diff options
Diffstat (limited to 'src/toys/gear.cpp')
| -rw-r--r-- | src/toys/gear.cpp | 317 |
1 files changed, 317 insertions, 0 deletions
diff --git a/src/toys/gear.cpp b/src/toys/gear.cpp new file mode 100644 index 0000000..d2f2de2 --- /dev/null +++ b/src/toys/gear.cpp @@ -0,0 +1,317 @@ +/* + * GearToy - displays involute gears + * + * Copyright 2006 Michael G. Sloan <mgsloan@gmail.com> + * Copyright 2006 Aaron Spike <aaron@ekips.org> + * + * This library is free software; you can redistribute it and/or + * modify it either under the terms of the GNU Lesser General Public + * License version 2.1 as published by the Free Software Foundation + * (the "LGPL") or, at your option, under the terms of the Mozilla + * Public License Version 1.1 (the "MPL"). If you do not alter this + * notice, a recipient may use your version of this file under either + * the MPL or the LGPL. + * + * You should have received a copy of the LGPL along with this library + * in the file COPYING-LGPL-2.1; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * You should have received a copy of the MPL along with this library + * in the file COPYING-MPL-1.1 + * + * The contents of this file are subject to the Mozilla Public License + * Version 1.1 (the "License"); you may not use this file except in + * compliance with the License. You may obtain a copy of the License at + * http://www.mozilla.org/MPL/ + * + * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY + * OF ANY KIND, either express or implied. See the LGPL or the MPL for + * the specific language governing rights and limitations. + * + */ + +#include <2geom/d2.h> +#include <2geom/sbasis.h> +#include <2geom/bezier-to-sbasis.h> +#include <2geom/path.h> + +#include <toys/path-cairo.h> +#include <toys/toy-framework-2.h> + +using std::vector; +using namespace Geom; + +class Gear { +public: + // pitch circles touch on two properly meshed gears + // all measurements are taken from the pitch circle + double pitch_diameter() {return (_number_of_teeth * _module) / M_PI;} + double pitch_radius() {return pitch_diameter() / 2.0;} + void pitch_radius(double R) {_module = (2 * M_PI * R) / _number_of_teeth;} + + // base circle serves as the basis for the involute toothe profile + double base_diameter() {return pitch_diameter() * cos(_pressure_angle);} + double base_radius() {return base_diameter() / 2.0;} + + // diametrical pitch + double diametrical_pitch() {return _number_of_teeth / pitch_diameter();} + + // height of the tooth above the pitch circle + double addendum() {return 1.0 / diametrical_pitch();} + // depth of the tooth below the pitch circle + double dedendum() {return addendum() + _clearance;} + + // root circle specifies the bottom of the fillet between teeth + double root_radius() {return pitch_radius() - dedendum();} + double root_diameter() {return root_radius() * 2.0;} + + // outer circle is the outside diameter of the gear + double outer_radius() {return pitch_radius() + addendum();} + double outer_diameter() {return outer_radius() * 2.0;} + + // angle covered by the tooth on the pitch circle + double tooth_thickness_angle() {return M_PI / _number_of_teeth;} + + Geom::Point centre() {return _centre;} + void centre(Geom::Point c) {_centre = c;} + + double angle() {return _angle;} + void angle(double a) {_angle = a;} + + int number_of_teeth() {return _number_of_teeth;} + + Geom::Path path(); + Gear spawn(int N, double a); + + Gear(int n, double m, double phi) { + _number_of_teeth = n; + _module = m; + _pressure_angle = phi; + _clearance = 0.0; + _angle = 0.0; + _centre = Geom::Point(0.0,0.0); + } +private: + int _number_of_teeth; + double _pressure_angle; + double _module; + double _clearance; + double _angle; + Geom::Point _centre; + D2<SBasis> _involute(double start, double stop) { + D2<SBasis> B; + D2<SBasis> I; + Linear bo = Linear(start,stop); + + B[0] = cos(bo,2); + B[1] = sin(bo,2); + + I = B - Linear(0,1) * derivative(B); + I = I*base_radius() + _centre; + return I; + } + D2<SBasis> _arc(double start, double stop, double R) { + D2<SBasis> B; + Linear bo = Linear(start,stop); + + B[0] = cos(bo,2); + B[1] = sin(bo,2); + + B = B*R + _centre; + return B; + } + // angle of the base circle used to create the involute to a certain radius + double involute_swath_angle(double R) { + if (R <= base_radius()) return 0.0; + return sqrt(R*R - base_radius()*base_radius())/base_radius(); + } + + // angle of the base circle between the origin of the involute and the intersection on another radius + double involute_intersect_angle(double R) { + if (R <= base_radius()) return 0.0; + return (sqrt(R*R - base_radius()*base_radius())/base_radius()) - acos(base_radius()/R); + } +}; + +void makeContinuous(D2<SBasis> &a, Point const b) { + for(unsigned d=0;d<2;d++) + a[d][0][0] = b[d]; +} + +Geom::Path Gear::path() { + Geom::Path pb; + + // angle covered by a full tooth and fillet + double tooth_rotation = 2.0 * tooth_thickness_angle(); + // angle covered by an involute + double involute_advance = involute_intersect_angle(outer_radius()) - involute_intersect_angle(root_radius()); + // angle covered by the tooth tip + double tip_advance = tooth_thickness_angle() - (2 * (involute_intersect_angle(outer_radius()) - involute_intersect_angle(pitch_radius()))); + // angle covered by the toothe root + double root_advance = (tooth_rotation - tip_advance) - (2.0 * involute_advance); + // begin drawing the involute at t if the root circle is larger than the base circle + double involute_t = involute_swath_angle(root_radius())/involute_swath_angle(outer_radius()); + + //rewind angle to start drawing from the leading edge of the tooth + double first_tooth_angle = _angle - ((0.5 * tip_advance) + involute_advance); + + Geom::Point prev; + for (int i=0; i < _number_of_teeth; i++) + { + double cursor = first_tooth_angle + (i * tooth_rotation); + + D2<SBasis> leading_I = compose(_involute(cursor, cursor + involute_swath_angle(outer_radius())), Linear(involute_t,1)); + if(i != 0) makeContinuous(leading_I, prev); + pb.append(SBasisCurve(leading_I)); + cursor += involute_advance; + prev = leading_I.at1(); + + D2<SBasis> tip = _arc(cursor, cursor+tip_advance, outer_radius()); + makeContinuous(tip, prev); + pb.append(SBasisCurve(tip)); + cursor += tip_advance; + prev = tip.at1(); + + cursor += involute_advance; + D2<SBasis> trailing_I = compose(_involute(cursor, cursor - involute_swath_angle(outer_radius())), Linear(1,involute_t)); + makeContinuous(trailing_I, prev); + pb.append(SBasisCurve(trailing_I)); + prev = trailing_I.at1(); + + if (base_radius() > root_radius()) { + Geom::Point leading_start = trailing_I.at1(); + Geom::Point leading_end = (root_radius() * unit_vector(leading_start - _centre)) + _centre; + prev = leading_end; + pb.appendNew<LineSegment>(leading_end); + } + + D2<SBasis> root = _arc(cursor, cursor+root_advance, root_radius()); + makeContinuous(root, prev); + pb.append(SBasisCurve(root)); + cursor += root_advance; + prev = root.at1(); + + if (base_radius() > root_radius()) { + Geom::Point trailing_start = root.at1(); + Geom::Point trailing_end = (base_radius() * unit_vector(trailing_start - _centre)) + _centre; + pb.appendNew<LineSegment>(trailing_end); + prev = trailing_end; + } + } + + return pb; +} +Gear Gear::spawn(int N, double a) { + Gear gear(N, _module, _pressure_angle); + double dist = gear.pitch_radius() + pitch_radius(); + gear.centre(Geom::Point::polar(a, dist) + _centre); + double new_angle = 0.0; + if (gear.number_of_teeth() % 2 == 0) + new_angle -= gear.tooth_thickness_angle(); + new_angle -= (_angle) * (pitch_radius() / gear.pitch_radius()); + new_angle += (a) * (pitch_radius() / gear.pitch_radius()); + gear.angle(new_angle + a); + return gear; +} + +class GearToy: public Toy { + public: + PointSetHandle hand; + GearToy () { + for(unsigned i = 0; i < 4; i++) + hand.pts.emplace_back(uniform()*400, uniform()*400); + handles.push_back(&hand); + } + void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override { + cairo_set_source_rgba (cr, 0., 0., 0, 0.8); + cairo_set_line_width (cr, 0.5); + + //Geom::Point centre = Geom::Point(width/2,height/2); + /* draw cross hairs + double dominant_dim = std::max(width,height); + double minor_dim = std::min(width,height); + for(unsigned i = 1; i < 2; i++) { + cairo_move_to(cr, centre[0]-minor_dim/4, centre[1]); + cairo_line_to(cr, centre[0]+minor_dim/4, centre[1]); + cairo_move_to(cr, centre[0], centre[1]-minor_dim/4); + cairo_line_to(cr, centre[0], centre[1]+minor_dim/4); + } + cairo_stroke(cr);*/ + + double pressure_angle = (hand.pts[3][0] / 10) * M_PI / 180; + Gear gear(int(hand.pts[2][0] / 10),200.0,pressure_angle); + Geom::Point gear_centre = hand.pts[1]; + gear.pitch_radius(Geom::distance(gear_centre, hand.pts[0])); + gear.angle(atan2(hand.pts[0] - gear_centre)); + gear.centre(gear_centre); + + // draw radii + cairo_new_sub_path(cr); + cairo_arc(cr, gear_centre[0], gear_centre[1], gear.base_radius(), 0, M_PI*2); + cairo_set_source_rgba (cr, 0., 0., 0.5, 1); + cairo_stroke(cr); + + cairo_new_sub_path(cr); + cairo_arc(cr, gear_centre[0], gear_centre[1], gear.pitch_radius(), 0, M_PI*2); + cairo_set_source_rgba (cr, 0.5, 0., 0., 1); + cairo_stroke(cr); + + cairo_new_sub_path(cr); + cairo_arc(cr, gear_centre[0], gear_centre[1], gear.outer_radius(), 0, M_PI*2); + cairo_set_source_rgba (cr, 0., 0.5, 0., 1); + cairo_stroke(cr); + + cairo_new_sub_path(cr); + cairo_arc(cr, gear_centre[0], gear_centre[1], gear.root_radius(), 0, M_PI*2); + cairo_set_source_rgba (cr, 0., 0.5, 0., 1); + cairo_stroke(cr); + + //draw gear + Geom::Path p = gear.path(); + cairo_path(cr, p); + cairo_set_source_rgba (cr, 0., 0., 0., 0.5); + cairo_set_line_width (cr, 2.0); + cairo_stroke(cr); + + Gear gear2 = gear.spawn(5, -2.0 * M_PI / 8.0); + Geom::Path p2 = gear2.path(); + cairo_path(cr, p2); + cairo_set_source_rgba (cr, 0., 0., 0., 0.5); + cairo_set_line_width (cr, 2.0); + cairo_stroke(cr); + + Gear gear3 = gear2.spawn(8, 0.0 * M_PI / 8.0); + Geom::Path p3 = gear3.path(); + cairo_path(cr, p3); + cairo_set_source_rgba (cr, 0., 0., 0., 0.5); + cairo_set_line_width (cr, 2.0); + cairo_stroke(cr); + + Gear gear4 = gear.spawn(6, 3.0 * M_PI / 4.0); + Geom::Path p4 = gear4.path(); + cairo_path(cr, p4); + cairo_set_source_rgba (cr, 0., 0., 0., 0.5); + cairo_set_line_width (cr, 2.0); + cairo_stroke(cr); + + *notify << "angle = " << gear.angle(); + + Toy::draw(cr, notify, width, height, save,timer_stream); + } +}; + +int main(int argc, char **argv) { + init(argc, argv, new GearToy()); + + return 0; +} + +/* + Local Variables: + mode:c++ + c-file-style:"stroustrup" + c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) + indent-tabs-mode:nil + fill-column:99 + End: +*/ +// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : |