involute_gears.scad

// Parametric Involute Bevel and Spur Gears by GregFrost
// It is licensed under the Creative Commons - GNU LGPL 2.1 license.
// © 2010 by GregFrost, thingiverse.com/Amp
// http://www.thingiverse.com/thing:3575 and http://www.thingiverse.com/thing:3752

// Simple Test:
//gear (circular_pitch=700,
//  gear_thickness = 12,
//  rim_thickness = 15,
//  hub_thickness = 17,
//  circles=8);

//Complex Spur Gear Test:
//test_gears ();

// Meshing Double Helix:
//test_meshing_double_helix ();

module test_meshing_double_helix(){
    meshing_double_helix ();
}

// Demonstrate the backlash option for Spur gears.
//test_backlash ();

// Demonstrate how to make meshing bevel gears.
//test_bevel_gear_pair();

module test_bevel_gear_pair(){
    bevel_gear_pair ();
}

module test_bevel_gear(){bevel_gear();}

//bevel_gear();

pi=3.1415926535897932384626433832795;

//==================================================
// Bevel Gears:
// Two gears with the same cone distance, circular pitch (measured at the cone distance)
// and pressure angle will mesh.

module bevel_gear_pair (
    gear1_teeth = 41,
    gear2_teeth = 7,
    axis_angle = 90,
    outside_circular_pitch=1000)
{
    outside_pitch_radius1 = gear1_teeth * outside_circular_pitch / 360;
    outside_pitch_radius2 = gear2_teeth * outside_circular_pitch / 360;
    pitch_apex1=outside_pitch_radius2 * sin (axis_angle) +
        (outside_pitch_radius2 * cos (axis_angle) + outside_pitch_radius1) / tan (axis_angle);
    cone_distance = sqrt (pow (pitch_apex1, 2) + pow (outside_pitch_radius1, 2));
    pitch_apex2 = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius2, 2));
    echo ("cone_distance", cone_distance);
    pitch_angle1 = asin (outside_pitch_radius1 / cone_distance);
    pitch_angle2 = asin (outside_pitch_radius2 / cone_distance);
    echo ("pitch_angle1, pitch_angle2", pitch_angle1, pitch_angle2);
    echo ("pitch_angle1 + pitch_angle2", pitch_angle1 + pitch_angle2);

    rotate([0,0,90])
    translate ([0,0,pitch_apex1+20])
    {
        translate([0,0,-pitch_apex1])
        bevel_gear (
            number_of_teeth=gear1_teeth,
            cone_distance=cone_distance,
            pressure_angle=30,
            outside_circular_pitch=outside_circular_pitch);

        rotate([0,-(pitch_angle1+pitch_angle2),0])
        translate([0,0,-pitch_apex2])
        bevel_gear (
            number_of_teeth=gear2_teeth,
            cone_distance=cone_distance,
            pressure_angle=30,
            outside_circular_pitch=outside_circular_pitch);
    }
}

//Bevel Gear Finishing Options:
bevel_gear_flat = 0;
bevel_gear_back_cone = 1;

module bevel_gear (
    number_of_teeth=11,
    cone_distance=100,
    face_width=20,
    outside_circular_pitch=1000,
    pressure_angle=30,
    clearance = 0.2,
    bore_diameter=5,
    gear_thickness = 15,
    backlash = 0,
    involute_facets=0,
    finish = -1)
{
    echo ("bevel_gear",
        "teeth", number_of_teeth,
        "cone distance", cone_distance,
        face_width,
        outside_circular_pitch,
        pressure_angle,
        clearance,
        bore_diameter,
        involute_facets,
        finish);

    // Pitch diameter: Diameter of pitch circle at the fat end of the gear.
    outside_pitch_diameter  =  number_of_teeth * outside_circular_pitch / 180;
    outside_pitch_radius = outside_pitch_diameter / 2;

    // The height of the pitch apex.
    pitch_apex = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius, 2));
    pitch_angle = asin (outside_pitch_radius/cone_distance);

    echo ("Num Teeth:", number_of_teeth, " Pitch Angle:", pitch_angle);

    finish = (finish != -1) ? finish : (pitch_angle < 45) ? bevel_gear_flat : bevel_gear_back_cone;

    apex_to_apex=cone_distance / cos (pitch_angle);
    back_cone_radius = apex_to_apex * sin (pitch_angle);

    // Calculate and display the pitch angle. This is needed to determine the angle to mount two meshing cone gears.

