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@ -1,338 +1,287 @@
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//This is a modification of " Public Domain Parametric Involute Spur Gear (and involute helical gear and involute rack)
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// by Leemon Baird, 2011, Leemon@Leemon.com
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//http://www.thingiverse.com/thing:5505 "
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// Kopfspiel
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spiel = 0.05;
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// Hoehe des Zahnkopfes ueber dem Teilkreis
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modul=1;
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// Laenge der Zahnstange
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laenge_stange=50;
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// Anzahl der Radzaehne
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zahnzahl_ritzel=32;
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// Hoehe der Zahnstange bis zur Waelzgeraden
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hoehe_stange=4;
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// Durchmesser der Mittelbohrung des Stirnrads
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bohrung_ritzel=4;
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// Breite der Zaehne
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breite=8.8;
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// Eingriffswinkel, Standardwert = 20 grad gemaess DIN 867. Sollte nicht groesser als 45 grad sein.
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eingriffswinkel=20;
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// Schraegungswinkel zur Rotationsachse, Standardwert = 0 grad (Geradverzahnung)
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schraegungswinkel=20;
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// Komponenten zusammengebaut fuer Konstruktion oder auseinander zum 3D-Druck
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zusammen_gebaut=0;
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// Loecher zur Material-/Gewichtsersparnis bzw. Oberflaechenvergoesserung erzeugen, wenn Geometrie erlaubt
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optimiert = 1;
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//Modifications by racatack June 2016:
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// v1.0, 6/24/16:
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// -Incorporated 'module InvoluteGear_rack()' from the 11/11/15 comment by quisam2342 in thing:5505 to fix noted problems in rack generation at various tooth sizes
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// -Added a section for an optional 'backboard' that can be used to stiffen an otherwise skinny rack
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// -Added sections for optional Stop Blocks at either or both ends of a rack
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// -Removed extra gears from the example since I only need one pinion. See thing:5505 example section to gain more insight into gear generation.
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//v1.1, 6/28/16:
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// -Added sections to optionally create mounting flanges on the bottom/backside of the rack. Flanges can be at either or both ends, or longitudinal.
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/* Bibliothek fuer ein Zahstangen-Radpaar fuer Thingiverse Customizer
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//TO GENERATE A CUSTOM RACK AND PINION ENTER INPUTS AT LINES 345-377
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Enthaelt die Module
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zahnstange(modul, laenge, hoehe, breite, eingriffswinkel = 20, schraegungswinkel = 0)
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stirnrad(modul, zahnzahl, breite, bohrung, eingriffswinkel = 20, schraegungswinkel = 0, optimiert = true)
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zahnstange_und_ritzel (modul, laenge_stange, zahnzahl_ritzel, hoehe_stange, bohrung_ritzel, breite, eingriffswinkel=20, schraegungswinkel=0, zusammen_gebaut=true, optimiert=true)
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Autor: Dr Joerg Janssen
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Stand: 6. Januar 2017
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Version: 2.0
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Lizenz: Creative Commons - Attribution, Non Commercial, Share Alike
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Erlaubte Module nach DIN 780:
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0.05 0.06 0.08 0.10 0.12 0.16
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0.20 0.25 0.3 0.4 0.5 0.6
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0.7 0.8 0.9 1 1.25 1.5
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2 2.5 3 4 5 6
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8 10 12 16 20 25
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32 40 50 60
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*/
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//////////////////////////////////////////////////////////////////////////////////////////////
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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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// by Leemon Baird, 2011, Leemon@Leemon.com
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//http://www.thingiverse.com/thing:5505
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//
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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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// no warranty of any kind, including its correctness, usefulness, or safety.
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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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// 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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// and I now release it into the public domain.
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//
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// http://en.wikipedia.org/wiki/Involute_gear
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// http://en.wikipedia.org/wiki/Gear
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// http://en.wikipedia.org/wiki/List_of_gear_nomenclature
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// http://gtrebaol.free.fr/doc/catia/spur_gear.html
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// http://www.cs.cmu.edu/~rapidproto/mechanisms/chpt7.html
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//
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// The module gear() gives 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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// The module gear() gives a gear in the XY plane, centered on the origin, with one tooth centered on
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// the positive Y axis. The various functions below it take the same parameters, and return various
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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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// 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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// 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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//
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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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// 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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// 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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// 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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// 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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//
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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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//
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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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// 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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// 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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// 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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//
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//////////////////////////////////////////////////////////////////////////////////////////////
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/* [Hidden] */
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pi = 3.14159;
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rad = 57.29578;
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$fn = 96;
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//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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//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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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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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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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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) {
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assign(pi = 3.1415926)
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assign(p = mm_per_tooth * number_of_teeth / pi / 2) //radius of pitch circle
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assign(c = p + mm_per_tooth / pi - clearance) //radius of outer circle
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assign(b = p*cos(pressure_angle)) //radius of base circle
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assign(r = p-(c-p)-clearance) //radius of root circle
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assign(t = mm_per_tooth/2-backlash/2) //tooth thickness at pitch circle
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assign(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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for (i = [0:number_of_teeth-teeth_to_hide-1] )
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rotate([0,0,i*360/number_of_teeth])
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linear_extrude(height = thickness, center = true, convexity = 10, twist = twist)
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polygon(
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points=[
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[0, -hole_diameter/10],
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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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],
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paths=[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]
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);
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cylinder(h=2*thickness+1, r=hole_diameter/2, center=true, $fn=20);
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/* Wandelt Radian in Grad um */
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function grad(eingriffswinkel) = eingriffswinkel*rad;
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/* Wandelt Grad in Radian um */
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function radian(eingriffswinkel) = eingriffswinkel/rad;
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/* Wandelt 2D-Polarkoordinaten in kartesische um
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Format: radius, phi; phi = Winkel zur x-Achse auf xy-Ebene */
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function pol_zu_kart(polvect) = [
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polvect[0]*cos(polvect[1]),
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polvect[0]*sin(polvect[1])
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];
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/* Kreisevolventen-Funktion:
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Gibt die Polarkoordinaten einer Kreisevolvente aus
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r = Radius des Grundkreises
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rho = Abrollwinkel in Grad */
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function ev(r,rho) = [
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r/cos(rho),
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grad(tan(rho)-radian(rho))
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];
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/* Wandelt Kugelkoordinaten in kartesische um
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Format: radius, theta, phi; theta = Winkel zu z-Achse, phi = Winkel zur x-Achse auf xy-Ebene */
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function kugel_zu_kart(vect) = [
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vect[0]*sin(vect[1])*cos(vect[2]),
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vect[0]*sin(vect[1])*sin(vect[2]),
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vect[0]*cos(vect[1])
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];
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/* prueft, ob eine Zahl gerade ist
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= 1, wenn ja
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= 0, wenn die Zahl nicht gerade ist */
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function istgerade(zahl) =
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(zahl == floor(zahl/2)*2) ? 1 : 0;
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/* Kopiert und dreht einen Koerper */
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module kopiere(vect, zahl, abstand, winkel){
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for(i = [0:zahl-1]){
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translate(v=vect*abstand*i)
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rotate(a=i*winkel, v = [0,0,1])
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children(0);
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}
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}
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/* Zahnstange
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modul = Hoehe des Zahnkopfes ueber der Waelzgeraden
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laenge = Laenge der Zahnstange
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hoehe = Hoehe der Zahnstange bis zur Waelzgeraden
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breite = Breite der Zaehne
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eingriffswinkel = Eingriffswinkel, Standardwert = 20 grad gemaess DIN 867. Sollte nicht groesser als 45 grad sein.
