Interpret the backlash as "Circumferential Backlash"

This fixes some unit mismatch, as the backlash is specified as length,
but the involute tooth generation code used to interpret it as angular
value in radians (no idea why it was additionaly diveded by four; we need
the half on each side of the tooth).
Now half of the value specified as "backlash" can be directly measured at
the pitch circle when comparing each tooth flank of a gear with and
without backlash.

freecad/gears/features.py

@@ -194,7 +194,8 @@ class InvoluteGear(BaseGear):
                         "computed", "transverse_pitch", 1)
 
     def add_tolerance_properties(self, obj):
-        obj.addProperty("App::PropertyLength", "backlash", "tolerance", "backlash")
+        obj.addProperty("App::PropertyLength", "backlash", "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.")
         obj.addProperty("App::PropertyBool", "reversed_backlash", "tolerance", "backlash direction")
         obj.addProperty(
             "App::PropertyFloat", "clearance", "tolerance", "clearance")
@@ -358,7 +359,8 @@ class InternalInvoluteGear(BaseGear):
         obj.addProperty("App::PropertyFloat", "root_fillet", "fillets", "a fillet for the tooth-root, radius = root_fillet x module")
 
     def add_tolerance_properties(self, obj):
-        obj.addProperty("App::PropertyLength", "backlash", "tolerance", "backlash")
+        obj.addProperty("App::PropertyLength", "backlash", "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.")
         obj.addProperty("App::PropertyBool", "reversed_backlash", "tolerance", "backlash direction")
         obj.addProperty("App::PropertyFloat", "head", "tolerance", "head_value * modul_value = additional length of head")
         obj.addProperty("App::PropertyFloat", "clearance", "tolerance", "clearance")
@@ -887,7 +889,8 @@ class CycloidGear(BaseGear):
 
     def add_tolerance_properties(self, obj):
         obj.addProperty("App::PropertyFloat", "clearance", "tolerance", "clearance")
-        obj.addProperty("App::PropertyLength", "backlash", "tolerance", "backlash in mm")
+        obj.addProperty("App::PropertyLength", "backlash", "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.")
         obj.addProperty("App::PropertyFloat", "head", "tolerance", "head_value * modul_value = additional length of head")
 
     def add_cycloid_properties(self, obj):
@@ -969,7 +972,8 @@ class BevelGear(BaseGear):
         obj.addProperty("App::PropertyFloat", "clearance", "tolerance", "clearance")
         obj.addProperty("App::PropertyInteger", "numpoints", "precision", "number of points for spline")
         obj.addProperty("App::PropertyBool", "reset_origin", "base", "if value is true the gears outer face will match the z=0 plane")
-        obj.addProperty("App::PropertyLength", "backlash", "tolerance", "backlash in mm")
+        obj.addProperty("App::PropertyLength", "backlash", "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.")
         obj.addProperty("App::PropertyPythonObject", "gear", "base", "test")
         obj.addProperty("App::PropertyAngle", "beta","helical", "angle used for spiral bevel-gears")
         obj.gear = self.bevel_tooth

pygears/bevel_tooth.py

@@ -30,6 +30,7 @@ class BevelTooth(object):
         self.z = z
         self.clearance = clearance
         self.backlash = backlash
+        self.angular_backlash = backlash / (z * module / 2)
         self.module = module
 
         self.involute_end = arccos(
@@ -108,7 +109,7 @@ class BevelTooth(object):
         intersection_point = intersection_line_circle(xy[i], point, r_cut)
         xy = array([intersection_point] + list(xy[i+1:]))
         xyz = [[p[0], p[1], 1] for p in xy]
-        backlash_rot = rotation3D(self.backlash / 4)
+        backlash_rot = rotation3D(self.angular_backlash / 2)
         xyz = backlash_rot(xyz)
         return(xyz)
 

pygears/cycloid_tooth.py

@@ -40,6 +40,7 @@ class CycloidTooth():
         self.da = self.d + 2 * (1 + self.head) * self.m
         self.di = self.d - 2 * (1 + self.clearance) * self.m
         self.phipart = 2 * pi / self.z
+        self.angular_backlash = self.backlash / (self.d / 2)
 
     def epicycloid_x(self):
         def func(t):
@@ -92,7 +93,7 @@ class CycloidTooth():
         pts_outer = transpose([pts_outer_x, pts_outer_y])
         pts_inner = transpose([pts_inner_x, pts_inner_y])
         pts1 = vstack([pts_inner[:-2], pts_outer])
-        rot = rotation(self.phipart / 4 - self.backlash)
+        rot = rotation(self.phipart / 4 - self.angular_backlash / 2)
         pts1 = rot(pts1)
         ref = reflection(0.)
         pts2 = ref(pts1)[::-1]

pygears/involute_tooth.py

@@ -69,6 +69,7 @@ class InvoluteTooth():
         self.involute_rot2 = 1 / self.z * \
             (pi / 2 + 2 * self.shift * tan(self.pressure_angle_t))
         self.involute_rot = self.involute_rot1 + self.involute_rot2
+        self.angular_backlash = self.backlash / (self.d / 2)
         self.involute_start = 0.
         if self.dg <= self.df:
             self.involute_start = sqrt(self.df ** 2 - self.dg ** 2) / self.dg
@@ -81,7 +82,7 @@ class InvoluteTooth():
         y = array(list(map(fy, pts)))
         xy = transpose([x, y])
         rotate = rotation(
-            self.undercut_rot + self.phipart / 2 - self.backlash / 4)
+            self.undercut_rot + self.phipart / 2 - self.angular_backlash / 2)
         xy = rotate(xy)
         return(array(xy))
 
@@ -91,7 +92,7 @@ class InvoluteTooth():
         x = array(list(map(fx, pts)))
         fy = self.involute_function_y()
         y = array(list(map(fy, pts)))
-        rot = rotation(self.involute_rot - self.backlash / 4)
+        rot = rotation(self.involute_rot - self.angular_backlash / 2)
         xy = rot(transpose(array([x, y])))
         return(xy)