// Parametric Involute Spur Gear by GregFrost

// It is licensed under the Creative Commons - GNU GPL license.

// © 2010 by GregFrost

module gear(

num_teeth=8,

circular_pitch=10,

pressure_angle=28,

involute_facets=7,

clearance=0.5,

backlash=0.5)

{

 root_radius=root_radius(num_teeth,circular_pitch,clearance);

 base_radius=base_radius(num_teeth,circular_pitch,pressure_angle);

 pitch_radius=pitch_radius(num_teeth,circular_pitch);

 outside_radius=outside_radius(num_teeth,circular_pitch,clearance);

 

 //Create the involute curve with even steps from the root radius to the outside radius

 //First calculate the radii that we will compute points for.

 radius_list=\[for(i=\[0:involute_facets\]) max(root_radius,base_radius)+(outside_radius-max(root_radius,base_radius))\*i/involute_facets\];

 //Compute the involute angle associated with that radius.

 involute_angle=\[for(i=\[0:involute_facets\]) involute_angle(radius_list\[i\],base_radius)\];

 //For each of those involute angles, calculate the involute points, adding a root point if needed.

 involute_points=concat((base_radius>root_radius)?\[\[root_radius,0\]\]:\[\],

                        \[for(i=\[0:involute_facets\]) involute_point(base_radius,involute_angle\[i\])\]);

 //Calculate the involute point on the pitch circle and determine its rotation.

 pitch_involute_angle=involute_angle(pitch_radius,base_radius);

 pitch_involute_point=involute_point(base_radius,pitch_involute_angle);

 pitch_rotation=atan2(pitch_involute_point\[1\],pitch_involute_point\[0\]);

 

 //Calculate the backlash angle. This is 1/4 of the backlash because it is applied on both 

 //sides of the tooth and is assumed to be applied to both meshing gears.

 backlash_angle=backlash/(circular_pitch\*num_teeth)\*360/4;

 

 //Calculate the angular span of half a tooth taking backlash into account.

 half_tooth_angle=360/num_teeth/4-backlash_angle;

 

 //Rotate the tooth edge so the it where it should be to make the tooth straddle the X Axis.

 first_tooth_half=rotate_list(pitch_rotation+half_tooth_angle,involute_points);

 //The second half of the tooth will bjust be mirrored about the x axis.

 second_tooth_half=\[for(i=\[0:len(first_tooth_half)-1\]) \[first_tooth_half\[len(first_tooth_half)-1-i\]\[0\],

                                             -first_tooth_half\[len(first_tooth_half)-1-i\]\[1\]\]\];

 tooth=concat(first_tooth_half,second_tooth_half);

 // Create all teeth.

 gear_points=flatten(\[for(i=\[0:num_teeth-1\]) rotate_list(-360/num_teeth\*i,tooth)\]);

 polygon(gear_points);

}

module rack(

num_teeth=8,

circular_pitch=10,

pressure_angle=28,

involute_facets=7,

clearance=0.5,

backlash=0.5,

rack_thickness=4)

{

addendum=addendum(circular_pitch=circular_pitch,clearance=clearance);

dedendum=dedendum(circular_pitch=circular_pitch,clearance=clearance);;

top_land_width=circular_pitch/2-backlash/2-2*tan(pressure_angle)*addendum;

root_width=circular_pitch/2-backlash/2+2*tan(pressure_angle)*dedendum;

tooth_profile=[[-root_width/2,-dedendum],[-top_land_width/2,addendum],[top_land_width/2,addendum],[root_width/2,-dedendum]];

rack=concat(flatten([for (i=[0:num_teeth]) translate_list([circular_pitch*i,0],tooth_profile)]),

           \[\[num_teeth\*circular_pitch+root_width/2,-dedendum-rack_thickness\],

            \[-root_width/2,-dedendum-rack_thickness\]\]);

polygon(rack);

