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Added ability to make spiral bevel gears.
This commit is contained in:
Revar Desmera
@@ -2,15 +2,15 @@
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// Public Domain Parametric Involute Spur Gear (and involute helical gear and involute rack)
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// Public Domain Parametric Involute Spur Gear (and involute helical gear and involute rack)
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// version 1.1
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// version 1.1
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// by Leemon Baird, 2011, Leemon@Leemon.com
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// by Leemon Baird, 2011, Leemon@Leemon.com
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// Corrected and tweaked by Revar Desmera, 2017, revarbat@gmail.com
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// http://www.thingiverse.com/thing:5505
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//http://www.thingiverse.com/thing:5505
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// Tweaked, and improved by Revar Desmera, 2017-2019, revarbat@gmail.com
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//
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//
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// This file is public domain. Use it for any purpose, including commercial
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// This file is public domain. Use it for any purpose, including commercial
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// applications. Attribution would be nice, but is not required. There is
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// applications. Attribution would be nice, but is not required. There is
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// no warranty of any kind, including its correctness, usefulness, or safety.
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// no warranty of any kind, including its correctness, usefulness, or safety.
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//
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//
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// This is parameterized involute spur (or helical) gear. It is much simpler and less powerful than
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// This is parameterized involute spur (or helical) gear. It is much simpler and less powerful than
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// others on Thingiverse. But it is public domain. I implemented it from scratch from the
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// others on Thingiverse. But it is public domain. I implemented it from scratch from the
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// descriptions and equations on Wikipedia and the web, using Mathematica for calculations and testing,
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// descriptions and equations on Wikipedia and the web, using Mathematica for calculations and testing,
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// and I now release it into the public domain.
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// and I now release it into the public domain.
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//
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//
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@@ -27,36 +27,113 @@
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// measurements for the gear. The most important is pitch_radius, which tells how far apart to space
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// measurements for the gear. The most important is pitch_radius, which tells how far apart to space
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// gears that are meshing, and adendum_radius, which gives the size of the region filled by the gear.
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// gears that are meshing, and adendum_radius, which gives the size of the region filled by the gear.
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// A gear has a "pitch circle", which is an invisible circle that cuts through the middle of each
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// A gear has a "pitch circle", which is an invisible circle that cuts through the middle of each
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// tooth (though not the exact center). In order for two gears to mesh, their pitch circles should
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// tooth (though not the exact center). In order for two gears to mesh, their pitch circles should
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// just touch. So the distance between their centers should be pitch_radius() for one, plus pitch_radius()
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// just touch. So the distance between their centers should be pitch_radius() for one, plus pitch_radius()
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// for the other, which gives the radii of their pitch circles.
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// for the other, which gives the radii of their pitch circles.
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//
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//
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// In order for two gears to mesh, they must have the same mm_per_tooth and pressure_angle parameters.
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// In order for two gears to mesh, they must have the same mm_per_tooth and pressure_angle parameters.
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// mm_per_tooth gives the number of millimeters of arc around the pitch circle covered by one tooth and one
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// mm_per_tooth gives the number of millimeters of arc around the pitch circle covered by one tooth and one
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// space between teeth. The pitch angle controls how flat or bulged the sides of the teeth are. Common
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// space between teeth. The pitch angle controls how flat or bulged the sides of the teeth are. Common
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// values include 14.5 degrees and 20 degrees, and occasionally 25. Though I've seen 28 recommended for
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// values include 14.5 degrees and 20 degrees, and occasionally 25. Though I've seen 28 recommended for
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// plastic gears. Larger numbers bulge out more, giving stronger teeth, so 28 degrees is the default here.
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// plastic gears. Larger numbers bulge out more, giving stronger teeth, so 28 degrees is the default here.
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//
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//
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// The ratio of number_of_teeth for two meshing gears gives how many times one will make a full
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// The ratio of number_of_teeth for two meshing gears gives how many times one will make a full
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// revolution when the the other makes one full revolution. If the two numbers are coprime (i.e.
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// revolution when the the other makes one full revolution. If the two numbers are coprime (i.e.
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// are not both divisible by the same number greater than 1), then every tooth on one gear
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// are not both divisible by the same number greater than 1), then every tooth on one gear
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// will meet every tooth on the other, for more even wear. So coprime numbers of teeth are good.
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// will meet every tooth on the other, for more even wear. So coprime numbers of teeth are good.
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//
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//
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// The module rack() gives a rack, which is a bar with teeth. A rack can mesh with any
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// The module rack() gives a rack, which is a bar with teeth. A rack can mesh with any
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// gear that has the same mm_per_tooth and pressure_angle.
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// gear that has the same mm_per_tooth and pressure_angle.
