SharpCoder · December 5, 2024 15:15 · Jan 28, 2020 · Jan 28, 2020 · Jan 28, 2020 · Jan 25, 2020
diff --git a/README.md → _Gear Generator README.md b/README.md → _Gear Generator README.md
diff --git a/README.md b/README.md
@@ -1,7 +1,5 @@
 # gears.scad
 
-![picture of the openscad output](https://i.imgur.com/W8r2YJl.png "A gear generated with this script")
-
 In order to use this code, you will need to copy gears.scad to your Libraries folder.
 https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Libraries
 
@@ -31,4 +29,7 @@ Which takes the following parameters:
 - N2 = Tooth count of the second gear
 - P = Diametral Pitch
 
-The output of this function will be the mm distance you must space both gears for them to mesh perfectly.
+The output of this function will be the mm distance you must space both gears for them to mesh perfectly.
+
+
+![picture of the openscad output](https://i.imgur.com/W8r2YJl.png "A gear generated with this script")
diff --git a/README.md b/README.md
@@ -1,5 +1,7 @@
 # gears.scad
 
+![picture of the openscad output](https://i.imgur.com/W8r2YJl.png "A gear generated with this script")
+
 In order to use this code, you will need to copy gears.scad to your Libraries folder.
 https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Libraries
 

diff --git a/gears.md → README.md b/gears.md → README.md
diff --git a/Untitled.scad → gear-generation-example.scad b/Untitled.scad → gear-generation-example.scad
diff --git a/README.md → gears.md b/README.md → gears.md
diff --git a/Untitled.scad b/Untitled.scad
@@ -1,6 +1,6 @@
 include <gears.scad>
 
-Teeth = 20;
+Teeth = 18;
 Pitch = 12;
 
 linear_extrude(6)

diff --git a/README.md b/README.md
@@ -5,4 +5,28 @@ https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Libraries
 
 And then you can run *Untitled.scad* as any other normal scad project file.
 
-If you don't want to mess around with the library, just combine the two code files together into one.
+If you don't want to mess around with the library, just combine the two code files together into one.
+
+## Library Functions
+
+This code will provide a function
+
+**spur_gear()**
+
+Which takes the following parameters:
+- N = Number of teeth
+- P = Diametral Pitch (defaults to 12)
+- pa = Pressure Angle (defaults to 14.5)
+
+The output of this method will be a 2D gear (converted to mm) which you simply need to *linear_extrude* in order to print on a 3D printer.
+
+The library also includes a number of other mathematical functions including:
+
+**calc_center_distance()**
+
+Which takes the following parameters:
+- N1 = Tooth count of the first gear
+- N2 = Tooth count of the second gear
+- P = Diametral Pitch
+
+The output of this function will be the mm distance you must space both gears for them to mesh perfectly.
diff --git a/README.md b/README.md
@@ -0,0 +1,8 @@
+# gears.scad
+
+In order to use this code, you will need to copy gears.scad to your Libraries folder.
+https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Libraries
+
+And then you can run *Untitled.scad* as any other normal scad project file.
+
+If you don't want to mess around with the library, just combine the two code files together into one.
diff --git a/Untitled.scad b/Untitled.scad
@@ -3,14 +3,16 @@ include <gears.scad>
 Teeth = 20;
 Pitch = 12;
 
-linear_extrude(5)
+linear_extrude(6)
 difference() {
     spur_gear(N=Teeth, P=Pitch);
     circle(d=19.1);
 }
-
-// Calculate distance between another gear (may need to add 1mm tolerance)
-OtherGearTeeth = 34;
+// 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("***");
diff --git a/gears.scad b/gears.scad
@@ -27,7 +27,7 @@ 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);
+function calc_center_distance(N1, N2, P) = in_to_mm * (N1 + N2) /(2 * P);
 
 /**
 	Modules
@@ -44,6 +44,7 @@ module spur_gear(N, P = 12, pa = 14.5) {
     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);
 
@@ -57,30 +58,36 @@ module spur_gear(N, P = 12, pa = 14.5) {
     beta = ((360 / (4*N)) - alpha) * 2;
 
     module involute_tooth() {
-        x = function(t) (r * cos(t*rad_to_deg)) + (r * t * sin(t*rad_to_deg));
-        y = function(t) (r * sin(t*rad_to_deg)) - (r * t * cos(t*rad_to_deg));    
+        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=1);
-        involute_2_points = parametric_points(fx=x2, fy=y2, t1=1);
+        involute_1_points = parametric_points(fx=x, fy=y, t1=.68);
+        involute_2_points = parametric_points(fx=x2, fy=y2, t1=.68);
 
-        union() {
-            polygon(
-                concat(
-                    involute_1_points,
-                    reverse(involute_2_points)
-                )
-            );
+        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));
-
-        rotate(-p) // This rotate doesn't really matter
         circular_mirror(d=0, steps=N) involute_tooth();
     }
 }
@@ -100,4 +107,4 @@ module circular_mirror(x=0, y=0, d, steps) {
             }    
         }
     }
-}
+}
diff --git a/Untitled.scad b/Untitled.scad
@@ -1,10 +1,16 @@
 include <gears.scad>
 
+Teeth = 20;
+Pitch = 12;
+
 linear_extrude(5)
 difference() {
-    // Generate spur gear with 20 teeth
-    spur_gear(N=20);
-
-    // Add the bore for a shaft.
+    spur_gear(N=Teeth, P=Pitch);
     circle(d=19.1);
-}
+}
+
+// Calculate distance between another gear (may need to add 1mm tolerance)
+OtherGearTeeth = 34;
+echo("***");
+echo("center distance (mm)", calc_center_distance(Teeth, OtherGearTeeth, Pitch));
+echo("***");
diff --git a/Untitled.scad b/Untitled.scad
@@ -0,0 +1,10 @@
+include <gears.scad>
+
+linear_extrude(5)
+difference() {
+    // Generate spur gear with 20 teeth
+    spur_gear(N=20);
+
+    // Add the bore for a shaft.
+    circle(d=19.1);
+}
diff --git a/gears.scad b/gears.scad
@@ -0,0 +1,103 @@
+/**
+    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);
+    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)) + (r * t * sin(t*rad_to_deg));
+        y = function(t) (r * sin(t*rad_to_deg)) - (r * 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=1);
+        involute_2_points = parametric_points(fx=x2, fy=y2, t1=1);
+
+        union() {
+            polygon(
+                concat(
+                    involute_1_points,
+                    reverse(involute_2_points)
+                )
+            );
+
+        }
+
+    }
+
+    difference() {
+        circle(d=(dp + 2*a));
+
+        rotate(-p) // This rotate doesn't really matter
+        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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