}

function flatten(l) = [ for (a = l) for (b = a) b ] ;

function rotate_list(angle,list)=

[for(i=[0:len(list)-1]) rotate_point(angle,list[i])];

function translate_list(translation,list)=

[for(i=[0:len(list)-1]) [list[i][0]+translation[0],list[i][1]+translation[1]]];

function involute_angle(target_radius,base_radius)=

 sqrt(pow(target_radius/base_radius,2)-1)\*180/PI;

function involute_point(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)),

];

function rotate_point(rotate, coord) =

[

cos(rotate)\*coord\[0\]+sin(rotate)\*coord\[1\],

cos(rotate)\*coord\[1\]-sin(rotate)\*coord\[0\]

];

// The radius of the gear's pitch circle.

function pitch_radius(

 num_teeth=12,

 circular_pitch=10)=

 num_teeth\*circular_pitch/(2\*PI);

// Calculate the base radius (that the involute curve unwinds from).

function base_radius(

 num_teeth=12,

 circular_pitch=10,

 pressure_angle=28)=

 pitch_radius(num_teeth,circular_pitch)\*cos(pressure_angle);

// The addendum is the distance from the pitch circle to the outer circle (the top of the teeth).

function addendum(

 circular_pitch=10,

 clearance=0.5)=

circular_pitch/PI-clearance/2;

// The distance from the pitch circle to tooth root (the bottom of the teeth).

function dedendum(

 circular_pitch=10,

 clearance=0.5)=

addendum(circular_pitch=circular_pitch,clearance=clearance)+clearance/2;

// The radius of the top of the teeth.

function outside_radius(

 num_teeth=12,

 circular_pitch=10,

 clearance=0.5)=

     pitch_radius(num_teeth,circular_pitch)+

     addendum(circular_pitch=circular_pitch,clearance=clearance);

 

// The radius of the tooth depth.

function root_radius(

 num_teeth=12,

 circular_pitch=10,

 clearance=0.5)=

     pitch_radius(num_teeth,circular_pitch)-

     dedendum(circular_pitch=circular_pitch,clearance=clearance);

I downloaded a script from Thingiverse to make spur gears but when I run
it, an error is generated that says, “No top level geometry to render “.

The script is copyrighted 2010, so I am guessing the Open Scad software
has changed over the last 12 years and is causing the errors.

Can someone help me understand how to fix this script, or point me to a
working spur gear script?

Here is the code in that script:

// Parametric Involute Spur Gear by GregFrost

// It is licensed under the Creative Commons - GNU GPL license.

// © 2010 by GregFrost

module gear(

num_teeth=8,

circular_pitch=10,

pressure_angle=28,

involute_facets=7,

clearance=0.5,

backlash=0.5)

{

root_radius=root_radius(num_teeth,circular_pitch,clearance);

base_radius=base_radius(num_teeth,circular_pitch,pressure_angle);

pitch_radius=pitch_radius(num_teeth,circular_pitch);

outside_radius=outside_radius(num_teeth,circular_pitch,clearance);

//Create the involute curve with even steps from the root radius to the
outside radius

//First calculate the radii that we will compute points for.

radius_list=[for(i=[0:involute_facets])
max(root_radius,base_radius)+(outside_radius-max(root_radius,base_radius))*i/involute_facets];

//Compute the involute angle associated with that radius.

involute_angle=[for(i=[0:involute_facets])
involute_angle(radius_list[i],base_radius)];

//For each of those involute angles, calculate the involute points, adding
a root point if needed.

involute_points=concat((base_radius>root_radius)?[[root_radius,0]]:[],

[for(i=[0:involute_facets])
involute_point(base_radius,involute_angle[i])]);

//Calculate the involute point on the pitch circle and determine its
rotation.

pitch_involute_angle=involute_angle(pitch_radius,base_radius);

pitch_involute_point=involute_point(base_radius,pitch_involute_angle);

pitch_rotation=atan2(pitch_involute_point[1],pitch_involute_point[0]);

//Calculate the backlash angle. This is 1/4 of the backlash because it is
applied on both

//sides of the tooth and is assumed to be applied to both meshing gears.

backlash_angle=backlash/(circular_pitch*num_teeth)*360/4;