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//
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//
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// Some terminology:
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// Some terminology:
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// The outline of a gear is a smooth circle (the "pitch circle") which has mountains and valleys
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// The outline of a gear is a smooth circle (the "pitch circle") which has mountains and valleys
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// added so it is toothed. So there is an inner circle (the "root circle") that touches the
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// added so it is toothed. So there is an inner circle (the "root circle") that touches the
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// base of all the teeth, an outer circle that touches the tips of all the teeth,
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// base of all the teeth, an outer circle that touches the tips of all the teeth,
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// and the invisible pitch circle in between them. There is also a "base circle", which can be smaller than
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// and the invisible pitch circle in between them. There is also a "base circle", which can be smaller than
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// all three of the others, which controls the shape of the teeth. The side of each tooth lies on the path
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// all three of the others, which controls the shape of the teeth. The side of each tooth lies on the path
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// that the end of a string would follow if it were wrapped tightly around the base circle, then slowly unwound.
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// that the end of a string would follow if it were wrapped tightly around the base circle, then slowly unwound.
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// That shape is an "involute", which gives this type of gear its name.
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// That shape is an "involute", which gives this type of gear its name.
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//
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//
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//////////////////////////////////////////////////////////////////////////////////////////////
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//////////////////////////////////////////////////////////////////////////////////////////////
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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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) {
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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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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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translate([0,-r,0])
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polygon(
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points=[
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polar(r-1, -181/number_of_teeth),
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polar(r, -181/number_of_teeth),
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polar(r, r<b ? k : -180/number_of_teeth),
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q7(0/5,r,b,c,k, 1),q7(1/5,r,b,c,k, 1),q7(2/5,r,b,c,k, 1),q7(3/5,r,b,c,k, 1),q7(4/5,r,b,c,k, 1),q7(5/5,r,b,c,k, 1),
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q7(5/5,r,b,c,k,-1),q7(4/5,r,b,c,k,-1),q7(3/5,r,b,c,k,-1),q7(2/5,r,b,c,k,-1),q7(1/5,r,b,c,k,-1),q7(0/5,r,b,c,k,-1),
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polar(r, r<b ? -k : 180/number_of_teeth),
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polar(r, 181/number_of_teeth),
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polar(r-1, 181/number_of_teeth),
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]
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);
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}
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// Creates a 2D involute spur gear, with reasonable defaults for all the parameters.
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// Normally, you should just specify the first 2 parameters, and let the rest be default values.
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// Meshing gears must match in mm_per_tooth, pressure_angle, and twist,
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// and be separated by the sum of their pitch radii, which can be found with pitch_radius().
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// mm_per_tooth = This is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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// number_of_teeth = Total number of teeth along the rack
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// teeth_to_hide = Number of teeth to delete to make this only a fraction of a circle
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// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
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// clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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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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// 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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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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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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rotate(i*360/number_of_teeth) {
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translate([0,r,0]) {
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gear_tooth_profile(
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mm_per_tooth = mm_per_tooth,
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number_of_teeth = number_of_teeth,
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pressure_angle = pressure_angle,
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clearance = clearance,
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backlash = backlash,
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bevelang = bevelang
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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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// Creates an involute spur gear, with reasonable defaults for all the parameters.
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// Creates an involute spur gear, with reasonable defaults for all the parameters.
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// Normally, you should just choose the first 4 parameters, and let the rest be default values.
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// Normally, you should just choose the first 4 parameters, and let the rest be default values.
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// Meshing gears must match in mm_per_tooth, pressure_angle, and twist,
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// Meshing gears must match in mm_per_tooth, pressure_angle, and twist,
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@@ -65,55 +142,67 @@
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// number_of_teeth = Total number of teeth along the rack
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// number_of_teeth = Total number of teeth along the rack
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// thickness = Thickness of rack in mm (affects each tooth)
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// thickness = Thickness of rack in mm (affects each tooth)
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// hole_diameter = Diameter of centeral shaft hole.
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// hole_diameter = Diameter of centeral shaft hole.
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// twist = 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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// teeth_to_hide = Number of teeth to delete to make this only a fraction of a circle
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// teeth_to_hide = Number of teeth to delete to make this only a fraction of a circle
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// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
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// pressure_angle = Controls how straight or bulged the tooth sides are. In degrees.
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// clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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// clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters)
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// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
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// backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle
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// twist = 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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// scale = Scale of top of gear compared to bottom. Useful for making crown gears.
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// slices = Number of slices to divide gear into. Useful for refining gears with `twist`.