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schraegungswinkel = Schraegungswinkel zur Zahnstangen-Querachse; 0 grad = Geradverzahnung */
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module zahnstange(modul, laenge, hoehe, breite, eingriffswinkel = 20, schraegungswinkel = 0) {
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// Dimensions-Berechnungen
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//modul=0.99;// modul*(1-spiel);
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c = modul / 6; // Kopfspiel
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mx = modul/cos(schraegungswinkel); // Durch Schraegungswinkel verzerrtes modul in x-Richtung
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a = 2*mx*tan(eingriffswinkel)+c*tan(eingriffswinkel); // Flankenbreite
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b = pi*mx/2-2*mx*tan(eingriffswinkel); // Kopfbreite
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x = breite*tan(schraegungswinkel); // Verschiebung der Oberseite in x-Richtung durch Schraegungswinkel
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nz = ceil((laenge+abs(2*x))/(pi*mx)); // Anzahl der Zaehne
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translate([-pi*mx*(floor(nz/2)-1)-a-b/2,-modul,0]){
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intersection(){
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kopiere([1,0,0], nz, pi*mx, 0){
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polyhedron(
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points=[[0,-c,0], [a,2*modul,0], [a+b,2*modul,0], [2*a+b,-c,0], [pi*mx,-c,0], [pi*mx,modul-hoehe,0], [0,modul-hoehe,0], // Unterseite
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[0+x,-c,breite], [a+x,2*modul,breite], [a+b+x,2*modul,breite], [2*a+b+x,-c,breite], [pi*mx+x,-c,breite], [pi*mx+x,modul-hoehe,breite], [0+x,modul-hoehe,breite]], // Oberseite
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faces=[[6,5,4,3,2,1,0], // Unterseite
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[1,8,7,0],
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[9,8,1,2],
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[10,9,2,3],
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[11,10,3,4],
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[12,11,4,5],
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[13,12,5,6],
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[7,13,6,0],
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[7,8,9,10,11,12,13], // Oberseite
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]
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);
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};
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translate([abs(x),-hoehe+modul-0.5,-0.5]){
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cube([laenge,hoehe+modul+1,breite+1]);
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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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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)/3.1415926*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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//a rack, which is a straight line with teeth (the same as a segment from a giant gear with a huge number of teeth).
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//The "pitch circle" is a line along the X axis.
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//module rack (
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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 along the rack
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// thickness = 6, //thickness of rack in mm (affects each tooth)
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// height = 120, //height of rack in mm, from tooth top to far side 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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//) {
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// assign(pi = 3.1415926)
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// assign(a = mm_per_tooth / pi) //addendum
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// assign(t = a*cos(pressure_angle)-1) //tooth side is tilted so top/bottom corners move this amount
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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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// polygon(
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// points=[
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// [-mm_per_tooth * 3/4, a-height],
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// [-mm_per_tooth * 3/4 - backlash, -a],
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// [-mm_per_tooth * 1/4 + backlash - t, -a],
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// [-mm_per_tooth * 1/4 + backlash + t, a],
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// [ mm_per_tooth * 1/4 - backlash - t, a],
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// [ mm_per_tooth * 1/4 - backlash + t, -a],
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// [ mm_per_tooth * 3/4 + backlash, -a],
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// [ mm_per_tooth * 3/4, 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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//rac note - This section generates the rack body and teeth. It is from the 11/11/15 comment by quisam2342 in thing:5505 to fix noted problems with rack generation, and replaces the original 'module rack()'
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////////////////////////////////////////////////////////////////////////////////////////////////
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// The module InvoluteGear_rack() gives a involute gear rack, which is a bar with teeth.
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// A rack can mesh with any gear that has the same mm_per_tooth and pressure_angle.
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// The "pitch circle" is a line along the X axis.
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//
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// mm_per_tooth this is the "circular pitch", the circumference of the pitch circle
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// divided by the number of teeth
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//
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// number_of_teeth total number of teeth along the rack
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//
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// thickness thickness of rack in mm
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//
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// height height of rack in mm, from tooth top to far side of rack
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//
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// pressure_angle controls how straight or bulged the tooth sides are, in degrees
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//
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// clearance gap between top of a tooth on one gear and bottom of valley
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// on a meshing gear, in millimeters
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//
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// backlash gap between two meshing teeth, in the direction along the circumference
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// of the pitch circle
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////////////////////////////////////////////////////////////////////////////////////////////////
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module InvoluteGear_rack (
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//Default numbers in this section get overridden by numbers in 'example rack and pinion' section, so set your values there.