//Calculate the angular span of half a tooth taking backlash into account.

half_tooth_angle=360/num_teeth/4-backlash_angle;

//Rotate the tooth edge so the it where it should be to make the tooth
straddle the X Axis.

first_tooth_half=rotate_list(pitch_rotation+half_tooth_angle,involute_points);

//The second half of the tooth will bjust be mirrored about the x axis.

second_tooth_half=[for(i=[0:len(first_tooth_half)-1])
[first_tooth_half[len(first_tooth_half)-1-i][0],

-first_tooth_half[len(first_tooth_half)-1-i][1]]];

tooth=concat(first_tooth_half,second_tooth_half);

// Create all teeth.

gear_points=flatten([for(i=[0:num_teeth-1])
rotate_list(-360/num_teeth*i,tooth)]);

polygon(gear_points);

}

module rack(

num_teeth=8,

circular_pitch=10,

pressure_angle=28,

involute_facets=7,

clearance=0.5,

backlash=0.5,

rack_thickness=4)

{

addendum=addendum(circular_pitch=circular_pitch,clearance=clearance);

dedendum=dedendum(circular_pitch=circular_pitch,clearance=clearance);;

top_land_width=circular_pitch/2-backlash/2-2*tan(pressure_angle)*addendum;

root_width=circular_pitch/2-backlash/2+2*tan(pressure_angle)*dedendum;

tooth_profile=[[-root_width/2,-dedendum],[-top_land_width/2,addendum],[top_land_width/2,addendum],[root_width/2,-dedendum]];

rack=concat(flatten([for (i=[0:num_teeth])
translate_list([circular_pitch*i,0],tooth_profile)]),

[[num_teeth*circular_pitch+root_width/2,-dedendum-rack_thickness],

[-root_width/2,-dedendum-rack_thickness]]);

polygon(rack);

}

function flatten(l) = [ for (a = l) for (b = a) b ] ;

function rotate_list(angle,list)=

[for(i=[0:len(list)-1]) rotate_point(angle,list[i])];

function translate_list(translation,list)=

[for(i=[0:len(list)-1])
[list[i][0]+translation[0],list[i][1]+translation[1]]];

function involute_angle(target_radius,base_radius)=

sqrt(pow(target_radius/base_radius,2)-1)*180/PI;

function involute_point(base_radius,involute_angle) =

[

base_radius*(cos(involute_angle)+involute_anglePI/180sin(involute_angle)),

base_radius*(sin(involute_angle)-involute_anglePI/180cos(involute_angle)),

];

function rotate_point(rotate, coord) =

[

cos(rotate)*coord[0]+sin(rotate)*coord[1],

cos(rotate)*coord[1]-sin(rotate)*coord[0]

];

// The radius of the gear's pitch circle.

function pitch_radius(

num_teeth=12,

circular_pitch=10)=

num_teethcircular_pitch/(2PI);

// Calculate the base radius (that the involute curve unwinds from).

function base_radius(

num_teeth=12,

circular_pitch=10,

pressure_angle=28)=

pitch_radius(num_teeth,circular_pitch)*cos(pressure_angle);

// The addendum is the distance from the pitch circle to the outer circle
(the top of the teeth).

function addendum(

circular_pitch=10,

clearance=0.5)=

circular_pitch/PI-clearance/2;

// The distance from the pitch circle to tooth root (the bottom of the
teeth).

function dedendum(

circular_pitch=10,

clearance=0.5)=

addendum(circular_pitch=circular_pitch,clearance=clearance)+clearance/2;

// The radius of the top of the teeth.

function outside_radius(

num_teeth=12,

circular_pitch=10,

clearance=0.5)=

pitch_radius(num_teeth,circular_pitch)+

addendum(circular_pitch=circular_pitch,clearance=clearance);

// The radius of the tooth depth.

function root_radius(

num_teeth=12,

circular_pitch=10,

clearance=0.5)=

pitch_radius(num_teeth,circular_pitch)-

dedendum(circular_pitch=circular_pitch,clearance=clearance);

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