From 37751495914cca4335328b6be17dfa93424e09e0 Mon Sep 17 00:00:00 2001
From: Revar Desmera <revarbat@gmail.com>
Date: Fri, 21 Jul 2023 00:05:53 -0700
Subject: [PATCH 1/2] Fixes for gear tooth profiles.

---
 gears.scad | 43 ++++++++++++++++++++++---------------------
 1 file changed, 22 insertions(+), 21 deletions(-)

diff --git a/gears.scad b/gears.scad
index d56e9d9..a3ef1b9 100644
--- a/gears.scad
+++ b/gears.scad
@@ -2002,6 +2002,9 @@ function _gear_tooth_profile(
     helical = 0,
     internal = false,
     profile_shift = 0.0,
+    mod,
+    diam_pitch,
+    pitch,
     center = false
 ) = let(
     // Calculate a point on the involute curve, by angle.
@@ -2009,6 +2012,7 @@ function _gear_tooth_profile(
         let(b=a*PI/180) base_r * [cos(a)+b*sin(a), sin(a)-b*cos(a)],
 
     steps = 16,
+    circ_pitch = circular_pitch(pitch=pitch, circ_pitch=circ_pitch, diam_pitch=diam_pitch, mod=mod),
 
     // Calculate the important circle radii
     arad = outer_radius(circ_pitch, teeth, helical=helical, profile_shift=profile_shift, internal=internal),
@@ -2072,8 +2076,8 @@ function _gear_tooth_profile(
 
     // The u values to use when generating the tooth.
     us = [
-        for (i=[0:1:20-1]) 0.2*sin(i/20*90),
-        for (i=[2:1:steps-1]) i/(steps-1),
+        for (i=[0.0:0.02:0.2-EPSILON]) i,
+        for (i=[0:1:steps-1]) 0.2 + i/(steps-1)*0.8,
     ],
 
     // Generate the left half of the tooth.
@@ -2089,26 +2093,23 @@ function _gear_tooth_profile(
         ) polar_to_xy(ma_rad, a),
     ]),
 
-    // Find undercut bottom "jaggie" if it exists.
-    minima = [
-        for (i = idx(tooth_half_raw))
-            let(p = tooth_half_raw[i])
-            if (i > 0 && i < len(tooth_half_raw)-1 && norm(p) <= prad)
-            let(
-                pp = tooth_half_raw[i-1],
-                np = tooth_half_raw[i+1]
-            )
-            if (p.x > pp.x && p.x > np.x)
-            i
-    ],
-
     // Strip "jaggies" if found.
-    tooth_half = len(minima)<2? tooth_half_raw : [
-        for (i = idx(tooth_half_raw))
-            let(p = tooth_half_raw[i])
-            if (i <= minima[0] || i >= last(minima))
-            p
-    ],
+    strip_left = function(path,i)
+        i > len(path)? [] :
+        norm(path[i]) >= prad? [for (j=idx(path)) if(j>=i) path[j]] :
+        let(
+            angs = [
+                for (j=[i+1:1:len(path)-1]) let(
+                    p = path[i],
+                    np = path[j],
+                    r = norm(np),
+                    a = v_theta(np-p)
+                ) if(r<prad) a
+            ],
+            mti = !angs? 0 : min_index(angs),
+            out = concat([path[i]], strip_left(path, i + mti + 1))
+        ) out,
+    tooth_half = strip_left(tooth_half_raw, 0),
 
     // Mirror the tooth to complete it.
     tooth = deduplicate([

From d88c960c38f6c88ea200cbdea2fa58ed0847460f Mon Sep 17 00:00:00 2001
From: Revar Desmera <revarbat@gmail.com>
Date: Fri, 21 Jul 2023 01:04:02 -0700
Subject: [PATCH 2/2] Tweaks to worm() and worm_gear()

---
 gears.scad | 19 +++++++++++++------
 1 file changed, 13 insertions(+), 6 deletions(-)

diff --git a/gears.scad b/gears.scad
index a3ef1b9..f39ea26 100644
--- a/gears.scad
+++ b/gears.scad
@@ -1603,6 +1603,7 @@ function worm(
     diam_pitch,
     mod,
     pitch,
+    gear_spin=0,
     anchor=CENTER,
     spin=0,
     orient=UP
@@ -1620,7 +1621,7 @@ function worm(
     assert(is_finite(backlash) && backlash>=0)
     assert(is_bool(left_handed))
     assert(is_finite(profile_shift) && abs(profile_shift)<1)
-    //assert(is_finite(gear_spin))
+    assert(is_finite(gear_spin))
     let(
         helical = asin(starts * circ_pitch / PI / d),
         trans_pitch = circ_pitch / cos(helical),
@@ -1641,7 +1642,7 @@ function worm(
         ],
         steps = max(36, segs(d/2)),
         step = 360 / steps,
-        zsteps = ceil(l / circ_pitch * cos(helical) / starts * steps),
+        zsteps = ceil(l / trans_pitch / starts * steps),
         zstep = l / zsteps,
         profiles = [
             for (j = [0:1:zsteps]) [
@@ -1649,14 +1650,18 @@ function worm(
                     u = i / steps - 0.5,
                     ang = 360 * (1 - u) + 90,
                     z = j*zstep - l/2,
-                    zoff = circ_pitch * starts * u / cos(helical),
+                    zoff = trans_pitch * starts * u,
                     h = lookup(z+zoff, rack_profile)
                 )
                 cylindrical_to_xyz(d/2+h, ang, z)
             ]
         ],
         vnf1 = vnf_vertex_array(profiles, caps=true, col_wrap=true, style="alt"),
-        vnf = left_handed? xflip(p=vnf1) : vnf1
+        m = product([
+            zrot(gear_spin),
+            if (left_handed) xflip(),
+        ]),
+        vnf = apply(m, vnf1)
     ) reorient(anchor,spin,orient, d=d, l=l, p=vnf);
 
 
@@ -1690,6 +1695,8 @@ module worm(
         assert(is_bool(left_handed))
         assert(is_finite(gear_spin))
         assert(is_finite(profile_shift) && abs(profile_shift)<1);
+    helical = asin(starts * circ_pitch / PI / d);
+    trans_pitch = circ_pitch / cos(helical);
     vnf = worm(
         circ_pitch=circ_pitch,
         starts=starts,
@@ -1702,7 +1709,7 @@ module worm(
         mod=mod
     );
     attachable(anchor,spin,orient, d=d, l=l) {
-        zrot(gear_spin) vnf_polyhedron(vnf, convexity=ceil(l/circ_pitch)*2);
+        zrot(gear_spin) vnf_polyhedron(vnf, convexity=ceil(l/trans_pitch)*2);
         children();
     }
 }
@@ -1850,7 +1857,7 @@ function worm_gear(
                         left(hob_rad) *
                         zrot(-90) *
                         back(tbot) *
-                        scale(cos(u*worm_arc)) *
+                        scale(pow(cos(u*worm_arc),2)) *
                         fwd(tbot),
                     path3d(tooth_profile)
                 )