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/*
* G-code meta compiler
*
* Copyright (C) 2014 B. Stultiens
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
* Gear example
* ------------
* This example is by no means a complete or correct implementation of gears in
* any generic form. It is primarily for inspiration and to show what gcmc can
* do with relatively little coding. You may use this script as inspiration to
* create a better implementation if you like.
*
* Please note: The below parameters will shift the examples with an XY offset
* as indicated by the options. These are passed on the command-line when the
* examples are generated.
*
* @@@--svg-toolwidth 0.1 --svg-opacity 1 --svg-no-movelayer -x 110 -y 70@@@
*/
/*
* Gear terms:
* N - Number of Teeth
* Pa - Pressure Angle
* D - Pitch Diameter - D = N/P = Do - 2/P (Gear radius at center of the teeth)
* P - Diametral Pitch - P = N/D
* p - Circular Pitch - p = pi() / P
* Db - Base Diameter - Db = D * cos(Pa) (Bottom of teeth insertion)
* Dr - Root Diameter - Dr = D - 2b (Bottom of tooth cutout)
* Do - Outside Diameter - Do = D + 2a
* a - Addendum - a = 1/P
* b - Dedendum - b = ht - a
* ht - Whole Depth (Pa<20) - 2.157/P
* ht - Whole Depth (Pa>=20) - 2.2/P + 0.05mm (Total depth from outer dia to bottom)
* t - Tooth Thickness - t = pi()/(2*P) (Thinckness at Pitch Diameter)
*/
__ang_step = 2.0deg; /* Trace interval for curves */
/*
* Point on involute curve at specified angle, see https://en.wikipedia.org/wiki/Involute
* Cartesian:
* x = a * ( cos(t) + t * sin(t))
* y = a * ( sin(t) - t * cos(t))
* Polar:
* r = a * sqrt(1 + t^2) = sqrt(a^2 + (a*t)^2)
* phi = t - atan(t)
* where:
* - a = circle radius
* - t = angle (radians)
*
* For angle from circle radius: t^2 = (r/a)^2 - 1
*/
function involute_point(angle, radius)
{
angle = to_rad(angle); /* Multiplication must be in radians */
return radius * [cos(angle) + to_none(angle) * sin(angle), sin(angle) - to_none(angle) * cos(angle)];
}
function involute_angle(radius, outrad)
{
return to_rad(sqrt(pow(outrad/radius, 2.0) - 1));
}
/*
* Make a gear with:
* - nteeth Number of teeth
* - pressure_angle Teeth contact pressure angle
* - diametral_pitch Diametral pitch (teets/length)
*
* Return a vectorlist with outer points of the gear centered at [0,0]
*/
function gear_P(nteeth, pressure_angle, diametral_pitch)
{
/* The routine gets is serious trouble if you make the pressure angle
* too large or too small. Warn the user if such case occurs.
*/
if(pressure_angle > 24.6deg) {
warning("Pressure angle (", pressure_angle, ") too large, cannot fit teeth inside the set outside diameter");
}
if(pressure_angle < 12.0deg) {
warning("Pressure angle (", pressure_angle, ") too small, teeth may get stuck at pitch radius");
}
local i;
local pitch_diameter = nteeth / diametral_pitch;
local base_diameter = pitch_diameter * cos(pressure_angle);
local addendum = 1.0/diametral_pitch;
local ht = 2.157 / diametral_pitch;
local dedendum = ht - addendum;
local outside_diameter = pitch_diameter + 2.0*addendum;
local root_diameter = base_diameter - 2.0*dedendum;
local work_diameter = outside_diameter - 4.0*addendum;
local tooth = {}; // The curve for one tooth
/*
* message("nteeth=", nteeth, " pressure_angle=", pressure_angle, " diametral_pitch=", diametral_pitch);
* message("addendum=", addendum, " dedendum=", dedendum, " ht=", ht);
* message("pitch_diameter=", pitch_diameter);
* message("base_diameter=", base_diameter);
* message("outside_diameter=", outside_diameter);