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mm_per_tooth = 3, //all meshing gears need the same mm_per_tooth
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number_of_teeth = 11,
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thickness = 6,
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height = 4,
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//rac - Added variables for backboard, stop blocks and mounting flanges:
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//set your values in the 'example rack and pinion' section, as defaults given here will be overridden by that section
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backboard_thickness = 2.0,
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backboard_height = 1.0,
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side_flange_thickness = 0,
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side_flange_height = 0,
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flange_offset = 0,
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stop_height = backboard_height,
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left_stop_enable = 1,
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right_stop_enable = 1,
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flange_height = 0,
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left_flange_enable = 1,
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right_flange_enable = 1,
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//These defaults are not redefined in the example section:
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pressure_angle = 28, //all meshing gears need the same pressure_angle
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clearance = 0.0,
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backlash = 0.0
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)
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{
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// addendum - tooth height above pitch line
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assign(addendum = module_value(mm_per_tooth) - clearance)
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// dedendum - tooth height below pitch line
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assign(dedendum = 1.25 * module_value(mm_per_tooth) )
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for (i = [0:number_of_teeth-1] )
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translate([(i+0.5)*mm_per_tooth,height-addendum,0])
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linear_extrude(height = thickness, center = true, convexity = 10) //'height' parameter here is not the same as 'height' parameter of module. Here it effectively is the width or thickness as the rack is extruded from one side-face to the other.
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polygon(
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points=[
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[-1/2 * mm_per_tooth, addendum-height],
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[-1/2 * mm_per_tooth, -dedendum],
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[-1/4 * mm_per_tooth + backlash - dedendum * tan(pressure_angle), -dedendum],
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[-1/4 * mm_per_tooth + backlash + addendum * tan(pressure_angle), addendum],
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[ 1/4 * mm_per_tooth - backlash - addendum * tan(pressure_angle), addendum],
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[ 1/4 * mm_per_tooth - backlash + dedendum * tan(pressure_angle), -dedendum],
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[ 1/2 * mm_per_tooth, -dedendum],
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[ 1/2 * mm_per_tooth, addendum-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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//rac -added - This section optionally creates a 'stop block' at the left end of the rack
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translate([(-0.11)*mm_per_tooth,0,0.5*(-thickness)])
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linear_extrude(height = left_stop_enable*thickness, center = false, convexity = 10)
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polygon(
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points=[
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[-1/2 * mm_per_tooth,height+stop_height], //stop_height extends stop block above teeth, change the number to change the extension amount
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[-1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,height+stop_height], //stop_height extends stop block above teeth, change the number to change the extension amount
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],
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paths=[[0,1,2,3]]
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);
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//rac -added - This section optionally creates a 'stop block' at the right end of the rack
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translate([(0.11+number_of_teeth)*mm_per_tooth,0,0.5*(-thickness)])
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linear_extrude(height = right_stop_enable*thickness, center = false, convexity = 10)
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polygon(
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points=[
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[-1/2 * mm_per_tooth,height+stop_height], //stop_height extends stop block above teeth
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[-1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,height+stop_height], //stop_height extends stop block above teeth
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],
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paths=[[0,1,2,3]]
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);
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//rac -added - This section optionally creates a flange at the left rear of the rack
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translate([(-0.11)*mm_per_tooth,0,0.5*(-thickness)])
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linear_extrude(height = left_flange_enable*thickness, center = false, convexity = 10)
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polygon(
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points=[
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[-1/2 * mm_per_tooth,-flange_height], //flange_height extends flange beyond rack bottom
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[-1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,-flange_height], //flange_height extends flange beyond rack bottom
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],
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paths=[[0,1,2,3]]
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);
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//rac -added - This section optionally creates a flange at the right rear of the rack
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translate([(0.11+number_of_teeth)*mm_per_tooth,0,0.5*(-thickness)])
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linear_extrude(height = right_flange_enable*thickness, center = false, convexity = 10)
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polygon(
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points=[
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[-1/2 * mm_per_tooth,-flange_height], //flange_height extends flange beyond rack bottom
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[-1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,-flange_height], //flange_height extends flange beyond rack bottom
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],
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paths=[[0,1,2,3]]
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);
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//rac -added - This section optionally creates a 'Backboard' on one side of the rack. Can be used to add stiffness for a 'thin' rack (i.e. a rack with low height and/or thickness numbers) or if a large negative height is used it can extend under the rack as a mounting flange.