    // Base Circle for forming the involute teeth shape.
    base_radius = back_cone_radius * cos (pressure_angle);

    // Diametrial pitch: Number of teeth per unit length.
    pitch_diametrial = number_of_teeth / outside_pitch_diameter;

    // Addendum: Radial distance from pitch circle to outside circle.
    addendum = 1 / pitch_diametrial;
    // Outer Circle
    outer_radius = back_cone_radius + addendum;

    // Dedendum: Radial distance from pitch circle to root diameter
    dedendum = addendum + clearance;
    dedendum_angle = atan (dedendum / cone_distance);
    root_angle = pitch_angle - dedendum_angle;

    root_cone_full_radius = tan (root_angle)*apex_to_apex;
    back_cone_full_radius=apex_to_apex / tan (pitch_angle);

    back_cone_end_radius =
        outside_pitch_radius -
        dedendum * cos (pitch_angle) -
        gear_thickness / tan (pitch_angle);
    back_cone_descent = dedendum * sin (pitch_angle) + gear_thickness;

    // Root diameter: Diameter of bottom of tooth spaces.
    root_radius = back_cone_radius - dedendum;

    half_tooth_thickness = outside_pitch_radius * sin (360 / (4 * number_of_teeth)) - backlash / 4;
    half_thick_angle = asin (half_tooth_thickness / back_cone_radius);

    face_cone_height = apex_to_apex-face_width / cos (pitch_angle);
    face_cone_full_radius = face_cone_height / tan (pitch_angle);
    face_cone_descent = dedendum * sin (pitch_angle);
    face_cone_end_radius =
        outside_pitch_radius -
        face_width / sin (pitch_angle) -
        face_cone_descent / tan (pitch_angle);

    // For the bevel_gear_flat finish option, calculate the height of a cube to select the portion of the gear that includes the full pitch face.
    bevel_gear_flat_height = pitch_apex - (cone_distance - face_width) * cos (pitch_angle);

//  translate([0,0,-pitch_apex])
    difference ()
    {
        intersection ()
        {
            union()
            {
                rotate (half_thick_angle)
                translate ([0,0,pitch_apex-apex_to_apex])
                cylinder ($fn=number_of_teeth*2, r1=root_cone_full_radius,r2=0,h=apex_to_apex);
                for (i = [1:number_of_teeth])
//              for (i = [1:1])
                {
                    rotate ([0,0,i*360/number_of_teeth])
                    {
                        involute_bevel_gear_tooth (
                            back_cone_radius = back_cone_radius,
                            root_radius = root_radius,
                            base_radius = base_radius,
                            outer_radius = outer_radius,
                            pitch_apex = pitch_apex,
                            cone_distance = cone_distance,
                            half_thick_angle = half_thick_angle,
                            involute_facets = involute_facets);
                    }
                }
            }

            if (finish == bevel_gear_back_cone)
            {
                translate ([0,0,-back_cone_descent])
                cylinder (
                    $fn=number_of_teeth*2,
                    r1=back_cone_end_radius,
                    r2=back_cone_full_radius*2,
                    h=apex_to_apex + back_cone_descent);
            }
            else
            {
                translate ([-1.5*outside_pitch_radius,-1.5*outside_pitch_radius,0])
                cube ([3*outside_pitch_radius,
                    3*outside_pitch_radius,
                    bevel_gear_flat_height]);
            }
        }

        if (finish == bevel_gear_back_cone)
        {
            translate ([0,0,-face_cone_descent])
            cylinder (
                r1=face_cone_end_radius,
                r2=face_cone_full_radius * 2,
                h=face_cone_height + face_cone_descent+pitch_apex);
        }

        translate ([0,0,pitch_apex - apex_to_apex])
        cylinder (r=bore_diameter/2,h=apex_to_apex);
    }
}

module involute_bevel_gear_tooth (
    back_cone_radius,
    root_radius,
    base_radius,
    outer_radius,
    pitch_apex,
    cone_distance,
    half_thick_angle,
    involute_facets)
{
//  echo ("involute_bevel_gear_tooth",
//      back_cone_radius,
//      root_radius,
//      base_radius,
//      outer_radius,
//      pitch_apex,
//      cone_distance,
//      half_thick_angle);

    min_radius = max (base_radius*2,root_radius*2);

    pitch_point =
        involute (
            base_radius*2,
            involute_intersect_angle (base_radius*2, back_cone_radius*2));
    pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
    centre_angle = pitch_angle + half_thick_angle;