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// Example:
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// Example:
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// gear(mm_per_tooth=5, number_of_teeth=20, thickness=5, hole_diameter=5);
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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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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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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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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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hole_diameter = 3, //diameter of the hole in the center, in mm
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twist = 0, //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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teeth_to_hide = 0, //number of teeth to delete to make this only a fraction of a circle
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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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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 = 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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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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) {
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p = mm_per_tooth * number_of_teeth / PI / 2; //radius of pitch circle
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p = mm_per_tooth * number_of_teeth / PI / 2; //radius of pitch circle
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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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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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r = p-(c-p)-clearance; //radius of root circle
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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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difference() {
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difference() {
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linear_extrude(height = thickness, center = true, convexity = 10, twist = twist, slices = ceil(abs(twist)/5)+1)
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linear_extrude(height=thickness, center=true, convexity=10, twist=twist, scale=p2/p, slices=slices) {
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for (i = [0:number_of_teeth-teeth_to_hide-1] )
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gear2d(
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rotate([0,0,i*360/number_of_teeth])
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mm_per_tooth = mm_per_tooth,
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polygon(
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number_of_teeth = number_of_teeth,
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points=[
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teeth_to_hide = teeth_to_hide,
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polar(hole_diameter/10, -181/number_of_teeth),
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pressure_angle = pressure_angle,
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polar(r, -181/number_of_teeth),
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clearance = clearance,
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polar(r, r<b ? k : -180/number_of_teeth),
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backlash = backlash,
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q7(0/5,r,b,c,k, 1),q7(1/5,r,b,c,k, 1),q7(2/5,r,b,c,k, 1),q7(3/5,r,b,c,k, 1),q7(4/5,r,b,c,k, 1),q7(5/5,r,b,c,k, 1),
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bevelang = bevelang
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q7(5/5,r,b,c,k,-1),q7(4/5,r,b,c,k,-1),q7(3/5,r,b,c,k,-1),q7(2/5,r,b,c,k,-1),q7(1/5,r,b,c,k,-1),q7(0/5,r,b,c,k,-1),
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);
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polar(r, r<b ? -k : 180/number_of_teeth),
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}
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polar(r, 181/number_of_teeth),
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if (hole_diameter > 0) {
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polar(hole_diameter/10, 181/number_of_teeth),
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cylinder(h=2*thickness+1, r=hole_diameter/2, center=true);
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],
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}
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paths=[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]]
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if (bevelang != 0) {
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);
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h = (c-r)*sin(bevelang);
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cylinder(h=2*thickness+1, r=hole_diameter/2, center=true);
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translate([0,0,-thickness/2]) {
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difference() {
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cube([2*c/cos(bevelang),2*c/cos(bevelang),2*h], center=true);
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cylinder(h=h, r1=r, r2=c, center=false);
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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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}
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//these 4 functions are used by gear
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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 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 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 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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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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||||||
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||||||
// Creates a rack, which is a straight line with teeth.
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// Creates a rack, which is a straight line with teeth.
|
||||||
// The same as a segment of teeth from an infinite diameter gear.
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// The same as a segment of teeth from an infinite diameter gear.
|
||||||
@@ -154,7 +243,8 @@ module rack (
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|||||||
],
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],
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paths=[[0,1,2,3,4,5,6,7]]
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paths=[[0,1,2,3,4,5,6,7]]
|
||||||
);
|
);
|
||||||
};
|
}
|
||||||
|
|
||||||
|
|
||||||
//These 5 functions let the user find the derived dimensions of the gear.
|
//These 5 functions let the user find the derived dimensions of the gear.
|
||||||
//A gear fits within a circle of radius outer_radius, and two gears should have
|
//A gear fits within a circle of radius outer_radius, and two gears should have
|
||||||
@@ -166,10 +256,11 @@ function dedendum (mm_per_tooth=5) = 1.25 * module_value(mm_per_tooth);
|
|||||||
function module_value (mm_per_tooth=5) = mm_per_tooth / PI; //tooth density expressed as "module" or "modulus" in millimeters
|
function module_value (mm_per_tooth=5) = mm_per_tooth / PI; //tooth density expressed as "module" or "modulus" in millimeters
|
||||||
function pitch_radius (mm_per_tooth=5,number_of_teeth=11) = mm_per_tooth * number_of_teeth / PI / 2;
|
function pitch_radius (mm_per_tooth=5,number_of_teeth=11) = mm_per_tooth * number_of_teeth / PI / 2;
|
||||||
function outer_radius (mm_per_tooth=5,number_of_teeth=11,clearance=0.1) //The gear fits entirely within a cylinder of this radius.
|
function outer_radius (mm_per_tooth=5,number_of_teeth=11,clearance=0.1) //The gear fits entirely within a cylinder of this radius.
|
||||||
= mm_per_tooth*(1+number_of_teeth/2)/PI - clearance;
|
= mm_per_tooth*(1+number_of_teeth/2)/PI - clearance;
|
||||||
|
|
||||||
|
|
||||||
//////////////////////////////////////////////////////////////////////////////////////////////
|
//////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
//example gear train.
|
//example gear train.
|
||||||
//Try it with OpenSCAD View/Animate command with 20 steps and 24 FPS.
|
//Try it with OpenSCAD View/Animate command with 20 steps and 24 FPS.
|
||||||
//The gears will continue to be rotated to mesh correctly if you change the number of teeth.
|
//The gears will continue to be rotated to mesh correctly if you change the number of teeth.
|
||||||
|
|
||||||
|
|||||||
Reference in New Issue
Block a user