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for (i = [0:number_of_teeth-1] )
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translate([(i+0.5)*mm_per_tooth,0,0.5*(-thickness+backboard_thickness)])
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//0.5*(-thickness+backboard_thickness) starts the backboard at one side of the rack and extrudes it inward
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linear_extrude(height = backboard_thickness, center = true, convexity = 10)
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polygon(
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points=[
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[-1/2 * mm_per_tooth,height+backboard_height], //backboard_height extends backboard above teeth
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[-1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,height+backboard_height], //backboard_height extends backboard above teeth
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],
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paths=[[0,1,2,3]]
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);
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//rac -added - This section optionally creates a Rear Side-Flange on along one side of the rack. Can be used to add stiffness for a 'thin' rack (i.e. a rack with low height and/or thickness numbers) or it can be used as a mounting flange.
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for (i = [0:number_of_teeth-1] )
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translate([(i+0.5)*mm_per_tooth,0,0.5*(-thickness+side_flange_thickness)+flange_offset])
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//0.5*(-side_flange_thickness) starts the backboard at one side of the rack and extrudes it inward. flange_offset moves the flange toward the other side of the rack
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linear_extrude(height = side_flange_thickness, center = true, convexity = 10)
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polygon(
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points=[
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[-1/2 * mm_per_tooth,-side_flange_height], //side_flange_height extends side_flange beyond rack bottom
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[-1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,0],
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[ 1/2 * mm_per_tooth,-side_flange_height], //side_flange_height extends backboard beyond rack bottom
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],
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paths=[[0,1,2,3]]
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);
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}
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/* Stirnrad
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modul = Hoehe des Zahnkopfes ueber dem Teilkreis
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zahnzahl = Anzahl der Radzaehne
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breite = Zahnbreite
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bohrung = Durchmesser der Mittelbohrung
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eingriffswinkel = Eingriffswinkel, Standardwert = 20 grad gemaess DIN 867. Sollte nicht groesser als 45 grad sein.
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schraegungswinkel = Schraegungswinkel zur Rotationsachse; 0 grad = Geradverzahnung
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optimiert = Loecher zur Material-/Gewichtsersparnis bzw. Oberflaechenvergoesserung erzeugen, wenn Geometrie erlaubt (= 1, wenn wahr) */
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module stirnrad(modul, zahnzahl, breite, bohrung, eingriffswinkel = 20, schraegungswinkel = 0, optimiert = true) {
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//These 5 functions let the user find the derived dimensions of the gear.