    start_angle = involute_intersect_angle (base_radius*2, min_radius);
    stop_angle = involute_intersect_angle (base_radius*2, outer_radius*2);

    res=(involute_facets!=0)?involute_facets:($fn==0)?5:$fn/4;

    translate ([0,0,pitch_apex])
    rotate ([0,-atan(back_cone_radius/cone_distance),0])
    translate ([-back_cone_radius*2,0,-cone_distance*2])
    union ()
    {
        for (i=[1:res])
        {
            let (
                point1=
                    involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i-1)/res),
                point2=
                    involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i)/res))
            {
                let (
                    side1_point1 = rotate_point (centre_angle, point1),
                    side1_point2 = rotate_point (centre_angle, point2),
                    side2_point1 = mirror_point (rotate_point (centre_angle, point1)),
                    side2_point2 = mirror_point (rotate_point (centre_angle, point2)))
                {
                    polyhedron (
                        points=[
                            [back_cone_radius*2+0.1,0,cone_distance*2],
                            [side1_point1[0],side1_point1[1],0],
                            [side1_point2[0],side1_point2[1],0],
                            [side2_point2[0],side2_point2[1],0],
                            [side2_point1[0],side2_point1[1],0],
                            [0.1,0,0]],
                        triangles=[[0,2,1],[0,3,2],[0,4,3],[0,1,5],[1,2,5],[2,3,5],[3,4,5],[0,5,4]]);
                }
            }
        }
    }
}

module gear (
    number_of_teeth=15,
    circular_pitch=undef, diametral_pitch=undef,
    pressure_angle=28,
    clearance = undef,
    gear_thickness=5,
    rim_thickness=undef,
    rim_width=undef,
    hub_thickness=undef,
    hub_diameter=undef,
    spokes=0,
    spoke_width=undef,
    spoke_thickness=undef,
    spoke_square=false,
    centered_gear=false,
    centered_hub=false,
    bore_diameter=undef,
    circles=0,
    circle_diameter=undef,
    backlash=0,
    twist=0,
    involute_facets=0,
    flat=false)
{
    // Check for undefined circular pitch (happens when neither circular_pitch or diametral_pitch are specified)
    if (circular_pitch==undef)
        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!=undef?circular_pitch:pi/diametral_pitch);

    // Calculate default clearance if not specified
    clearance = (clearance!=undef?clearance:0.25 * circular_pitch / pi);

    // Pitch diameter: Diameter of pitch circle.
    pitch_diameter  =  number_of_teeth * circular_pitch / pi;
    pitch_radius = pitch_diameter/2;
    echo (str("Teeth: ", number_of_teeth, ", Pitch Radius: ", pitch_radius, ", Clearance: ", clearance));

    // Base Circle
    base_radius = pitch_radius*cos(pressure_angle);

    // 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;

    // 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;
    backlash_angle = backlash / pitch_radius * 180 / pi;
    half_thick_angle = (360 / number_of_teeth - backlash_angle) / 4;

    // Variables controlling the rim.
    rim_thickness = (rim_thickness!=undef?(rim_thickness!=0?rim_thickness:gear_thickness):gear_thickness * 1.5);
    rim_width = (rim_width!=undef?rim_width:root_radius * .1);
    rim_radius = root_radius - rim_width;

    // Variables controlling the hub
    hub_thickness = (hub_thickness!=undef?(hub_thickness!=0?hub_thickness:gear_thickness):gear_thickness * 2);
    hub_diameter = (hub_diameter!=undef?hub_diameter:root_radius * .3);
    hub_base = (centered_hub == false)? 0 : rim_thickness/2 - hub_thickness/2;

    // Variables controlling the spokes
    spokes = spokes == undef? 0 : spokes;
    spoke_thickness = (spoke_thickness == undef)? rim_thickness : spoke_thickness;
    spoke_width = (spokes==0)? 1 : (spoke_width == undef)?  0.75 * pi * hub_diameter / spokes : spoke_width; 
    //spoke_depth is depth spoke must penetrate into hub to ensure complete penetration
    spoke_depth = ((hub_diameter/2)^2-(spoke_width/2)^2)^0.5 +.01;
    //spoke length is length of spoke including the depth sunk into the hub
    spoke_length = spoke_depth+rim_radius-(hub_diameter/2.0);
    //spoke raius is the distance from gear center to base of the spoke(inside the hub)
    spoke_radius = (hub_diameter/2.0)-spoke_depth;
    //echo (str("spoke_width: ",spoke_width,", hub_diameter: ",hub_diameter, ", spoke_depth: ",spoke_depth));
    
