def involute_intersect_angle(Rb, R):
Rb, R = float(Rb), float(R)
return (sqrt(Rb**2 - R**2) / (R)) - (acos(R / Rb))
def effect(self):
teeth = self.options.teeth
pitch = self.unittouu( str(self.options.pitch) + self.options.unit)
angle = self.options.angle # Angle of tangent to tooth at circular pitch wrt radial line.
centerdiameter = self.unittouu( str(self.options.centerdiameter) + self.options.unit)
# print >>sys.stderr, "Teeth: %s\n" % teeth
two_pi = 2.0 * pi
# Pitch (circular pitch): Length of the arc from one tooth to the next)
# Pitch diameter: Diameter of pitch circle.
pitch_diameter = float( teeth ) * pitch / pi
pitch_radius = pitch_diameter / 2.0
# Base Circle
base_diameter = 2 * pitch_diameter - pitch_diameter * cos( radians( angle ) )
base_radius = base_diameter / 2.0
# Diametrial pitch: Number of teeth per unit length.
pitch_diametrial = float( teeth )/ pitch_diameter
# Addendum: Radial distance from pitch circle to outside circle.
addendum = 1.0 / pitch_diametrial
# Inner Circle
inner_radius = pitch_radius - addendum
inner_diameter = inner_radius * 2.0
# Tooth thickness: Tooth width along pitch circle.
tooth = ( pi * pitch_diameter ) / ( 2.0 * float( teeth ) )
# Undercut?
undercut = (2.0 / ( sin( radians( angle ) ) ** 2))
needs_undercut = teeth < undercut
# Clearance: Radial distance between top of tooth on one gear to bottom of gap on another.
clearance = 0.0
# Dedendum: Radial distance from pitch circle to root diameter.
dedendum = addendum + clearance
# Root diameter: Diameter of bottom of tooth spaces.
root_radius = pitch_radius + dedendum
root_diameter = root_radius * 2.0
half_thick_angle = two_pi / (4.0 * float( teeth ) )
pitch_to_base_angle = involute_intersect_angle( base_radius, pitch_radius )
pitch_to_inner_angle = involute_intersect_angle( base_radius, inner_radius ) - pitch_to_base_angle
centers = [(x * two_pi / float( teeth) ) for x in range( teeth ) ]
points = []
for c in centers:
# Angles
pitch1 = c - half_thick_angle
base1 = pitch1 - pitch_to_base_angle
inner1 = pitch1 + pitch_to_inner_angle
pitch2 = c + half_thick_angle
base2 = pitch2 + pitch_to_base_angle
inner2 = pitch2 - pitch_to_inner_angle
# Points
b1 = point_on_circle( base_radius, base1 )
p1 = point_on_circle( pitch_radius, pitch1 )
i1 = point_on_circle( inner_radius, inner1 )
b2 = point_on_circle( base_radius, base2 )
p2 = point_on_circle( pitch_radius, pitch2 )
i2 = point_on_circle( inner_radius, inner2 )
if root_radius < base_radius:
pitch_to_root_angle = pitch_to_base_angle - involute_intersect_angle(base_radius, root_radius )
root1 = pitch1 - pitch_to_root_angle
root2 = pitch2 + pitch_to_root_angle
r1 = point_on_circle(root_radius, root1)
r2 = point_on_circle(root_radius, root2)
p_tmp = [r1,p1,i1,i2,p2,r2]
else:
r1 = point_on_circle(root_radius, base1)
r2 = point_on_circle(root_radius, base2)
p_tmp = [r1,b1,p1,i1,i2,p2,b2,r2]
points.extend( p_tmp )
path = points_to_svgd( points )
I want to generate inner gears. . I have adapted existing code that generates outer?? gears through intuition. I am not a mechanical engineer and cant seem to find theory for inner gears either. Can someone with understanding of the theory validate the adapted code? It seems to do what I want, though.
Thank you so much for your time!