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|
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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=3) = mm_per_tooth; //tooth density expressed as "circular pitch" in millimeters
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|
|
function diametral_pitch (mm_per_tooth=3) = 3.1415926 / mm_per_tooth; //tooth density expressed as "diametral pitch" in teeth per millimeter
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|
function module_value (mm_per_tooth=3) = mm_per_tooth / 3.1415926; //tooth density expressed as "module" or "modulus" in millimeters
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function pitch_radius (mm_per_tooth=3,number_of_teeth=11) = mm_per_tooth * number_of_teeth / 3.1415926 / 2;
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function outer_radius (mm_per_tooth=3,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)/3.1415926 - clearance;
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|
|
// Dimensions-Berechnungen
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d = modul * zahnzahl; // Teilkreisdurchmesser
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|
r = d / 2; // Teilkreisradius
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alpha_stirn = atan(tan(eingriffswinkel)/cos(schraegungswinkel));// Schraegungswinkel im Stirnschnitt
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|
db = d * cos(alpha_stirn); // Grundkreisdurchmesser
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|
rb = db / 2; // Grundkreisradius
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da = (modul <1)? d + modul * 2.2 : d + modul * 2; // Kopfkreisdurchmesser nach DIN 58400 bzw. DIN 867
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ra = da / 2; // Kopfkreisradius
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|
c = (zahnzahl <3)? 0 : modul/6; // Kopfspiel
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df = d - 2 * (modul + c); // Fusskreisdurchmesser
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|
|
rf = df / 2; // Fusskreisradius
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|
rho_ra = acos(rb/ra); // maximaler Abrollwinkel;
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|
// Evolvente beginnt auf Grundkreis und endet an Kopfkreis
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|
|
rho_r = acos(rb/r); // Abrollwinkel am Teilkreis;
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|
// Evolvente beginnt auf Grundkreis und endet an Kopfkreis
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|
phi_r = grad(tan(rho_r)-radian(rho_r)); // Winkel zum Punkt der Evolvente auf Teilkreis
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|
gamma = rad*breite/(r*tan(90-schraegungswinkel)); // Torsionswinkel fuer Extrusion
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|
schritt = rho_ra/16; // Evolvente wird in 16 Stuecke geteilt
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|
tau = 360/zahnzahl; // Teilungswinkel
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|
|
r_loch = (2*rf - bohrung)/8; // Radius der Loecher fuer Material-/Gewichtsersparnis
|
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|
|
rm = bohrung/2+2*r_loch; // Abstand der Achsen der Loecher von der Hauptachse
|
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|
|
z_loch = floor(2*pi*rm/(3*r_loch)); // Anzahl der Loecher fuer Material-/Gewichtsersparnis
|
|
|
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|
|
optimiert = (optimiert && r >= breite*1.5 && d > 2*bohrung); // ist Optimierung sinnvoll?
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|
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|
|
// Zeichnung
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|
|
union(){
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rotate([0,0,-phi_r-90*(1-spiel)/zahnzahl]){ // Zahn auf x-Achse zentrieren;
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// macht Ausrichtung mit anderen Raedern einfacher
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linear_extrude(height = breite, twist = gamma){
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difference(){
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union(){
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zahnbreite = (180*(1-spiel))/zahnzahl+2*phi_r;
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circle(rf); // Fusskreis
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for (rot = [0:tau:360]){
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rotate (rot){ // "Zahnzahl-mal" kopieren und drehen
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polygon(concat( // Zahn
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[[0,0]], // Zahnsegment beginnt und endet im Ursprung
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[for (rho = [0:schritt:rho_ra]) // von null Grad (Grundkreis)
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// bis maximalen Evolventenwinkel (Kopfkreis)
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pol_zu_kart(ev(rb,rho))], // Erste Evolventen-Flanke
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[pol_zu_kart(ev(rb,rho_ra))], // Punkt der Evolvente auf Kopfkreis
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[for (rho = [rho_ra:-schritt:0]) // von maximalen Evolventenwinkel (Kopfkreis)
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// bis null Grad (Grundkreis)
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pol_zu_kart([ev(rb,rho)[0], zahnbreite-ev(rb,rho)[1]])]
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// Zweite Evolventen-Flanke
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// (180*(1-spiel)) statt 180 Grad,
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// um Spiel an den Flanken zu erlauben
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)
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);
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}
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}
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}
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circle(r = rm+r_loch*1.49); // "Bohrung"
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}
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}