    // Variables controlling the bore
    bore_diameter = bore_diameter!=undef?bore_diameter:root_radius * .1;

    // Variables controlling the circular holes in the gear.
    circle_orbit_diameter=hub_diameter/2+rim_radius;
    circle_orbit_curcumference=pi*circle_orbit_diameter;

    // Limit the circle size to 90% of the gear face.
    circle_default_diameter = min (
        0.70*circle_orbit_curcumference/circles, 
        (rim_radius+hub_diameter/2)*0.9);
    circle_diameter=(circle_diameter != undef)? circle_diameter : circle_default_diameter;
    echo(str("cir_orb_dia: ", circle_orbit_diameter, ", cir_orb_circumf: ", circle_orbit_curcumference, ", default cir dia: ",circle_default_diameter, ", cir_dia:",circle_diameter));
    difference()
    {
        union ()
        {
            difference ()
            {
                //start with a plane toothed disk gear
                linear_extrude_flat_option(flat=flat, height=rim_thickness, convexity=10, twist=twist)
                gear_shape (
                    number_of_teeth,
                    pitch_radius = pitch_radius,
                    root_radius = root_radius,
                    base_radius = base_radius,
                    outer_radius = outer_radius,
                    half_thick_angle = half_thick_angle,
                    involute_facets=involute_facets);

                //if we have a 0 hub thickness, then hub must be removed
                if (hub_thickness == 0)
                    translate ([0,0,-1])
                    cylinder (r=rim_radius,h=rim_thickness+2);
                //if the rim is thicker than the gear, carve out gear body
                else if (rim_thickness>gear_thickness){
                    //if not centered, carve out only the top
                    if (centered_gear == false){
                        translate ([0,0,gear_thickness])
                        cylinder (r=rim_radius,h=rim_thickness);
                    }
                    else
                        //carve out half from top and half from bottom
                        union ()
                        {
                            translate ([0,0,(gear_thickness + rim_thickness)/2])
                                cylinder (r=rim_radius,h=rim_thickness+1);
                            translate ([0,0,-1 -(gear_thickness + rim_thickness)/2])
                                cylinder (r=rim_radius,h=rim_thickness+1);
                        }
                
                }
            }
            
            //extend the gear body if gear_thickness > rim_thickness unless spoked, 
            if (gear_thickness > rim_thickness)
            {
                if (centered_gear == false)
                {
                    linear_extrude_flat_option(flat=flat, height=gear_thickness)
                    circle (r=rim_radius);
                }
                else
                {
                    translate ([0,0,-(gear_thickness - rim_thickness)/2])
                    linear_extrude_flat_option(flat=flat, height=gear_thickness)
                    circle (r=rim_radius);
                }
                //if rim is thicker than body, body protrudes into rim
            }
            //add the hub
            translate ([0,0,hub_base])
            linear_extrude_flat_option(flat=flat, height=hub_thickness)
                circle (r=hub_diameter/2);
            
            //add in spokes
            if (spokes>0)
            {          
                for(i=[0:spokes-1])
                    translate([0,0,rim_thickness/2])
                    rotate([90,0,i*360/spokes])
                    translate([0,0,spoke_radius])
                    {
                        if (spoke_square==true){
                             resize([spoke_width,spoke_thickness,spoke_length])
                            translate([0,0,.5])
                            cube(1,center=true);
                        }
                        if (spoke_square==false){
                            resize([spoke_width,spoke_thickness,spoke_length])
                            cylinder(h=10,d=10);
                        }
                    }
            }
        }
        
        //remove the center bore
        translate ([0,0,-1])
        linear_extrude_flat_option(flat =flat, height=2+max(rim_thickness,hub_thickness,gear_thickness))
        circle (r=bore_diameter/2);
        
        //remove circles from gear body
        if (circles>0)
        {
            for(i=[0:circles-1])
                rotate([0,0,i*360/circles])
                translate([circle_orbit_diameter/2,0,-1])
                linear_extrude_flat_option(flat =flat, height=max(gear_thickness,rim_thickness)+3)
                circle(r=circle_diameter/2);
        }
    }
}

module rack(
        number_of_teeth=15,
        circular_pitch=false, diametral_pitch=false,
        pressure_angle=28,
        clearance=0.2,
        rim_thickness=8,
        rim_width=5,
        flat=false)
{

