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Added gear2d(), fixed clearance calculations.
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Revar Desmera
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5b7a026244
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086ccfc753
1 changed files with 61 additions and 51 deletions
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@ -59,17 +59,22 @@
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//gear_tooth_profile(mm_per_tooth=5, number_of_teeth=20, pressure_angle=20);
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module gear_tooth_profile(
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mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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number_of_teeth = 11, //total number of teeth around the entire perimeter
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pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
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clearance = 0.0, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
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bevelang = 0.0
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mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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number_of_teeth = 11, //total number of teeth around the entire perimeter
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pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
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backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
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bevelang = 0.0, //Gear face angle for bevelled gears.
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clearance = undef //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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) {
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p = mm_per_tooth * number_of_teeth / PI / 2; //radius of pitch circle
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c = p + mm_per_tooth / PI - clearance; //radius of outer circle
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b = p*cos(pressure_angle); //radius of base circle
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r = p-(c-p)-clearance; //radius of root circle
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function polar(r,theta) = r*[sin(theta), cos(theta)]; //convert polar to cartesian coordinates
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function iang(r1,r2) = sqrt((r2/r1)*(r2/r1) - 1)/PI*180 - acos(r1/r2); //unwind a string this many degrees to go from radius r1 to radius r2
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function q7(f,r,b,r2,t,s) = q6(b,s,t,(1-f)*max(b,r)+f*r2); //radius a fraction f up the curved side of the tooth
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function q6(b,s,t,d) = polar(d,s*(iang(b,d)+t)); //point at radius d on the involute curve
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p = pitch_radius(mm_per_tooth, number_of_teeth);
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c = outer_radius(mm_per_tooth, number_of_teeth);
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r = root_radius(mm_per_tooth, number_of_teeth, clearance);
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b = base_radius(mm_per_tooth, number_of_teeth, pressure_angle);
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t = mm_per_tooth/2-backlash/2; //tooth thickness at pitch circle
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k = -iang(b, p) - t/2/p/PI*180; //angle to where involute meets base circle on each side of tooth
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scale([1, 1/cos(bevelang), 1])
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@ -103,17 +108,15 @@ module gear_tooth_profile(
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// gear2d(mm_per_tooth=5, number_of_teeth=20);
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// linear_extrude(height=5*20/PI/2/2, scale=0.5) gear2d(mm_per_tooth=5, number_of_teeth=20);
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module gear2d(
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mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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number_of_teeth = 11, //total number of teeth around the entire perimeter
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teeth_to_hide = 0, //number of teeth to delete to make this only a fraction of a circle
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pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
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clearance = 0.0, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
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mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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number_of_teeth = 11, //total number of teeth around the entire perimeter
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teeth_to_hide = 0, //number of teeth to delete to make this only a fraction of a circle
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pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
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clearance = undef, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
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bevelang = 0.0
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) {
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p = mm_per_tooth * number_of_teeth / PI / 2; //radius of pitch circle
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c = p + mm_per_tooth / PI - clearance; //radius of outer circle
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r = p-(c-p)-clearance; //radius of root circle
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r = root_radius(mm_per_tooth, number_of_teeth, clearance);
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union() {
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circle(r=r-0.5, $fn=number_of_teeth);
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for (i = [0:number_of_teeth-teeth_to_hide-1] ) {
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@ -152,23 +155,23 @@ module gear2d(
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// Example:
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// gear(mm_per_tooth=5, number_of_teeth=20, thickness=10*cos(45), hole_diameter=5, twist=-30, bevelang=45, slices=12, $fa=1, $fs=1);
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// gear(mm_per_tooth=5, number_of_teeth=20, thickness=8, hole_diameter=5, $fa=1, $fs=1);
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module gear (
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module gear(
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mm_per_tooth = 3, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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number_of_teeth = 11, //total number of teeth around the entire perimeter
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thickness = 6, //thickness of gear in mm
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hole_diameter = 3, //diameter of the hole in the center, in mm
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teeth_to_hide = 0, //number of teeth to delete to make this only a fraction of a circle
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pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
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clearance = 0.0, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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clearance = undef, //gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
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bevelang = 0.0, //angle of bevelled gear face.