* message("root_diameter=", root_diameter);
* message("work_diameter=", work_diameter);
*/
/*
* Show the different diameters:
* hole([0, 0], pitch_diameter/2.0);
* hole([0, 0], base_diameter/2.0);
* hole([0, 0], outside_diameter/2.0);
* hole([0, 0], root_diameter/2.0);
* hole([0, 0], work_diameter/2.0);
*/
// Fillet radius is approx. Will not reach root exactly, but close enough
// Otherwise need to calculate intersection with root-circle
local filletrad = (base_diameter - root_diameter)/8.0;
// Center of the fillet arc, involute makes a ~240deg angle with fillet arc
// The fillet arc runs from the root to the working depth of the gear
local center = rotate_xy([-filletrad, 0.0mm], 60.0deg) + [work_diameter/2.0, 0];
// Trace the fillet arc from ~root-circle to working depth at involute arc starting Y-level
for(i = 180.0deg; i > 60.0deg; i -= __ang_step*2.5) {
tooth += { [cos(i), sin(i)] * filletrad + center };
}
if(i != 60.0deg) {
// Add the last point if we did not reach the working depth
tooth += { [cos(60.0deg), sin(60.0deg)] * filletrad + center };
}
// Calculate the maximum involute angle to intersect at the outside radius
local max_a = involute_angle(base_diameter/2.0, outside_diameter/2.0);
// Trace the involute arc from the base up to outside radius
for(i = 0.0deg; i < max_a; i += __ang_step) {
tooth += { involute_point(i, base_diameter/2.0)};
}
if(i != max_a) {
// Add the last point if we did not reach the outside radius
tooth += { involute_point(max_a, base_diameter/2.0)};
}
// We now have one side of the tooth. Rotate to be at tooth-symmetry on X-axis
tooth = rotate_xy(tooth, -90.0deg / nteeth);
// Add the same curve mirrored to make the other side of the tooth
// Coordinates reverse to have them all in one direction only
tooth += reverse(scale(tooth, [1, -1]));
// Create all teeth of the gear by adding each tooth at correct angle
local gear = {};
repeat(nteeth; i) {
gear += rotate_xy(tooth, 360.0deg * i / nteeth);
}
return gear;
}
/* -------------------- Helper Functions -------------------- */
/*
* Trace a path at given offset
*/
function trace(path, offset)
{
goto(path[-1] + offset);
foreach(path; v) {
move(v + offset);
}
}
/*
* Make a hole at center point with given radius
*/
function hole(point, radius)
{
goto(point - [radius]);
circle_cw_r([radius, 0]);
}
/* -------------------- Main Program -------------------- */
//ngcgui: info: Involute-gear example
//ngcgui: umode = 1; //, units: 1:mm, 0:inch
//ngcgui: D = 100.0; //, Pitch Dia
//ngcgui: HD = 6.0; //, Hole Dia
//ngcgui: N = 9; //, Number of teeth
//ngcgui: PA = 20.0; //, Pressure Angle (deg)
//ngcgui: frate = 600; //, Feedrate
//ngcgui: xoffset = 0;
//ngcgui: yoffset = 0;
//ngcgui: howmany = 1; //, howmany (1 | 2)
//ngcgui: verbose = 0;
include("ensure_units.gcmc"); //avoid preamble conflict
if (umode == 1) {
zero = 0.0mm;
} else {
zero = 0.0in;
}
// ngcgui entries are unitless so these additions are used
// to ensure 1) floatingpoint and 2) units per umode setting
frate = frate + zero;
HD = HD + zero;
D = D + zero;
PA = PA + 0.0deg;
P = N/D; // Diametral pitch
feedrate(frate);
location = [xoffset,yoffset];
if (howmany == 1) {
hole(location, HD/2.0);
trace(gear_P(N, PA, P), location);
} elif (howmany == 2) {
hole(location + [D/2.0, 0.0mm], HD/2.0);
trace(gear_P(N, PA, P), location + [D/2.0, 0.0mm]);
hole(location + [-D/2.0, 0.0mm], HD/2.0);
trace(gear_P(N, PA, P), location + [-D/2, 0.0mm]);
} else {
error("howmany must be 1 or 2");
}
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