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//test_involute_curve();
//test_gears();
//demo_3d_gears();
// Geometry Sources:
// http://www.cartertools.com/involute.html
// gears.py (inkscape extension: /usr/share/inkscape/extensions/gears.py)
// Usage:
// Diametral pitch: Number of teeth per unit length.
// Circular pitch: Length of the arc from one tooth to the next
// Clearance: Radial distance between top of tooth on one gear to bottom of gap on another.
module gear(number_of_teeth,
circular_pitch=false, diametral_pitch=false,
pressure_angle=20, clearance = 0)
{
if (circular_pitch==false && diametral_pitch==false) echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch");
//Convert diametrial pitch to our native circular pitch
circular_pitch = (circular_pitch!=false?circular_pitch:180/diametral_pitch);
// Pitch diameter: Diameter of pitch circle.
pitch_diameter = number_of_teeth * circular_pitch / 180;
pitch_radius = pitch_diameter/2;
// Base Circle
base_diameter = pitch_diameter*cos(pressure_angle);
base_radius = base_diameter/2;
// Diametrial pitch: Number of teeth per unit length.
pitch_diametrial = number_of_teeth / pitch_diameter;
// Addendum: Radial distance from pitch circle to outside circle.
addendum = 1/pitch_diametrial;
//Outer Circle
outer_radius = pitch_radius+addendum;
outer_diameter = outer_radius*2;
// 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;
half_thick_angle = 360 / (4 * number_of_teeth);
union()
{
rotate(half_thick_angle) circle($fn=number_of_teeth*2, r=root_radius*1.001);
for (i= [1:number_of_teeth])
//for (i = [0])
{
rotate([0,0,i*360/number_of_teeth])
{
involute_gear_tooth(
pitch_radius = pitch_radius,
root_radius = root_radius,
base_radius = base_radius,
outer_radius = outer_radius,
half_thick_angle = half_thick_angle);
}
}
}
}
module involute_gear_tooth(
pitch_radius,
root_radius,
base_radius,
outer_radius,
half_thick_angle
)
{
pitch_to_base_angle = involute_intersect_angle( base_radius, pitch_radius );
outer_to_base_angle = involute_intersect_angle( base_radius, outer_radius );
base1 = 0 - pitch_to_base_angle - half_thick_angle;
pitch1 = 0 - half_thick_angle;
outer1 = outer_to_base_angle - pitch_to_base_angle - half_thick_angle;
b1 = polar_to_cartesian([ base1, base_radius ]);
p1 = polar_to_cartesian([ pitch1, pitch_radius ]);
o1 = polar_to_cartesian([ outer1, outer_radius ]);
b2 = polar_to_cartesian([ -base1, base_radius ]);
p2 = polar_to_cartesian([ -pitch1, pitch_radius ]);
o2 = polar_to_cartesian([ -outer1, outer_radius ]);
// ( root_radius > base_radius variables )
pitch_to_root_angle = pitch_to_base_angle - involute_intersect_angle(base_radius, root_radius );
root1 = pitch1 - pitch_to_root_angle;
root2 = -pitch1 + pitch_to_root_angle;
r1_t = polar_to_cartesian([ root1, root_radius ]);
r2_t = polar_to_cartesian([ -root1, root_radius ]);
// ( else )
r1_f = polar_to_cartesian([ base1, root_radius ]);
r2_f = polar_to_cartesian([ -base1, root_radius ]);
if (root_radius > base_radius)
{
//echo("true");
polygon( points = [
r1_t,p1,o1,o2,p2,r2_t
], convexity = 3);
}
else
{
polygon( points = [
r1_f, b1,p1,o1,o2,p2,b2,r2_f
], convexity = 3);
}
}
// Mathematical Functions
//===============
// Finds the angle of the involute about the base radius at the given distance (radius) from it's center.
//source: http://www.mathhelpforum.com/math-help/geometry/136011-circle-involute-solving-y-any-given-x.html
function involute_intersect_angle(base_radius, radius) = sqrt( pow(radius/base_radius,2) - 1);
// Polar coord [angle, radius] to cartesian coord [x,y]
function polar_to_cartesian(polar) = [
polar[1]*cos(polar[0]),
polar[1]*sin(polar[0])
];
// Test Cases
//===============
module test_gears()
{
gear(number_of_teeth=51,circular_pitch=200);
translate([0, 50])gear(number_of_teeth=17,circular_pitch=200);
translate([-50,0]) gear(number_of_teeth=17,diametral_pitch=1);
}
module demo_3d_gears()
{
//double helical gear
// (helics don't line up perfectly - for display purposes only ;)
translate([50,0])
{
linear_extrude(height = 10, center = true, convexity = 10, twist = -45)
gear(number_of_teeth=17,diametral_pitch=1);
translate([0,0,10]) linear_extrude(height = 10, center = true, convexity = 10, twist = 45)
gear(number_of_teeth=17,diametral_pitch=1);
}
//spur gear
translate([0,-50]) linear_extrude(height = 10, center = true, convexity = 10, twist = 0)
gear(number_of_teeth=17,diametral_pitch=1);
}
module test_involute_curve()
{
for (i=[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15])
{
translate(polar_to_cartesian([involute_intersect_angle( 0.1,i) , i ])) circle($fn=15, r=0.5);
}
}