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twist = undef, //teeth rotate this many degrees from bottom of gear to top. 360 makes the gear a screw with each thread going around once
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slices = undef //Number of slices to divide gear into. Useful for refining gears with `twist`.
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) {
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p = mm_per_tooth * number_of_teeth / PI / 2; //radius of pitch circle
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p = pitch_radius(mm_per_tooth, number_of_teeth);
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c = outer_radius(mm_per_tooth, number_of_teeth);
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r = root_radius(mm_per_tooth, number_of_teeth, clearance);
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p2 = p - (thickness*tan(bevelang));
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c = p + mm_per_tooth / PI - clearance; //radius of outer circle
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r = p-(c-p)-clearance; //radius of root circle
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difference() {
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linear_extrude(height=thickness, center=true, convexity=10, twist=twist, scale=p2/p, slices=slices) {
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gear2d(
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@ -197,13 +200,6 @@ module gear (
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}
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//these 4 functions are used by gear
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function polar(r,theta) = r*[sin(theta), cos(theta)]; //convert polar to cartesian coordinates
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function iang(r1,r2) = sqrt((r2/r1)*(r2/r1) - 1)/PI*180 - acos(r1/r2); //unwind a string this many degrees to go from radius r1 to radius r2
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function q7(f,r,b,r2,t,s) = q6(b,s,t,(1-f)*max(b,r)+f*r2); //radius a fraction f up the curved side of the tooth
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function q6(b,s,t,d) = polar(d,s*(iang(b,d)+t)); //point at radius d on the involute curve
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// Creates a rack, which is a straight line with teeth.
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// The same as a segment of teeth from an infinite diameter gear.
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// The "pitch circle" is a line along the X axis.
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@ -215,21 +211,22 @@ function q6(b,s,t,d) = polar(d,s*(iang(b,d)+t)); //p
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// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
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// Example:
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// rack(mm_per_tooth=5, number_of_teeth=30, thickness=5, height=5, pressure_angle=20);
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module rack (
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module rack(
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mm_per_tooth = 5, //this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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number_of_teeth = 20, //total number of teeth along the rack
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thickness = 5, //thickness of rack in mm (affects each tooth)
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height = 10, //height of rack in mm, from tooth top to back of rack.
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pressure_angle = 28, //Controls how straight or bulged the tooth sides are. In degrees.
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backlash = 0.0 //gap between two meshing teeth, in the direction along the circumference of the pitch circle
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backlash = 0.0, //gap between two meshing teeth, in the direction along the circumference of the pitch circle
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clearance = undef
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) {
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a = adendum(mm_per_tooth);
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d = dedendum(mm_per_tooth);
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d = dedendum(mm_per_tooth, clearance);
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xa = a * sin(pressure_angle);
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xd = d * sin(pressure_angle);
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linear_extrude(height = thickness, center = true, convexity = 10)
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for (i = [0:number_of_teeth-1] )
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translate([i*mm_per_tooth,0,0])
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linear_extrude(height = thickness, center = true, convexity = 10) {
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for (i = [0:number_of_teeth-1] ) {
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translate([i*mm_per_tooth,0,0]) {
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polygon(
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points=[
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[-1/2 * mm_per_tooth - 0.01, a-height],
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@ -240,23 +237,36 @@ module rack (
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[ 1/4 * mm_per_tooth - backlash + xd, -d],
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[ 1/2 * mm_per_tooth, -d],
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[ 1/2 * mm_per_tooth + 0.01, a-height],
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],
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paths=[[0,1,2,3,4,5,6,7]]
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]
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);
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}
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}
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}
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}
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//These 5 functions let the user find the derived dimensions of the gear.
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//These functions let the user find the derived dimensions of the gear.
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//A gear fits within a circle of radius outer_radius, and two gears should have
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//their centers separated by the sum of their pictch_radius.
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function circular_pitch (mm_per_tooth=5) = mm_per_tooth; //tooth density expressed as "circular pitch" in millimeters
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function diametral_pitch (mm_per_tooth=5) = PI / mm_per_tooth; //tooth density expressed as "diametral pitch" in teeth per millimeter
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function adendum (mm_per_tooth=5) = module_value(mm_per_tooth);
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function dedendum (mm_per_tooth=5) = 1.25 * module_value(mm_per_tooth);
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function module_value (mm_per_tooth=5) = mm_per_tooth / PI; //tooth density expressed as "module" or "modulus" in millimeters
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function pitch_radius (mm_per_tooth=5,number_of_teeth=11) = mm_per_tooth * number_of_teeth / PI / 2;
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function outer_radius (mm_per_tooth=5,number_of_teeth=11,clearance=0.1) //The gear fits entirely within a cylinder of this radius.
