
p2 = polar_to_cartesian([ -pitch1, pitch_radius ]); p2 = polar_to_cartesian([ -pitch1, pitch_radius ]);
o2 = polar_to_cartesian([ -outer1, outer_radius ]); o2 = polar_to_cartesian([ -outer1, outer_radius ]);
// ( root_radius > base_radius variables ) // ( root_radius > base_radius variables )
pitch_to_root_angle = pitch_to_base_angle - involute_intersect_angle(base_radius, root_radius ); pitch_to_root_angle = pitch_to_base_angle - involute_intersect_angle(base_radius, root_radius );
root1 = pitch1 - pitch_to_root_angle; root1 = pitch1 - pitch_to_root_angle;
root2 = -pitch1 + pitch_to_root_angle; root2 = -pitch1 + pitch_to_root_angle;
r1_t = polar_to_cartesian([ root1, root_radius ]); r1_t = polar_to_cartesian([ root1, root_radius ]);
r2_t = polar_to_cartesian([ -root1, root_radius ]); r2_t = polar_to_cartesian([ -root1, root_radius ]);
// ( else ) // ( else )
r1_f = polar_to_cartesian([ base1, root_radius ]); r1_f = polar_to_cartesian([ base1, root_radius ]);
r2_f = polar_to_cartesian([ -base1, root_radius ]); r2_f = polar_to_cartesian([ -base1, root_radius ]);
if (root_radius > base_radius) if (root_radius > base_radius)
{ {
//echo("true"); //echo("true");
@ -115,7 +115,7 @@ module involute_gear_tooth(
r1_f, b1,p1,o1,o2,p2,b2,r2_f r1_f, b1,p1,o1,o2,p2,b2,r2_f
], convexity = 3); ], convexity = 3);
} }
} }
// Mathematical Functions // Mathematical Functions
@ -157,7 +157,7 @@ module demo_3d_gears()
translate([0,0,10]) linear_extrude(height = 10, center = true, convexity = 10, twist = 45) translate([0,0,10]) linear_extrude(height = 10, center = true, convexity = 10, twist = 45)
gear(number_of_teeth=17,diametral_pitch=1); gear(number_of_teeth=17,diametral_pitch=1);
} }
//spur gear //spur gear
translate([0,-50]) linear_extrude(height = 10, center = true, convexity = 10, twist = 0) translate([0,-50]) linear_extrude(height = 10, center = true, convexity = 10, twist = 0)
gear(number_of_teeth=17,diametral_pitch=1); gear(number_of_teeth=17,diametral_pitch=1);
@ -170,4 +170,4 @@ module test_involute_curve()
{ {
translate(polar_to_cartesian([involute_intersect_angle( 0.1,i) , i ])) circle($fn=15, r=0.5); translate(polar_to_cartesian([involute_intersect_angle( 0.1,i) , i ])) circle($fn=15, r=0.5);
} }
} }

52
involute_gears.scad
View file

@ -32,13 +32,13 @@ module test_bevel_gear_pair(){
module test_bevel_gear(){bevel_gear();} module test_bevel_gear(){bevel_gear();}
bevel_gear(); //bevel_gear();
pi=3.1415926535897932384626433832795; pi=3.1415926535897932384626433832795;
//================================================== //==================================================
// Bevel Gears: // Bevel Gears:
// Two gears with the same cone distance, circular pitch (measured at the cone distance) // Two gears with the same cone distance, circular pitch (measured at the cone distance)
// and pressure angle will mesh. // and pressure angle will mesh.
