From 7ce055373a7897d758b63fd314f67ac3d62d02de Mon Sep 17 00:00:00 2001 From: Chris Palmer Date: Tue, 7 Jul 2020 22:36:34 +0100 Subject: [PATCH] Add rack to mesh with involute spur gears. --- readme.md | 5 ++++- tests/gears.scad | 12 ++++++++++-- tests/png/gears.png | Bin 59122 -> 69151 bytes utils/gears.scad | 39 +++++++++++++++++++++++++++++++++++++-- 4 files changed, 51 insertions(+), 5 deletions(-) diff --git a/readme.md b/readme.md index 3aede3a..245f382 100644 --- a/readme.md +++ b/readme.md @@ -5239,6 +5239,8 @@ the practical minimum. The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter. +The origin of the rack is the left end of the pitch line and its width is below the pitch line. I.e. it does not include the addendum. + [utils/gears.scad](utils/gears.scad) Implementation. @@ -5254,7 +5256,8 @@ The clearance between tip and root defaults to module / 6, but can be overridden ### Modules | Module | Description | |:--- |:--- | -| ```involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20)``` | Calculate profile given module, number of teeth and pressure angle | +| ```involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20)``` | Calculate gear profile given module, number of teeth and pressure angle | +| ```involute_rack_profile(m, z, w, pa = 20, clearance = undef)``` | Calculate rack profile given module, number of teeth and pressure angle | ![gears](tests/png/gears.png) diff --git a/tests/gears.scad b/tests/gears.scad index 1bb2aeb..6833d44 100644 --- a/tests/gears.scad +++ b/tests/gears.scad @@ -35,7 +35,7 @@ $show_numbers = false; module gears() { color(pp1_colour) - rotate($t * 360) + rotate(-$t * 360) linear_extrude(eps, center = true, convexity = z1) difference() { involute_gear_profile(m, z1, pa); @@ -45,13 +45,21 @@ module gears() { color(pp2_colour) translate([centre_distance(m, z1, z2, pa), 0]) - rotate(180 + 180 / z2 + -$t * 360 * z1 / z2) + rotate(180 + 180 / z2 + $t * 360 * z1 / z2) linear_extrude(eps, center = true, convexity = z2) difference() { involute_gear_profile(m, z2, pa); circle(r = m * z2 / 10); } + + z3 = floor((z1 + z2) / PI); + angle = -$t * 360 + 90 - floor(z1 / 4) * 360 / z1; // Line up the rack 1/4 turn around the gear + pitch = m * PI; + color(pp3_colour) + translate([(angle % ((z3 / z1) * 360)) / 360 * z1 * pitch, -centre_distance(m, z1, 0, pa)]) + linear_extrude(eps, center = true) + involute_rack_profile(m, z3, 3 * m, pa); } rotate(is_undef($bom) ? 0 : [70, 0, 315]) diff --git a/tests/png/gears.png b/tests/png/gears.png index 07d3aa9148f9c5ab4f13389ffe9bf1dc5bfd26ea..3cb9dac9146f1c19562c80650390bb304b15cb9f 100644 GIT binary patch literal 69151 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zQ|eJVsnxtmrom^Cz~ByM)2dL+*s$0<(UIQ!A_D&kJ;D>*8yWVjbB5$PB8yT=NTqjk z>(3%6etjtm(_sYkj#M3yCr~h{e3=PrA^w|6Z&6({QZ@NdbFsbPT?3hj>4(J-;T<)8 z;6X#T#D9IjjaUArUGRnp*X)J*Y(aQGGU52c9VVRBM&rR01xA z&c#o315RJoYbRf5A&%lySQtn?UJa#Bq!#yPiJdpJM86-uZN$w^-)3_}0LncWr#Tg( z@e*Zb4kLu|wM=Rb^zDto$(eFij}FN2#D24NxsU-;J{%>Cx#}Za?vr?uZQ;q use function involute(r, u) = let(a = degrees(u), c = cos(a), s = sin(a)) r * [c + u * s, s - u * c]; //! Involute of circle radius r at angle u in radians -function profile_shift(z, pa) = max(1 - z * sqr(sin(pa)) / 2, 0); //! Calculate profile shift for small gears +function profile_shift(z, pa) = z ? max(1 - z * sqr(sin(pa)) / 2, 0) : 0; //! Calculate profile shift for small gears function centre_distance(m, z1, z2, pa) = //! Calculate distance between centres taking profile shift into account let(x1 = profile_shift(z1, pa), x2 = profile_shift(z2, pa)) m * (z1/2 + z2/2 + x1 + x2); -module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //! Calculate profile given module, number of teeth and pressure angle +module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //! Calculate gear profile given module, number of teeth and pressure angle assert(z >= 7, "Gears must have at least 7 teeth."); d = m * z; // Reference pitch circle diameter x = profile_shift(z, pa); // Profile shift @@ -94,3 +96,36 @@ module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //! circle(root_r); } } + +module involute_rack_profile(m, z, w, pa = 20, clearance = undef) { //! Calculate rack profile given module, number of teeth and pressure angle + p = PI * m; // Pitch + ha = m; // Addendum + hf = 1.25 * m; // Dedendum + hw = 2 * m; // Working depth + h = ha + hf; // Tooth depth + c = is_undef(clearance) ? m / 4 : clearance; // Tip root clearance + crest_w = p / 2 - 2 * ha * tan(pa); // Crest width + base_w = crest_w + 2 * hw * tan(pa); // Base width + root_w = p - base_w; // Root width + clearance_w = root_w - 2 * c * tan(pa); // Width of clearance without fillet + kx = tan(pa / 2 + 45); // Fillet ratio of radius and xoffset + pf = min(0.38 * m, kx * clearance_w / 2); // Dedendum fillet radius + x = pf / kx; // Fillet centre x offset from corner + + tooth = [ [root_w / 2, -hw / 2], [p / 2 - crest_w / 2, ha], [p / 2 + crest_w / 2, ha], [p - root_w / 2, -hw / 2] ]; + teeth = [for(i = [0 : z - 1], pt = tooth) [pt.x + i * p, pt.y] ]; + + difference() { + polygon(concat([[0, -w], [0, -hf]], teeth, [[z * p, -hf ], [z * p, -w]])); // Add the corners + + for(i = [0 : z]) // Add fillets + hull() { + for(side = [-1, 1]) + translate([i * p + side * (clearance_w / 2 - x), -hf + pf]) + circle(pf); + + translate([i * p, -hw /2 + eps / 2]) // Need to extend to fillet up to meet the root at high pressure angles + square([root_w, eps], center = true); + } + } +}