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= mm_per_tooth*(1+number_of_teeth/2)/PI - clearance;
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//their centers separated by the sum of their pitch_radius.
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function circular_pitch(mm_per_tooth=5) = mm_per_tooth; //tooth density expressed as "circular pitch" in millimeters
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function diametral_pitch(mm_per_tooth=5) = PI / mm_per_tooth; //tooth density expressed as "diametral pitch" in teeth per millimeter
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function module_value(mm_per_tooth=5) = mm_per_tooth / PI; //tooth density expressed as "module" or "modulus" in millimeters
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function adendum (mm_per_tooth=5) = module_value(mm_per_tooth);
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function dedendum (mm_per_tooth=5, clearance=undef) = (clearance==undef)? (1.25 * module_value(mm_per_tooth)) : (module_value(mm_per_tooth) + clearance);
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function pitch_radius(mm_per_tooth=5, number_of_teeth=11) = mm_per_tooth * number_of_teeth / PI / 2;
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//The gear fits entirely within a cylinder of this radius.
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function outer_radius(mm_per_tooth=5, number_of_teeth=11)
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= pitch_radius(mm_per_tooth, number_of_teeth) + adendum(mm_per_tooth);
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// Radius of circle at base of dedendum.
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function root_radius(mm_per_tooth=5, number_of_teeth=11, clearance=undef)
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= pitch_radius(mm_per_tooth, number_of_teeth) - dedendum(mm_per_tooth, clearance);
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// The base circle for involute teeth.
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function base_radius(mm_per_tooth=5, number_of_teeth=11, pressure_angle=28)
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= pitch_radius(mm_per_tooth, number_of_teeth) * cos(pressure_angle);
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//////////////////////////////////////////////////////////////////////////////////////////////
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@ -281,10 +291,10 @@ d13=pitch_radius(mm_per_tooth,n1) + pitch_radius(mm_per_tooth,n3);
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d14=pitch_radius(mm_per_tooth,n1) + pitch_radius(mm_per_tooth,n4);
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translate([ 0, 0, 0]) rotate([0,0, $t*360/n1]) color([1.00,0.75,0.75]) gear(mm_per_tooth,n1,thickness,hole);
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translate([ 0, d12, 0]) rotate([0,0,-($t+n2/2-0*n1+1/2)*360/n2]) color([0.75,1.00,0.75]) gear(mm_per_tooth,n2,thickness,hole,0);
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translate([ 0, d12, 0]) rotate([0,0,-($t+n2/2-0*n1+1/2)*360/n2]) color([0.75,1.00,0.75]) gear(mm_per_tooth,n2,thickness,hole);
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translate([ d13, 0, 0]) rotate([0,0,-($t-n3/4+n1/4+1/2)*360/n3]) color([0.75,0.75,1.00]) gear(mm_per_tooth,n3,thickness,hole);
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translate([ d13, 0, 0]) rotate([0,0,-($t-n3/4+n1/4+1/2)*360/n3]) color([0.75,0.75,1.00]) gear(mm_per_tooth,n3,thickness,hole);
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translate([-d14, 0, 0]) rotate([0,0,-($t-n4/4-n1/4+1/2-floor(n4/4)-3)*360/n4]) color([1.00,0.75,0.50]) gear(mm_per_tooth,n4,thickness,hole,0,n4-3);
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translate([-d14, 0, 0]) rotate([0,0,-($t-n4/4-n1/4+1/2-floor(n4/4)-3)*360/n4]) color([1.00,0.75,0.50]) gear(mm_per_tooth,n4,thickness,hole);
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translate([(-floor(n5/2)-floor(n1/2)+$t+n1/2-1/2)*9, -d1+0.0, 0]) rotate([0,0,0]) color([0.75,0.75,0.75]) rack(mm_per_tooth,n5,thickness,height);
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*/
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