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Gear generation code with openSCAD
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| /** | |
| Constants | |
| **/ | |
| in_to_mm = 25.4; | |
| rad_to_deg = 180 / PI; | |
| deg_to_rad = PI / 180; | |
| /** | |
| Functions | |
| **/ | |
| function parametric_points(fx, fy, t0=0, t1=10, delta=0.01) | |
| = [for(i = [t0:delta:t1]) [fx(i), fy(i)]]; | |
| function reverse(vector) | |
| = [for(i = [1:len(vector)]) vector[len(vector) - i]]; | |
| /** | |
| Maths | |
| **/ | |
| function calc_module(P) = in_to_mm / P; | |
| function calc_addendum(P) = (1/P) * in_to_mm; | |
| function calc_dedendum(P) = (1.25/P) * in_to_mm; | |
| function calc_dp(N, P) = (N/P) * in_to_mm; | |
| function calc_db(N, P, pa) = calc_dp(N,P) * cos(pa); | |
| function calc_dr(N, P) = calc_dp(N,P) - 2 * calc_dedendum(P); | |
| function calc_circular_pitch(P) = (PI / P) * in_to_mm; | |
| function calc_thickness(P) = (1.5708 / P) * in_to_mm; | |
| function calc_alpha(dp, db, pa) = ((sqrt(pow(dp,2) - pow(db,2))/db) * rad_to_deg - pa); | |
| function calc_clearance(P) = calc_dedendum(P) - calc_addendum(P); | |
| function calc_center_distance(N1, N2, P) = in_to_mm * (N1 + N2) /(2 * P); | |
| /** | |
| Modules | |
| **/ | |
| /** | |
| Given some parameters, this method will generate a spur gear | |
| with an involute curve. Accepted paramters include: | |
| - N = How many teeth | |
| - P = Diametral pitch (all gears should have the same P) | |
| - pa = pressure angle (recommended to remain at 14.5) | |
| **/ | |
| module spur_gear(N, P = 12, pa = 14.5) { | |
| dp = calc_dp(N, P); | |
| db = calc_db(N, P, pa); | |
| dr = calc_dr(N, P); | |
| a = calc_addendum(P); | |
| b = calc_dedendum(P); | |
| c = calc_clearance(P); | |
| p = calc_circular_pitch(P); | |
| // Undercut adjustment | |
| // NOTE: this might not be great? IDK | |
| undercut = 1 * c; | |
| // Calculate radius to begin the involute calculations | |
| r = (db - undercut) * .5; | |
| alpha = calc_alpha(dp, db, pa); | |
| beta = ((360 / (4*N)) - alpha) * 2; | |
| module involute_tooth() { | |
| x = function(t) (r * (cos(t*rad_to_deg) + t * sin(t*rad_to_deg))); | |
| y = function(t) (r * (sin(t * rad_to_deg) - t * cos(t * rad_to_deg))); | |
| x2 = function(t) r * (cos(-t*rad_to_deg - beta) - t * sin(-t * rad_to_deg - beta)); | |
| y2 = function(t) r * (sin(-t*rad_to_deg - beta) + t * cos(-t * rad_to_deg - beta)); | |
| involute_1_points = parametric_points(fx=x, fy=y, t1=.68); | |
| involute_2_points = parametric_points(fx=x2, fy=y2, t1=.68); | |
| difference() { | |
| union() { | |
| polygon( | |
| concat( | |
| [[ 0, 0 ]], | |
| involute_1_points, | |
| reverse(involute_2_points), | |
| [[ 0, 0]] | |
| ) | |
| ); | |
| } | |
| // Use subtraction to extend the invlute curve towards the base | |
| // circle and then stop it at that point. This will | |
| // add some square-shaped space at the base of the tooth | |
| // NOTE: usage of undercut might be overkill. | |
| circle(d=(dp - 2*b)); | |
| } | |
| } | |
| difference() { | |
| circle(d=(dp + 2*a)); | |
| circular_mirror(d=0, steps=N) involute_tooth(); | |
| } | |
| } | |
| /** | |
| Helper modules | |
| **/ | |
| module circular_mirror(x=0, y=0, d, steps) { | |
| aps = 360 / steps; | |
| for (step=[0:steps]) { | |
| current_angle = step * aps; | |
| unit_x = cos(current_angle); | |
| unit_y = sin(current_angle); | |
| translate([x, y, 0]) { | |
| translate([unit_x * d, unit_y * d, 0]) { | |
| rotate(current_angle) children(); | |
| } | |
| } | |
| } | |
| } |
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| include <gears.scad> | |
| Teeth = 20; | |
| Pitch = 12; | |
| linear_extrude(6) | |
| difference() { | |
| spur_gear(N=Teeth, P=Pitch); | |
| circle(d=19.1); | |
| } | |
| // Change this variable to calculate how far | |
| // this gear and another gear need to be spaced | |
| // in order to mesh properly. | |
| // (output will display in the console in units mm) | |
| OtherGearTeeth = 37; | |
| echo("***"); | |
| echo("center distance (mm)", calc_center_distance(Teeth, OtherGearTeeth, Pitch)); | |
| echo("***"); |
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