module bevel_gear_pair ( module bevel_gear_pair (
@ -49,7 +49,7 @@ module bevel_gear_pair (
{ {
outside_pitch_radius1 = gear1_teeth * outside_circular_pitch / 360; outside_pitch_radius1 = gear1_teeth * outside_circular_pitch / 360;
outside_pitch_radius2 = gear2_teeth * outside_circular_pitch / 360; outside_pitch_radius2 = gear2_teeth * outside_circular_pitch / 360;
pitch_apex1=outside_pitch_radius2 * sin (axis_angle) + pitch_apex1=outside_pitch_radius2 * sin (axis_angle) +
(outside_pitch_radius2 * cos (axis_angle) + outside_pitch_radius1) / tan (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)); cone_distance = sqrt (pow (pitch_apex1, 2) + pow (outside_pitch_radius1, 2));
pitch_apex2 = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius2, 2)); pitch_apex2 = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius2, 2));
@ -68,7 +68,7 @@ module bevel_gear_pair (
cone_distance=cone_distance, cone_distance=cone_distance,
pressure_angle=30, pressure_angle=30,
outside_circular_pitch=outside_circular_pitch); outside_circular_pitch=outside_circular_pitch);
rotate([0,-(pitch_angle1+pitch_angle2),0]) rotate([0,-(pitch_angle1+pitch_angle2),0])
translate([0,0,-pitch_apex2]) translate([0,0,-pitch_apex2])
bevel_gear ( bevel_gear (
@ -125,7 +125,7 @@ module bevel_gear (
// Calculate and display the pitch angle. This is needed to determine the angle to mount two meshing cone gears. // 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 Circle for forming the involute teeth shape.
base_radius = back_cone_radius * cos (pressure_angle); base_radius = back_cone_radius * cos (pressure_angle);
// Diametrial pitch: Number of teeth per unit length. // Diametrial pitch: Number of teeth per unit length.
pitch_diametrial = number_of_teeth / outside_pitch_diameter; pitch_diametrial = number_of_teeth / outside_pitch_diameter;
@ -143,9 +143,9 @@ module bevel_gear (
root_cone_full_radius = tan (root_angle)*apex_to_apex; root_cone_full_radius = tan (root_angle)*apex_to_apex;
back_cone_full_radius=apex_to_apex / tan (pitch_angle); back_cone_full_radius=apex_to_apex / tan (pitch_angle);
back_cone_end_radius = back_cone_end_radius =
outside_pitch_radius - outside_pitch_radius -
dedendum * cos (pitch_angle) - dedendum * cos (pitch_angle) -
gear_thickness / tan (pitch_angle); gear_thickness / tan (pitch_angle);
back_cone_descent = dedendum * sin (pitch_angle) + gear_thickness; back_cone_descent = dedendum * sin (pitch_angle) + gear_thickness;
@ -158,9 +158,9 @@ module bevel_gear (
face_cone_height = apex_to_apex-face_width / cos (pitch_angle); face_cone_height = apex_to_apex-face_width / cos (pitch_angle);
face_cone_full_radius = face_cone_height / tan (pitch_angle); face_cone_full_radius = face_cone_height / tan (pitch_angle);
face_cone_descent = dedendum * sin (pitch_angle); face_cone_descent = dedendum * sin (pitch_angle);
face_cone_end_radius = face_cone_end_radius =
outside_pitch_radius - outside_pitch_radius -
face_width / sin (pitch_angle) - face_width / sin (pitch_angle) -
face_cone_descent / tan (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. // 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.
@ -198,7 +198,7 @@ module bevel_gear (
{ {
translate ([0,0,-back_cone_descent]) translate ([0,0,-back_cone_descent])
cylinder ( cylinder (
$fn=number_of_teeth*2, $fn=number_of_teeth*2,
r1=back_cone_end_radius, r1=back_cone_end_radius,
r2=back_cone_full_radius*2, r2=back_cone_full_radius*2,
h=apex_to_apex + back_cone_descent); h=apex_to_apex + back_cone_descent);
@ -211,7 +211,7 @@ module bevel_gear (
bevel_gear_flat_height]); bevel_gear_flat_height]);
} }
} }
if (finish == bevel_gear_back_cone) if (finish == bevel_gear_back_cone)
{ {
translate ([0,0,-face_cone_descent]) translate ([0,0,-face_cone_descent])
@ -223,7 +223,7 @@ module bevel_gear (
translate ([0,0,pitch_apex - apex_to_apex]) translate ([0,0,pitch_apex - apex_to_apex])
cylinder (r=bore_diameter/2,h=apex_to_apex); cylinder (r=bore_diameter/2,h=apex_to_apex);
} }
} }