    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:pi/diametral_pitch);
    pitch = circular_pitch;

    addendum = circular_pitch / pi;
    dedendum = addendum + clearance;
    pitch_slope = tan(pressure_angle);

    linear_extrude_flat_option(flat=flat, height=rim_thickness)
        union()
        {
            translate([0,-dedendum-rim_width/2])
                square([number_of_teeth*pitch, rim_width],center=true);

            p1 = pitch / 4 + pitch_slope * dedendum;
            p2 = pitch / 4 - pitch_slope * addendum;
            for(i=[1:number_of_teeth])
                translate([pitch*(i-number_of_teeth/2-0.5),0])
                    polygon(points=[
                            [-p1,-dedendum],
                            [p1,-dedendum],
                            [p2,addendum],
                            [-p2,addendum]
                    ]);
        }
}

module linear_extrude_flat_option(flat =false, height = 10, center = false, convexity = 2, twist = 0)
{
    if(flat==false)
    {
        linear_extrude(height = height, center = center, convexity = convexity, twist= twist) children(0);
    }
    else
    {
        children(0);
    }

}

module gear_shape (
    number_of_teeth,
    pitch_radius,
    root_radius,
    base_radius,
    outer_radius,
    half_thick_angle,
    involute_facets)
{
    union()
    {
        rotate (half_thick_angle) circle ($fn=number_of_teeth*2, r=root_radius);

        for (i = [1:number_of_teeth])
        {
            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,
                    involute_facets=involute_facets);
            }
        }
    }
}

module involute_gear_tooth (
    pitch_radius,
    root_radius,
    base_radius,
    outer_radius,
    half_thick_angle,
    involute_facets)
{
    min_radius = max (base_radius,root_radius);

    pitch_point = involute (base_radius, involute_intersect_angle (base_radius, pitch_radius));
    pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
    centre_angle = pitch_angle + half_thick_angle;

    start_angle = involute_intersect_angle (base_radius, min_radius);
    stop_angle = involute_intersect_angle (base_radius, outer_radius);

    res=(involute_facets!=0)?involute_facets:($fn==0)?5:$fn/4;

    union ()
    {
        for (i=[1:res]) {
            point1=involute (base_radius,start_angle+(stop_angle - start_angle)*(i-1)/res);
            point2=involute (base_radius,start_angle+(stop_angle - start_angle)*i/res);
            side1_point1=rotate_point (centre_angle, point1);
            side1_point2=rotate_point (centre_angle, point2);
            side2_point1=mirror_point (rotate_point (centre_angle, point1));
            side2_point2=mirror_point (rotate_point (centre_angle, point2));
                polygon (
                    points=[[0,0],side1_point1,side1_point2,side2_point2,side2_point1],
                    paths=[[0,1,2,3,4,0]]);
            }
        }
}

// 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) * 180 / pi;

// Calculate the involute position for a given base radius and involute angle.

function rotated_involute (rotate, base_radius, involute_angle) =
[
    cos (rotate) * involute (base_radius, involute_angle)[0] + sin (rotate) * involute (base_radius, involute_angle)[1],
    cos (rotate) * involute (base_radius, involute_angle)[1] - sin (rotate) * involute (base_radius, involute_angle)[0]
];

function mirror_point (coord) =
[
    coord[0],
    -coord[1]
];

function rotate_point (rotate, coord) =
[
    cos (rotate) * coord[0] + sin (rotate) * coord[1],
    cos (rotate) * coord[1] - sin (rotate) * coord[0]
];

function involute (base_radius, involute_angle) =
[
    base_radius*(cos (involute_angle) + involute_angle*pi/180*sin (involute_angle)),
    base_radius*(sin (involute_angle) - involute_angle*pi/180*cos (involute_angle))
];


// Test Cases
//===============

module test_gears()
{
    $fs = 0.2;
    $fa =1;
    translate([17,-15])
    {
        gear (number_of_teeth=17,
            circular_pitch=500*pi/180,
            spokes=6,
            spoke_thickness=4,
            gear_thickness=0,
            rim_thickness=5,
            hub_thickness=5,
            hub_diameter=10,
            circles=0);

        rotate ([0,0,360*4/17])
        translate ([39.088888,0,0])
        {
            gear (number_of_teeth=11,
                circular_pitch=500*pi/180,
                hub_diameter=0,
                rim_width=65);
            translate ([0,0,8])
            {
                gear (number_of_teeth=6,
                    circular_pitch=300*pi/180,
                    hub_diameter=0,
                    rim_width=5,
                    rim_thickness=6,
                    pressure_angle=31);
                rotate ([0,0,360*5/6])
                translate ([22.5,0,1])
                gear (number_of_teeth=21,
                    circular_pitch=300*pi/180,
                    bore_diameter=2,
                    hub_diameter=4,
                    rim_width=1,
                    hub_thickness=4,
                    rim_thickness=4,
                    gear_thickness=3,
                    pressure_angle=31);
            }
        }