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}
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// mit Materialersparnis
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if (optimiert) {
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linear_extrude(height = breite){
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difference(){
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circle(r = (bohrung+r_loch)/2);
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circle(r = bohrung/2); // Bohrung
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}
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}
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linear_extrude(height = (breite-r_loch/2 < breite*2/3) ? breite*2/3 : breite-r_loch/2){
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difference(){
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circle(r=rm+r_loch*1.51);
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union(){
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circle(r=(bohrung+r_loch)/2);
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for (i = [0:1:z_loch]){
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translate(kugel_zu_kart([rm,90,i*360/z_loch]))
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circle(r = r_loch);
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}
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}
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}
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}
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}
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// ohne Materialersparnis
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else {
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linear_extrude(height = breite){
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difference(){
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circle(r = rm+r_loch*1.51);
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circle(r = bohrung/2);
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}
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}
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}
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}
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}
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/* Zahnstange und Ritzel
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modul = Hoehe des Zahnkopfes ueber dem Teilkreis
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laenge_stange = Laenge der Zahnstange
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zahnzahl_ritzel = Anzahl der Radzaehne am Ritzel
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hoehe_stange = Hoehe der Zahnstange bis zur Waelzgeraden
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bohrung_ritzel = Durchmesser der Mittelbohrung des Ritzels
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breite = Breite der Zaehne
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eingriffswinkel = Eingriffswinkel, Standardwert = 20 grad gemaess DIN 867. Sollte nicht groesser als 45 grad sein.
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schraegungswinkel = Schraegungswinkel, Standardwert = 0 grad (Geradverzahnung)
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optimiert = Loecher zur Material-/Gewichtsersparnis bzw. Oberflaechenvergoesserung erzeugen, wenn Geometrie erlaubt (= 1, wenn wahr)
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Rack and Pinion
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module = Height of the tooth head above the pitch circle
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rack_length = Length of the rack
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pinion_tooth_count = Number of teeth on the pinion
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rack_height = Height of the rack up to the pitch line
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pinion_bore = Diameter of the central bore of the pinion
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width = Width of the teeth
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contact_angle = Contact angle, default value = 20 degrees according to DIN 867. Should not exceed 45 degrees.
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helix_angle = Helix angle, default value = 0 degrees (straight tooth)
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optimized = Generate holes for material/weight saving or surface enhancement if geometry allows (= 1 if true)
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*/
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module zahnstange_und_rad (modul, laenge_stange, zahnzahl_ritzel, hoehe_stange, bohrung_ritzel, breite, eingriffswinkel=20, schraegungswinkel=0, zusammen_gebaut=true, optimiert=true) {
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abstand = zusammen_gebaut? modul*zahnzahl_ritzel/2 : modul*zahnzahl_ritzel;
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zahnstange(modul, laenge_stange, hoehe_stange, breite, eingriffswinkel, -schraegungswinkel);
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}
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module rad_und_zahnstange (modul, laenge_stange, zahnzahl_ritzel, hoehe_stange, bohrung_ritzel, breite, eingriffswinkel=20, schraegungswinkel=0, zusammen_gebaut=true, optimiert=true) {
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|
abstand = zusammen_gebaut? modul*zahnzahl_ritzel/2 : modul*zahnzahl_ritzel;
|
|
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|
|
translate([0, abstand, 0]) {
|
|
|
|
|
if (istgerade(zahnzahl_ritzel)) {
|
|
|
|
|
rotate(90 + 180/zahnzahl_ritzel) {
|
|
|
|
|
stirnrad (modul, zahnzahl_ritzel, breite, bohrung_ritzel, eingriffswinkel, schraegungswinkel, optimiert);
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
rotate(a=90) {
|
|
|
|
|
stirnrad (modul, zahnzahl_ritzel, breite, bohrung_ritzel, eingriffswinkel, schraegungswinkel, optimiert);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
//zahnstange_und_rad (modul, laenge_stange, zahnzahl_ritzel, hoehe_stange, bohrung_ritzel, breite, eingriffswinkel, schraegungswinkel, zusammen_gebaut, optimiert);
|