module involute_bevel_gear_tooth ( module involute_bevel_gear_tooth (
@ -247,9 +247,9 @@ module involute_bevel_gear_tooth (
min_radius = max (base_radius*2,root_radius*2); min_radius = max (base_radius*2,root_radius*2);
pitch_point = pitch_point =
involute ( involute (
base_radius*2, base_radius*2,
involute_intersect_angle (base_radius*2, back_cone_radius*2)); involute_intersect_angle (base_radius*2, back_cone_radius*2));
pitch_angle = atan2 (pitch_point[1], pitch_point[0]); pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
centre_angle = pitch_angle + half_thick_angle; centre_angle = pitch_angle + half_thick_angle;
@ -310,7 +310,7 @@ module gear (
involute_facets=0, involute_facets=0,
flat=false) flat=false)
{ {
if (circular_pitch==false && diametral_pitch==false) if (circular_pitch==false && diametral_pitch==false)
echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch"); echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch");
//Convert diametrial pitch to our native circular pitch //Convert diametrial pitch to our native circular pitch
@ -387,7 +387,7 @@ module gear (
circle (r=bore_diameter/2); circle (r=bore_diameter/2);
if (circles>0) if (circles>0)
{ {
for(i=[0:circles-1]) for(i=[0:circles-1])
rotate([0,0,i*360/circles]) rotate([0,0,i*360/circles])
translate([circle_orbit_diameter/2,0,-1]) translate([circle_orbit_diameter/2,0,-1])
linear_exturde_flat_option(flat =flat, height=max(gear_thickness,rim_thickness)+3) linear_exturde_flat_option(flat =flat, height=max(gear_thickness,rim_thickness)+3)
@ -488,15 +488,15 @@ function involute_intersect_angle (base_radius, radius) = sqrt (pow (radius/base
// Calculate the involute position for a given base radius and involute angle. // Calculate the involute position for a given base radius and involute angle.
function rotated_involute (rotate, base_radius, 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)[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] cos (rotate) * involute (base_radius, involute_angle)[1] - sin (rotate) * involute (base_radius, involute_angle)[0]
]; ];
function mirror_point (coord) = function mirror_point (coord) =
[ [
coord[0], coord[0],
-coord[1] -coord[1]
]; ];
@ -506,7 +506,7 @@ function rotate_point (rotate, coord) =
cos (rotate) * coord[1] - sin (rotate) * coord[0] cos (rotate) * coord[1] - sin (rotate) * coord[0]
]; ];
function involute (base_radius, involute_angle) = function involute (base_radius, involute_angle) =
[ [
base_radius*(cos (involute_angle) + involute_angle*pi/180*sin (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)), base_radius*(sin (involute_angle) - involute_angle*pi/180*cos (involute_angle)),
@ -523,7 +523,7 @@ module test_gears()
gear (number_of_teeth=17, gear (number_of_teeth=17,
circular_pitch=500, circular_pitch=500,
circles=8); circles=8);
rotate ([0,0,360*4/17]) rotate ([0,0,360*4/17])
translate ([39.088888,0,0]) translate ([39.088888,0,0])
{ {
@ -587,7 +587,7 @@ module test_gears()
circles=0); circles=0);
} }
} }
rotate ([0,0,360*-5/17]) rotate ([0,0,360*-5/17])
translate ([44.444444444,0,0]) translate ([44.444444444,0,0])
gear (number_of_teeth=15, gear (number_of_teeth=15,
@ -598,7 +598,7 @@ module test_gears()
gear_thickness=4, gear_thickness=4,
hub_thickness=6, hub_thickness=6,
circles=9); circles=9);
rotate ([0,0,360*-1/17]) rotate ([0,0,360*-1/17])
translate ([30.5555555,0,-1]) translate ([30.5555555,0,-1])
gear (number_of_teeth=5, gear (number_of_teeth=5,
@ -612,7 +612,7 @@ module test_gears()
module meshing_double_helix () module meshing_double_helix ()
{ {
test_double_helix_gear (); test_double_helix_gear ();
mirror ([0,1,0]) mirror ([0,1,0])
translate ([58.33333333,0,0]) translate ([58.33333333,0,0])
test_double_helix_gear (teeth=13,circles=6); test_double_helix_gear (teeth=13,circles=6);
@ -676,7 +676,7 @@ module test_backlash ()
bore_diameter=5, bore_diameter=5,
backlash = 2, backlash = 2,
circles=8); circles=8);
rotate ([0,0,360/teeth/4]) rotate ([0,0,360/teeth/4])
gear ( gear (
number_of_teeth = teeth, number_of_teeth = teeth,