        translate ([-61.1111111,0,0])
        {
            gear (number_of_teeth=27,
                circular_pitch=500*pi/180,
                circles=6,
                circle_diameter=12,
                spokes=6,
                gear_thickness=2,
                hub_thickness=10,
                centered_gear=true,
                spoke_thickness=3,
                hub_diameter=2*8.88888889);

            translate ([-37.5,0,0])
            rotate ([0,0,-90])
            rack (
                circular_pitch=500*pi/180
                 );

            translate ([0,0,10])
            {
                gear (
                    number_of_teeth=14,
                    circular_pitch=200*pi/180,
                    pressure_angle=5,
                    twist=30,
                    clearance = 0.2,
                    gear_thickness = 10,
                    rim_thickness = 10,
                    rim_width = 15,
                    bore_diameter=5,
                    circles=0);
                translate ([13.8888888,0,1])
                gear (
                    number_of_teeth=10,
                    circular_pitch=200*pi/180,
                    pressure_angle=5,
                    clearance = 0.2,
                    gear_thickness = 10,
                    rim_thickness = 8,
                    twist=-30*8/10,
                    rim_width = 15,
                    hub_thickness = 10,
                    centered_hub=true,
                    hub_diameter=7,
                    bore_diameter=4,
                    circles=0);
            }
        }

        rotate ([0,0,360*-5/17])
        translate ([44.444444444,0,0])
        gear (number_of_teeth=15,
            circular_pitch=500*pi/180,
            hub_diameter=10,
            rim_width=5,
            rim_thickness=5,
            gear_thickness=4,
            hub_thickness=6,
            circles=9);

        rotate ([0,0,360*-1/17])
        translate ([30.5555555,0,-1])
        gear (number_of_teeth=5,
            circular_pitch=500*pi/180,
            hub_diameter=0,
            rim_width=5,
            rim_thickness=10);
    }
}

module meshing_double_helix ()
{
    test_double_helix_gear ();

    mirror ([0,1,0])
    translate ([58.33333333,0,0])
    test_double_helix_gear (teeth=13,circles=6);
}

module test_double_helix_gear (
    teeth=17,
    circles=8)
{
    //double helical gear
    {
        twist=200;
        height=20;
        pressure_angle=30;

        gear (number_of_teeth=teeth,
            circular_pitch=700*pi/180,
            pressure_angle=pressure_angle,
            clearance = 0.2,
            gear_thickness = height/2*0.5,
            rim_thickness = height/2,
            rim_width = 5,
            hub_thickness = height/2*1.2,
            hub_diameter=15,
            bore_diameter=5,
            circles=circles,
            twist=twist/teeth);
        mirror([0,0,1])
        gear (number_of_teeth=teeth,
            circular_pitch=700*pi/180,
            pressure_angle=pressure_angle,
            clearance = 0.2,
            gear_thickness = height/2,
            rim_thickness = height/2,
            rim_width = 5,
            hub_thickness = height/2,
            hub_diameter=15,
            bore_diameter=5,
            circles=circles,
            twist=twist/teeth);
    }
}

module test_backlash ()
{
    backlash = 2;
    teeth = 15;

    translate ([-29.166666,0,0])
    {
        translate ([58.3333333,0,0])
        rotate ([0,0,-360/teeth/4])
        gear (
            number_of_teeth = teeth,
            circular_pitch=700*pi/180,
            gear_thickness = 12,
            rim_thickness = 15,
            rim_width = 5,
            hub_thickness = 17,
            hub_diameter=15,
            bore_diameter=5,
            backlash = 2,
            circles=8);

        rotate ([0,0,360/teeth/4])
        gear (
            number_of_teeth = teeth,
            circular_pitch=700*pi/180,
            gear_thickness = 12,
            rim_thickness = 15,
            rim_width = 5,
            hub_thickness = 17,
            hub_diameter=15,
            bore_diameter=5,
            backlash = 2,
            circles=8);
    }

    color([0,0,1,0.5])
    translate([0,0,-5])
    cylinder ($fn=20,r=backlash / 4,h=25);
}